Is there some equivalent library or function that will give me the next combination of a set of values like next_permutation in does for me?
Combinations: from Mark Nelson's article on the same topic we have next_combination http://marknelson.us/2002/03/01/next-permutation
Permutations: from STL we have std::next_permutation
template <typename Iterator>
inline bool next_combination(const Iterator first, Iterator k, const Iterator last)
{
if ((first == last) || (first == k) || (last == k))
return false;
Iterator itr1 = first;
Iterator itr2 = last;
++itr1;
if (last == itr1)
return false;
itr1 = last;
--itr1;
itr1 = k;
--itr2;
while (first != itr1)
{
if (*--itr1 < *itr2)
{
Iterator j = k;
while (!(*itr1 < *j)) ++j;
std::iter_swap(itr1,j);
++itr1;
++j;
itr2 = k;
std::rotate(itr1,j,last);
while (last != j)
{
++j;
++itr2;
}
std::rotate(k,itr2,last);
return true;
}
}
std::rotate(first,k,last);
return false;
}
I am not aware of one. The basic idea is to represent your elements as a bit array. So for example, you have the set S:
S = {a, b, c}
[i, j, k] // a is the first bit, b is the second bit, c is the third bit
To generate the Power Set of S(just generate all numbers that are of size == 3 bits by using the simple addition):
000 // {}
001 // {c}
010 // {b}
011 // {b, c}
100 // {a}
101 // {a, c}
110 // {a, b}
111 // {a, b, c}
All what you have to do is to find what bits are set, and to relate them to your set's elements.
On final note, there is one combination you can produce when you want all elements to be used and that combination is the set it self, because in combinations the order doesn't matter so for sure we are talking about a number of elements n where 0 <= n <= size(S)
I've used this library when I've needed to do this. It has an interface very similar to std::next_permutation so it will be easy to use if you've used that before.
Enumeration of the powerset (that is, all combinations of all sizes) can use an adaptation of the binary increment algorithm.
template< class I, class O > // I forward, O bidirectional iterator
O next_subset( I uni_first, I uni_last, // set universe in a range
O sub_first, O sub_last ) { // current subset in a range
std::pair< O, I > mis = std::mismatch( sub_first, sub_last, uni_first );
if ( mis.second == uni_last ) return sub_first; // finished cycle
O ret;
if ( mis.first == sub_first ) { // copy elements following mismatch
std::copy_backward( mis.first, sub_last, ++ (ret = sub_last) );
} else ret = std::copy( mis.first, sub_last, ++ O(sub_first) );
* sub_first = * mis.second; // add first element not yet in result
return ret; // return end of new subset. (Output range must accommodate.)
}
The requirement of a bidirectional iterator is unfortunate, and could be worked around.
I was going to make it handle identical elements (multisets), but I need to go to bed :v( .
Usage:
#include <iostream>
#include <vector>
using namespace std;
char const *fruits_a[] = { "apples", "beans", "cherries", "durian" };
vector< string > fruits( fruits_a, fruits_a + sizeof fruits_a/sizeof *fruits_a );
int main() {
vector< string > sub_fruits( fruits.size() );
vector< string >::iterator last_fruit = sub_fruits.begin();
while (
( last_fruit = next_subset( fruits.begin(), fruits.end(),
sub_fruits.begin(), last_fruit ) )
!= sub_fruits.begin() ) {
cerr << "size " << last_fruit - sub_fruits.begin() << ": ";
for ( vector<string>::iterator fit = sub_fruits.begin(); fit != last_fruit; ++ fit ) {
cerr << * fit << " ";
}
cerr << endl;
}
}
EDIT: Here is the version for multisets. The set doesn't have to be sorted but identical elements do have to be grouped together.
#include <iterator>
#include <algorithm>
#include <functional>
template< class I, class O > // I forward, O bidirectional iterator
I next_subset( I uni_first, I uni_last, // set universe in a range
O sub_first, O sub_last ) { // current subset in a range
std::pair< O, I > mis = std::mismatch( sub_first, sub_last, uni_first );
if ( mis.second == uni_last ) return sub_first; // finished cycle
typedef std::reverse_iterator<O> RO;
mis.first = std::find_if( RO(mis.first), RO(sub_first), std::bind1st(
std::not_equal_to< typename std::iterator_traits<O>::value_type >(),
* mis.second ) ).base(); // move mis.first before identical grouping
O ret;
if ( mis.first != sub_first ) { // copy elements after mismatch
ret = std::copy( mis.first, sub_last, ++ O(sub_first) );
} else std::copy_backward( mis.first, sub_last, ++ (ret = sub_last) );
* sub_first = * mis.second; // add first element not yet in result
return ret;
}
#include <vector>
#include <iostream>
using namespace std;
char const *fruits_a[] = { "apples", "apples", "beans", "beans", "cherries" };
vector< string > fruits( fruits_a, fruits_a + sizeof fruits_a/sizeof *fruits_a );
int main() {
vector< string > sub_fruits( fruits.size() );
vector< string >::iterator last_fruit = sub_fruits.begin();
while (
( last_fruit = next_subset( fruits.begin(), fruits.end(),
sub_fruits.begin(), last_fruit )
) != sub_fruits.begin() ) {
cerr << "size " << last_fruit - sub_fruits.begin() << ": ";
for ( vector<string>::iterator fit = sub_fruits.begin(); fit != last_fruit; ++ fit ) {
cerr << * fit << " ";
}
cerr << endl;
}
}
Output:
size 1: apples
size 2: apples apples
size 1: beans
size 2: apples beans
size 3: apples apples beans
size 2: beans beans
size 3: apples beans beans
size 4: apples apples beans beans
size 1: cherries
size 2: apples cherries
size 3: apples apples cherries
size 2: beans cherries
size 3: apples beans cherries
size 4: apples apples beans cherries
size 3: beans beans cherries
size 4: apples beans beans cherries
size 5: apples apples beans beans cherries
Googling for C++ "next_combination" turned up this.
search from "mid" backwards until you find an element that is smaller
than *(end - 1). This is the element
we should increment. Call this
"head_pos".
search from "end" backwards until you find the last element that is
still larger than *head_pos. Call it
"tail_pos".
swap head_pos and tail_pos. Re-order the elements from [head_pos + 1, mid[
and [tail_pos + 1, end[ in increasing
order.
In case You have no choice, but to implement Your own function maybe this horror can help a bit or maybe other horrors among answers to that question.
Algorithm to return all combinations of k elements from n
I wrote it some time ago and the full picture eludes me now :), but the basic idea is this:
You have the original set and current combination is a vector of iterators to the elements selected. To get the next combination, You scan your set from right to left looking for a "bubble". By "bubble" I mean one or more adjacent elements not selected. The "bubble" might be immediately at the right. Then, in Your combination, You exchange the first element at the left of the "bubble" and all other elements from the combination, that are to the right in the set, with a subset of adjacent elements that starts at the beginning of the "bubble".
Related
I have this problem: Given a vector with n numbers, sort the numbers so that the even ones will be on odd positions and the odd numbers will be on even positions. E.g. If I have the vector 2 6 7 8 9 3 5 1, the output should be 2 7 6 9 8 3 5 1 . The count should start from 1. So on position 1 which is actually index 0 should be an even number, on position 2 which is actually index 1 should be an odd number and so on. Now this is easy if the odd and even numbers are the same, let's say 4 even number and 4 odd numbers in the vector, but what if the number of odd numbers differs from the number of even numbers like in the above example? How do I solve that. I attached the code with one of the tries I did, but it doesn't work. Can I get some help please. I ask you to keep it simple that means only with vectors and such. No weird methods or anything cause I'm a beginner and I only know the basics. Thanks in advance!
I have to mention that n initial is globally declared and is the number of vector elements and v_initial is the initial vector with the elements that need to be rearranged.
The task says to add the remaining numbers to the end of the vector. Like if there are 3 odd and 5 even numbers, The 2 extra even numbers should be thrown at the end of the vector
void vector_pozitii_pare_impare(int v_initial[])
{
int v_pozitie[50],c1=0,c2=1;
for (i = 0; i < n_initial; i++)
{
if (v_initial[i] % 2 == 0)
{
bool isTrue = 1;
for (int k = i + 1; k < n_initial; k++)
{
if (v_initial[k] % 2 != 0)
isTrue = 0;
}
if (isTrue)
{
v_pozitie[c1] = v_initial[i];
c1++;
}
else
{
v_pozitie[c1] = v_initial[i];
c1 += 2;
}
}
else
{
bool isTrue = 1;
for (int j = i + 1; j < n_initial; j++)
{
if (v_initial[j] % 2 == 0)
{
isTrue = 0;
}
if (isTrue)
{
v_pozitie[c2] = v_initial[i];
c2++;
}
else
{
v_pozitie[c2] = v_initial[i];
c2 += 2;
}
}
}
}
This may not be a perfect solution and it just popped out right off my mind without being tested or verified, but it's just to give you an idea.
(Let A,B,C,D be odd numbers and 0,1,2 even numbers correspondingly)
Given:
A 0 B C D 1 2 (random ordered list of odd/even numbers)
Wanted:
A 0 B 1 C 2 D (input sequence altered to match the wanted odd/even criteria)
Next, we invent the steps required to get from given to wanted:
// look at 'A' -> match, next
// Result: A 0 B C D 1 2
// look at '0' -> match, next
// Result: A 0 B C D 1 2
// look at 'B' -> match, next
// Result: A 0 B C D 1 2
// look at 'C' -> mismatch, remember index and find first match starting from index+1
// Result: A 0 B C D ->1<- 2
// now swap the numbers found at the remembered index and the found one.
// Result: A 0 B 1 D C 2
// continue until the whole list has been consumed.
As I said, this algorithm may not be perfect, but my intention is to give you an example on how to solve these kinds of problems. It's not good to always think in code first, especially not with a problem like this. So you should first think about where you start, what you want to achieve and then carefully think of how to get there step by step.
I feel I have to mention that I did not provide an example in real code, because once you got the idea, the execution should be pretty much straight forward.
Oh, and just a small remark: Almost nothing about your code is C++.
A simple solution, that is not very efficient would be to split the vector into 2 vectors, that contain even and uneven numbers and then always take one from the even, one from the uneven and then the remainder, from the one that is not completely entered.
some c++ (that actually uses vectors, but you can use an array the same way, but need to change the pointer arithmetic)
I did not test it, but the principle should be clear; it is not very efficient though
EDIT: The answer below by #AAAAAAAAARGH outlines a better algorithmic idea, that is inplace and more efficient.
void change_vector_even_uneven(std::vector<unsigned>& in_vec){
std::vector<unsigned> even;
std::vector<unsigned> uneven;
for (auto it = in_vec.begin(); it != in_vec.end(); it++){
if ((*it) % 2 == 0)) even.push_back(*it);
else uneven.push_back(*it);
}
auto even_it = even.begin();
auto uneven_it = uneven.begin();
for (auto it = in_vec.begin(); it != in_vec.end(); it++){
if (even_it == even.end()){
(*it) = (*uneven_it);
uneven_it++;
continue;
}
if (uneven_it == uneven.end()){
(*it) = (*even_it);
even_it++;
continue;
}
if ((it - in_vec.begin()) % 2 == 0){
(*it) = (*even_it);
even_it++;
}
else{
(*it) = (*uneven_it);
uneven_it++;
}
}
}
The solutions is simple. We sort the even and odd values into a data structure. In a loop, we iterate over all source values. If they are even (val & 2 == 0) we add them at the end of a std::deque for evens and if odd, we add them to a std::deque for odds.
Later, we we will extract the the values from the front of the std::deque.
So, we have a first in first out principle.
The std::deque is optimized for such purposes.
Later, we make a loop with an alternating branch in it. We, alternatively extract data from the even queue and then from the odd queue. If a queue is empty, we do not extract data.
We do not need an additional std::vector and can reuse the old one.
With that, we do not need to take care for the same number of evens and odds. It will of course always work.
Please see below one of millions of possible solutions:
#include <iostream>
#include <vector>
#include <deque>
int main() {
std::vector testData{ 2, 6, 7, 8, 9, 3, 5, 1 };
// Show initial data
std::cout << "\nInitial data: ";
for (const int i : testData) std::cout << i << ' ';
std::cout << '\n';
// We will use a deques to store odd and even numbers
// With that we can efficiently push back and pop front
std::deque<int> evenNumbers{};
std::deque<int> oddNumbers{};
// Sort the original data into the specific container
for (const int number : testData)
if (number % 2 == 0)
evenNumbers.push_back(number);
else
oddNumbers.push_back(number);
// Take alternating the data from the even and the odd values
bool takeEven{ true };
for (size_t i{}; !evenNumbers.empty() && !oddNumbers.empty(); ) {
if (takeEven) { // Take even numbers
if (not evenNumbers.empty()) { // As long as there are even values
testData[i] = evenNumbers.front(); // Get the value from the front
evenNumbers.pop_front(); // Remove first value
++i;
}
}
else { // Now we take odd numbers
if (not oddNumbers.empty()) { // As long as there are odd values
testData[i] = oddNumbers.front(); // Get the value from the front
oddNumbers.pop_front(); // Remove first value
++i;
}
}
// Next take the other container
takeEven = not takeEven;
}
// Show result
std::cout << "\nResult: ";
for (const int i : testData) std::cout << i << ' ';
std::cout << '\n';
return 0;
}
Here is yet another solution (using STL), in case you want a stable result (that is, the order of your values is preserved).
#include <algorithm>
#include <vector>
auto ints = std::vector<int>{ 2, 6, 7, 8, 9, 3, 5, 1 };
// split list to even/odd sections -> [2, 6, 8, 7, 9, 3, 5, 1]
const auto it = std::stable_partition(
ints.begin(), ints.end(), [](auto value) { return value % 2 == 0; });
auto results = std::vector<int>{};
results.reserve(ints.size());
// merge both parts with equal size
auto a = ints.begin(), b = it;
while (a != it && b != ints.end()) {
results.push_back(*a++);
results.push_back(*b++);
}
// copy remaining values to end of list
std::copy(a, it, std::back_inserter(results));
std::copy(b, ints.end(), std::back_inserter(results));
The result ist [2, 7, 6, 9, 8, 3, 5, 1]. The complexity is O(n).
This answer, like some of the others, divides the data and then reassembles the result. The standard library std::partition_copy is used to separate the even and odd numbers into two containers. Then the interleave function assembles the result by alternately copying from two input ranges.
#include <algorithm>
#include <iostream>
#include <vector>
template <typename InIt1, typename InIt2, typename OutIt>
OutIt interleave(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2, OutIt dest)
{
for (;;) {
if (first1 == last1) {
return std::copy(first2, last2, dest);
}
*dest++ = *first1++;
if (first2 == last2) {
return std::copy(first1, last1, dest);
}
*dest++ = *first2++;
}
}
void reorder_even_odd(std::vector<int> &data)
{
auto is_even = [](int value) { return (value & 1) == 0; };
// split
std::vector<int> even, odd;
std::partition_copy(begin(data), end(data), back_inserter(even), back_inserter(odd), is_even);
// merge
interleave(begin(even), end(even), begin(odd), end(odd), begin(data));
}
int main()
{
std::vector<int> data{ 2, 6, 7, 8, 9, 3, 5, 1 };
reorder_even_odd(data);
for (int value : data) {
std::cout << value << ' ';
}
std::cout << '\n';
}
Demo on Compiler Explorer
As suggested, I am using vectors and STL.
No need to be a great mathematician to understand v_pozitie will start with pairs of odd and even and terminate with the integers not in the initial pairs.
I am then updating three iterators in v_positie (no need of temporary containers to calculate the result) : even, odd and end,(avoiding push_back) and would code this way :
#include <vector>
#include <algorithm>
void vector_pozitii_pare_impare(std::vector<int>& v_initial, std::vector<int>& v_pozitie) {
int nodd (0), neven (0);
std::for_each (v_initial.begin (), v_initial.end (), [&nodd] (const int& n) {
nodd += n%2;
});
neven = v_initial.size () - nodd;
int npair (neven < nodd ?neven:nodd);
npair *=2;
std::vector<int>::iterator iend (&v_pozitie [npair]), ieven (v_pozitie.begin ()), iodd (&v_pozitie [1]);
std::for_each (v_initial.begin (), v_initial.end (), [&iend, &ieven, &iodd, &npair] (const int& s) {
if (npair) {
switch (s%2) {
case 0 :
*ieven++ = s;
++ieven;
break;
case 1 :
*iodd++ = s;
++iodd;
break;
}
--npair;
}
else *iend++ = s;
});
}
int main (int argc, char* argv []) {
const int N = 8;
int tab [N] = {2, 6, 7, 8, 9, 3, 5, 1};
std::vector<int> v_initial (tab, (int*)&tab [N]);
std::cout << "\tv_initial == ";
std::for_each (v_initial.begin (), v_initial.end (), [] (const int& s) {std::cout << s << " ";});
std::cout << std::endl;
std::vector<int> v_pozitie (v_initial.size (), -1);
vector_pozitii_pare_impare (v_initial, v_pozitie);
std::cout << "\tv_pozitie == ";
std::for_each (v_pozitie.begin (), v_pozitie.end (), [] (const int& s) {std::cout << s << " ";});
std::cout << std::endl;
}
We have a set S {1,10,100,1000,10000}. Now we input an integer x (say x = 4).
Now we have to add every element of set's product with x to the set itself. So finally
S={1,10,100,1000,10000,4,40,400,4000,40000}
[S is not limited to only 5 entries initially]
We have to visit only the initial elements in the set.
I tried an approach like:
for(auto i=s.begin();i!=s.end();i++)
{
s.insert((*i)*x);
}
This doesnt give the desired result, as the size of set keeps increasing.
Another approach I tried was to store all the multiples (*i)*x in another temporary set/vector and to merge it with s later.
But since the original dataset is huge, it worsens the time complexity.
Any optimizations ?
Since the std::set is ordered, and iterators are not invalidated by insertion, you can simply insert while iterating as long as you don't insert to the range that is still left to be iterated.
If we can assume all numbers to be positive, then we can iterate in reverse direction, because the result of multiplication is always going to be greater than the inputs:
for (auto it = S.rbegin(); it != S.rend(); ++it)
S.insert(*it*x);
If x is negative and set contains only positive, then order of iteration doesn't matter. If the set may contain negative numbers, this becomes more challenging.
But since the original dataset is huge, it worsens the time complexity.
Inserting N elements into std::set is O(N log N). Merging std::sets is O(N log N). The merge approach does not worsen asymptotic time complexity.
If you were to use an std::unordered_set though, the merge approach would be O(N) in average case. It's still O(N log N) in worst case however. I recommend using the merge approach with an unordered set.
Here you are.
#include <iostream>
#include <set>
#include <iterator>
std::set<int> & update( std::set<int> &s, int value )
{
for ( auto it = rbegin( s ); it != rend( s ); ++it )
{
s.insert( *it * value );
}
return s;
}
int main()
{
std::set<int> s = { 1, 10, 100, 1000, 10000 };
for ( const auto &value : s )
{
std::cout << value << ' ';
}
std::cout << '\n';
for ( const auto &value : update( s, 4 ) )
{
std::cout << value << ' ';
}
std::cout << '\n';
return 0;
}
The program output is
1 10 100 1000 10000
1 4 10 40 100 400 1000 4000 10000 40000
According to the C++ 20 Standard (22.2.6 Associative containers)
9 The insert and emplace members shall not affect the validity of
iterators and references to the container, and the erase members shall
invalidate only iterators and references to the erased elements.
Or a more general approach
#include <iostream>
#include <set>
#include <iterator>
std::set<int> & update( std::set<int> &s, int value )
{
auto partition = s.lower_bound( 0 );
for ( auto it = rbegin( s ); it != std::set<int>::reverse_iterator( partition ); ++it )
{
s.insert( *it * value );
}
for ( auto it = begin( s ); it != partition; ++it )
{
s.insert( *it * value );
}
return s;
}
int main()
{
std::set<int> s = { -10000, -1000, -100, -10, -1, 1, 10, 100, 1000, 10000 };
for ( const auto &value : s )
{
std::cout << value << ' ';
}
std::cout << '\n';
for ( const auto &value : update( s, 4 ) )
{
std::cout << value << ' ';
}
std::cout << '\n';
return 0;
}
The program output is
-10000 -1000 -100 -10 -1 1 10 100 1000 10000
-40000 -10000 -4000 -1000 -400 -100 -40 -10 -4 -1 1 4 10 40 100 400 1000 4000 10000 40000
As mentioned in the comments, it's simplest to use a temporary set. With C++17, you can use std::set::merge with the temporary set casted to an rvalue:
#include <algorithm>
std::set<int> s2;
std::transform(s1.cbegin(), s1.cend(), std::inserter(s2, s2.end()),
[](int orig){ return 4*orig; });
s1.merge(std::move(s2));
Otherwise, note that iterators into the set aren't invalidated while inserting. Take this together with the fact that the set is ordered and in case of the scenario you described (scaling an existing value is larger than the original value, but less or equal than the next existing one), you can do it in a loop like this:
for (auto it = s1.begin(); it != s1.end(); ++it)
it = s.insert(*it*4).first;
For fewer restrictions, you can use this more verbose loop:
for (std::set<int>::iterator it1 = s.begin(), it2; it1 != s.end();
it1 = std::next(it1) == it2 ? std::next(it1, 2) : it2)
it2 = s.insert(*it1*4).first;
I have an array of n integers (not necessarily distinct!) and I would like to iterate over all subsets of size k. However I'd like to exclude all duplicate subsets.
e.g.
array = {1,2,2,3,3,3,3}, n = 7, k = 2
then the subsets I want to iterate over (each once) are:
{1,2},{1,3},{2,2},{2,3},{3,3}
What is an efficient algorithm for doing this?
Is a recursive approach the most efficient/elegant?
In case you have a language-specific answer, I'm using C++.
The same (or almost the same) algorithm which is used to generated combinations of a set of unique values in lexicographical order can be used to generate combinations of a multiset in lexicographical order. Doing it this way avoids the necessity to deduplicate, which is horribly expensive, and also avoids the necessity of maintaining all the generated combinations. It does require that the original list of values be sorted.
The following simple implementation finds the next k-combination of a multiset of n values in average (and worst-case) time O(n). It expects two ranges: the first range is a sorted k-combination, and the second range is the sorted multiset. (If either range is unsorted or the values in first range do not constitute a sub(multi)set of the second range, then the behaviour is undefined; no sanity checks are made.)
Only the end iterator from the second range is actually used, but I thought that made the calling convention a bit odd.
template<typename BidiIter, typename CBidiIter,
typename Compare = std::less<typename BidiIter::value_type>>
int next_comb(BidiIter first, BidiIter last,
CBidiIter /* first_value */, CBidiIter last_value,
Compare comp=Compare()) {
/* 1. Find the rightmost value which could be advanced, if any */
auto p = last;
while (p != first && !comp(*(p - 1), *--last_value)) --p;
if (p == first) return false;
/* 2. Find the smallest value which is greater than the selected value */
for (--p; comp(*p, *(last_value - 1)); --last_value) { }
/* 3. Overwrite the suffix of the subset with the lexicographically smallest
* sequence starting with the new value */
while (p != last) *p++ = *last_value++;
return true;
}
It should be clear that steps 1 and 2 combined make at most O(n) comparisons, because each of the n values is used in at most one comparison. Step 3 copies at most O(k) values, and we know that k≤n.
This could be improved to O(k) in the case where no values are repeated, by maintaining the current combination as a container of iterators into the value list rather than actual values. This would also avoid copying values, at the cost of extra dereferences. If in addition we cache the function which associates each value iterator with an iterator to the first instance of next largest value, we could eliminate Step 2 and reduce the algorithm to O(k) even for repeated values. That might be worthwhile if there are a large number of repeats and comparisons are expensive.
Here's a simple use example:
std::vector<int> values = {1,2,2,3,3,3,3};
/* Since that's sorted, the first subset is just the first k values */
const int k = 2;
std::vector<int> subset{values.cbegin(), values.cbegin() + k};
/* Print each combination */
do {
for (auto const& v : subset) std::cout << v << ' ';
std::cout << '\n';
} while (next_comb(subset.begin(), subset.end(),
values.cbegin(), values.cend()));
Live on coliru
I like bit-twiddling for this problem. Sure, it limits you to only 32 elements in your vector, but it's still cool.
First, given a bit mask, determine the next bitmask permutation (source):
uint32_t next(uint32_t v) {
uint32_t t = v | (v - 1);
return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1));
}
Next, given a vector and a bitmask, give a new vector based on that mask:
std::vector<int> filter(const std::vector<int>& v, uint32_t mask) {
std::vector<int> res;
while (mask) {
res.push_back(v[__builtin_ctz(mask)]);
mask &= mask - 1;
}
return res;
}
And with that, we just need a loop:
std::set<std::vector<int>> get_subsets(const std::vector<int>& arr, uint32_t k) {
std::set<std::vector<int>> s;
uint32_t max = (1 << arr.size());
for (uint32_t v = (1 << k) - 1; v < max; v = next(v)) {
s.insert(filter(arr, v));
}
return s;
}
int main()
{
auto s = get_subsets({1, 2, 2, 3, 3, 3, 3}, 2);
std::cout << s.size() << std::endl; // prints 5
}
The basic idea of this solution is a function like next_permutation but which generates the next ascending sequence of "digits". Here called ascend_ordered.
template< class It >
auto ascend_ordered( const int n_digits, const It begin, const It end )
-> bool
{
using R_it = reverse_iterator< It >;
const R_it r_begin = R_it( end );
const R_it r_end = R_it( begin );
int max_digit = n_digits - 1;
for( R_it it = r_begin ; it != r_end; ++it )
{
if( *it < max_digit )
{
++*it;
const int n_further_items = it - r_begin;
for( It it2 = end - n_further_items; it2 != end; ++it2 )
{
*it2 = *(it2 - 1) + 1;
}
return true;
}
--max_digit;
}
return false;
}
Main program for the case at hand:
auto main() -> int
{
vector<int> a = {1,2,2,3,3,3,3};
assert( is_sorted( begin( a ), end( a ) ) );
const int k = 2;
const int n = a.size();
vector<int> indices( k );
iota( indices.begin(), indices.end(), 0 ); // Fill with 0, 1, 2 ...
set<vector<int>> encountered;
for( ;; )
{
vector<int> current;
for( int const i : indices ) { current.push_back( a[i] ); }
if( encountered.count( current ) == 0 )
{
cout << "Indices " << indices << " -> values " << current << endl;
encountered.insert( current );
}
if( not ascend_ordered( n, begin( indices ), end( indices ) ) )
{
break;
}
}
}
Supporting includes and i/o:
#include <algorithm>
using std::is_sorted;
#include <assert.h>
#include <iterator>
using std::reverse_iterator;
#include <iostream>
using std::ostream; using std::cout; using std::endl;
#include <numeric>
using std::iota;
#include <set>
using std::set;
#include <utility>
using std::begin; using std::end;
#include <vector>
using std::vector;
template< class Container, class Enable_if = typename Container::value_type >
auto operator<<( ostream& stream, const Container& c )
-> ostream&
{
stream << "{";
int n_items_outputted = 0;
for( const int x : c )
{
if( n_items_outputted >= 1 ) { stream << ", "; }
stream << x;
++n_items_outputted;
}
stream << "}";
return stream;
}
Unlike the previous answer, this is not as efficient and doesn't do anything as fancy as a lot of the bit twiddling. However it does not limit the size of your array or the size of the subset.
This solution uses std::next_permutation to generate the combinations, and takes advantage of std::set's uniqueness property.
#include <algorithm>
#include <vector>
#include <set>
#include <iostream>
#include <iterator>
using namespace std;
std::set<std::vector<int>> getSubsets(const std::vector<int>& vect, size_t numToChoose)
{
std::set<std::vector<int>> returnVal;
// return the whole thing if we want to
// choose everything
if (numToChoose >= vect.size())
{
returnVal.insert(vect);
return returnVal;
}
// set up bool vector for combination processing
std::vector<bool> bVect(vect.size() - numToChoose, false);
// stick the true values at the end of the vector
bVect.resize(bVect.size() + numToChoose, true);
// select where the ones are set in the bool vector and populate
// the combination vector
do
{
std::vector<int> combination;
for (size_t i = 0; i < bVect.size() && combination.size() <= numToChoose; ++i)
{
if (bVect[i])
combination.push_back(vect[i]);
}
// sort the combinations
std::sort(combination.begin(), combination.end());
// insert this new combination in the set
returnVal.insert(combination);
} while (next_permutation(bVect.begin(), bVect.end()));
return returnVal;
}
int main()
{
std::vector<int> myVect = {1,2,2,3,3,3,3};
// number to select
size_t numToSelect = 3;
// get the subsets
std::set<std::vector<int>> subSets = getSubsets(myVect, numToSelect);
// output the results
for_each(subSets.begin(), subSets.end(), [] (const vector<int>& v)
{ cout << "subset "; copy(v.begin(), v.end(), ostream_iterator<int>(cout, " ")); cout << "\n"; });
}
Live example: http://coliru.stacked-crooked.com/a/beb800809d78db1a
Basically we set up a bool vector and populate a vector with the values that correspond with the position of the true items in the bool vector. Then we sort and insert this into a set. The std::next_permutation shuffles the true values in the bool array around and we just repeat.
Admittedly, not as sophisticated and more than likely slower than the previous answer, but it should do the job.
Given a string, I'm trying to count the occurrence of each letter in the string and then sort their frequency from highest to lowest. Then, for letters that have similar number of occurrences, I have to sort them alphabetically.
Here is what I have been able to do so far:
I created an int array of size 26 corresponding to the 26 letters of the alphabet with individual values representing the number of times it appeared in the sentence
I pushed the contents of this array into a vector of pairs, v, of int and char (int for the frequency, and char for the actual letter)
I sorted this vector of pairs using std::sort(v.begin(), v.end());
In displaying the frequency count, I just used a for loop starting from the last index to display the result from highest to lowest. I am having problems, however, with regard to those letters having similar frequencies, because I need them displayed in alphabetical order. I tried using a nested for loop with the inner loop starting with the lowest index and using a conditional statement to check if its frequency is the same as the outer loop. This seemed to work, but my problem is that I can't seem to figure out how to control these loops so that redundant outputs will be avoided. To understand what I'm saying, please see this example output:
Enter a string: hello world
Pushing the array into a vector pair v:
d = 1
e = 1
h = 1
l = 3
o = 2
r = 1
w = 1
Sorted first according to frequency then alphabetically:
l = 3
o = 2
d = 1
e = 1
h = 1
r = 1
w = 1
d = 1
e = 1
h = 1
r = 1
d = 1
e = 1
h = 1
d = 1
e = 1
d = 1
Press any key to continue . . .
As you can see, it would have been fine if it wasn't for the redundant outputs brought about by the incorrect for loops.
If you can suggest more efficient or better implementations with regard to my concern, then I would highly appreciate it as long as they're not too complicated or too advanced as I am just a C++ beginner.
If you need to see my code, here it is:
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
int main() {
cout<<"Enter a string: ";
string input;
getline(cin, input);
int letters[26]= {0};
for (int x = 0; x < input.length(); x++) {
if (isalpha(input[x])) {
int c = tolower(input[x] - 'a');
letters[c]++;
}
}
cout<<"\nPushing the array into a vector pair v: \n";
vector<pair<int, char> > v;
for (int x = 0; x < 26; x++) {
if (letters[x] > 0) {
char c = x + 'a';
cout << c << " = " << letters[x] << "\n";
v.push_back(std::make_pair(letters[x], c));
}
}
// Sort the vector of pairs.
std::sort(v.begin(), v.end());
// I need help here!
cout<<"\n\nSorted first according to frequency then alphabetically: \n";
for (int x = v.size() - 1 ; x >= 0; x--) {
for (int y = 0; y < x; y++) {
if (v[x].first == v[y].first) {
cout << v[y].second<< " = " << v[y].first<<endl;
}
}
cout << v[x].second<< " = " << v[x].first<<endl;
}
system("pause");
return 0;
}
You could simplify this a lot, in two steps:
First use a map to count the number of occurrences of each character in the string:
std::unordered_map<char, unsigned int> count;
for( char character : string )
count[character]++;
Use the values of that map as comparison criteria:
std::sort( std::begin( string ) , std::end( string ) ,
[&]( char lhs , char rhs )
{
return count[lhs] < count[rhs];
}
);
Here is a working example running at ideone.
If you want highest frequency then lowest letter, an easy way would be to store negative values for frequency, then negate it after you sort. A more efficient way would be to change the function used for sorting, but that is a touch trickier:
struct sort_helper {
bool operator()(std::pair<int,char> lhs, std::pair<int,char> rhs) const{
return std::make_pair(-lhs.first,lhs.second)<std::make_pair(-rhs.first,rhs.second);
}
};
std::sort(vec.begin(),vec.end(),sort_helper());
(Posted on behalf of the OP.)
Thanks to the responses of the awesome people here at Stack Overflow, I was finally able to fix my problem. Here is my final code in case anyone is interested or for future references of people who might be stuck in the same boat:
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
struct Letters
{
Letters() : freq(0){}
Letters(char letter,int freq) {
this->freq = freq;
this->letter = letter;
}
char letter;
int freq;
};
bool Greater(const Letters& a, const Letters& b)
{
if(a.freq == b.freq)
return a.letter < b.letter;
return a.freq > b.freq;
}
int main () {
cout<<"Enter a string: ";
string input;
getline(cin, input);
vector<Letters> count;
int letters[26]= {0};
for (int x = 0; x < input.length(); x++) {
if (isalpha(input[x])) {
int c = tolower(input[x] - 'a');
letters[c]++;
}
}
for (int x = 0; x < 26; x++) {
if (letters[x] > 0) {
char c = x + 'a';
count.push_back(Letters(c, letters[x]));
}
}
cout<<"\nUnsorted list..\n";
for (int x = 0 ; x < count.size(); x++) {
cout<<count[x].letter<< " = "<< count[x].freq<<"\n";
}
std::sort(count.begin(),count.end(),Greater);
cout<<"\nSorted list according to frequency then alphabetically..\n";
for (int x = 0 ; x < count.size(); x++) {
cout<<count[x].letter<< " = "<< count[x].freq<<"\n";
}
system("pause");
return 0;
}
Example output:
Enter a string: hello world
Unsorted list..
d = 1
e = 1
h = 1
l = 3
o = 2
r = 1
w = 1
Sorted list according to frequency then alphabetically..
l = 3
o = 2
d = 1
e = 1
h = 1
r = 1
w = 1
Press any key to continue . . .
I basically just followed the advice of #OliCharlesworth and implemented a custom comparator through the help of this guide: A Function Pointer as Comparison Function.
Although I'm pretty sure that my code can still be made more efficient, I'm still pretty happy with the results.
// CODE BY VIJAY JANGID in C language
// Using arrays, Time complexity - ( O(N) * distinct characters )
// Efficient answer
#include <stdio.h>
int main() {
int iSizeFrequencyArray= 58;
// 122 - 65 = 57 for A to z
int frequencyArray[iSizeFrequencyArray];
int iIndex = 0;
// Initializing frequency to zero for all
for (iIndex = 0; iIndex < iSizeFrequencyArray; iIndex++) {
frequencyArray[iIndex] = 0;
}
int iMyStringLength = 1000;
char chMyString[iMyStringLength];
// take input for the string
scanf("%s", &chMyString);
// calculating length
int iSizeMyString;
while(chMyString[++iSizeMyString]);
// saving each character frequency in the freq. array
for (iIndex = 0; iIndex < iSizeMyString; iIndex++) {
int currentChar = chMyString[iIndex];
frequencyArray[currentChar - 65]++;
}
/* // To print the frequency of each alphabet
for (iIndex = 0; iIndex < iSizeFrequencyArray; iIndex++) {
char currentChar = iIndex + 65;
printf("\n%c - %d", currentChar, frequencyArray[iIndex ]);
}
*/
int lowestDone = 0, lowest = 0, highestSeen = 0;
for( iIndex = 0; iIndex < iSizeFrequencyArray; iIndex++ ) {
if(frequencyArray[iIndex] > highestSeen) {
highestSeen = frequencyArray[iIndex];
}
}
// assigning sorted values to the current array
while (lowest != highestSeen) {
// calculating lowest frequency
for( iIndex = 0; iIndex < iSizeFrequencyArray; iIndex++ ) {
if( frequencyArray[iIndex] > lowestDone &&
frequencyArray[iIndex] < lowest) {
lowest = frequencyArray[iIndex]; // taking lowest value
}
}
// printing that frequency
for( iIndex =0; iIndex < iSizeFrequencyArray; iIndex++ ) {
// print that work for that times
if(frequencyArray[iIndex] == lowest){
char currentChar = iIndex + 65;
int iIndex3;
for(iIndex3 = 0; iIndex3 < lowest; iIndex3++){
printf("%c", currentChar);
}
}
}
// now that is done, move to next lowest
lowestDone = lowest;
// reset to highest value, to get the next lowest one
lowest = highestSeen+1;
}
return 0;
}
Explanation:
First create array to store repetition of size (112 - 65) to store asci characters from A to z.
Store the frequency of each character by incrementing at each occurrence.
Now find the highest frequency.
Run a loop where condition is (lowest != highest) where lowest = 0 initially.
Now in each iteration print character which whose frequency is equal to lowest. They will be alphabetically in order automatically.
At last find the next higher frequency and print then so on.
When lowest reach highest then break loop.
Using an unordered_map for counting characters as suggested by #Manu343726 is a good idea. However, in order to produce your sorted output, another step is required.
My solution is also in C++11 and uses a lambda expression. This way you neither need to define a custom struct nor a comparison function. The code is almost complete, I just skipped reading the input:
#include <unordered_map>
#include <iostream>
#include <set>
int main() {
string input = "hello world";
unordered_map<char, unsigned int> count;
for (char character : input)
if (character >= 'a' && character <= 'z')
count[character]++;
cout << "Unsorted list:" << endl;
for (auto const &kv : count)
cout << kv.first << " = " << kv.second << endl;
using myPair = pair<char, unsigned int>;
auto comp = [](const myPair& a, const myPair& b) {
return (a.second > b.second || a.second == b.second && a.first < b.first);
};
set<myPair, decltype(comp)> sorted(comp);
for(auto const &kv : count)
sorted.insert(kv);
cout << "Sorted list according to frequency then alphabetically:" << endl;
for (auto const &kv : sorted)
cout << kv.first << " = " << kv.second << endl;
return 0;
}
Output:
Unsorted list:
r = 1
h = 1
e = 1
d = 1
o = 2
w = 1
l = 3
Sorted list according to frequency then alphabetically:
l = 3
o = 2
d = 1
e = 1
h = 1
r = 1
w = 1
Note 1: Instead of inserting each element from the unordered_map into the set, it might be more efficient to use the function std::transform or std:copy, but my code is at least short.
Note 2: Instead of using a custom sorted set which maintains the order you want, it might be more efficient to use a vector of pairs and sort it once in the end, but your solution is already similar to this.
Code on Ideone
#include<stdio.h>
// CODE BY AKSHAY BHADERIYA
char iFrequencySort (char iString[]);
void vSort (int arr[], int arr1[], int len);
int
main ()
{
int iLen, iCount;
char iString[100], str[100];
printf ("Enter a string : ");
scanf ("%s", iString);
iFrequencySort (iString);
return 0;
}
char
iFrequencySort (char iString[])
{
int iFreq[100] = { 0 };
int iI, iJ, iK, iAsc, iLen1 = 0, iLen = 0;
while (iString[++iLen]);
int iOccurrence[94];
int iCharacter[94];
for (iI = 0; iI < iLen; iI++)
{ //frequency of the characters
iAsc = (int) iString[iI];
iFreq[iAsc - 32]++;
}
for (iI = 0, iJ = 0; iI < 94; iI++)
{ //the characters and occurrence arrays
if (iFreq[iI] != 0)
{
iCharacter[iJ] = iI;
iOccurrence[iJ] = iFreq[iI];
iJ++;
}
}
iLen1 = iJ;
vSort (iOccurrence, iCharacter, iLen1); //sorting both arrays
/*letter array consists only the index of iFreq array.
Converting it to the ASCII value of corresponding character */
for (iI = 0; iI < iLen1; iI++)
{
iCharacter[iI] += 32;
}
iK = 0;
for (iI = 0; iI < iLen1; iI++)
{ //characters into original string
for (iJ = 0; iJ < iOccurrence[iI]; iJ++)
{
iString[iK++] = (char) iCharacter[iI];
}
}
printf ("%s", iString);
}
void
vSort (int iOccurrence[], int iCharacter[], int len)
{
int iI, iJ, iTemp;
for (iI = 0; iI < len - 1; iI++)
{
for (iJ = iI + 1; iJ < len; iJ++)
{
if (iOccurrence[iI] > iOccurrence[iJ])
{
iTemp = iOccurrence[iI];
iOccurrence[iI] = iOccurrence[iJ];
iOccurrence[iJ] = iTemp;
iTemp = iCharacter[iI];
iCharacter[iI] = iCharacter[iJ];
iCharacter[iJ] = iTemp;
}
}
}
}
Answers are given and one is accepted. I would like to give an additional answer showing the standard approach for this task.
There is often the requirement to first count things and then to get back their rank or some topmost value or other information.
One of the most common solution is to use a so called associative container for that, and, here specifically, a std::map or even better a std::unordered_map. This, because we need a key value, in the above described way a letter and an associted value, here the count for this letter. The key is unique. There cannot be more than one of the same letter in it. This would of course not make any sense.
Associative containers are very efficient by accessing their elements by their key value.
OK, there are 2 of them. The std::map and the std::unordered_map. One uses a tree to store the key in a sorted manner and the other use fast hashing algorithms to access the key values. Since we are later not interested in sorted keys, but in sorted count of occurence, we can choose the std::unordred_map. As a futher benefit, this will use fast the hashing algorithms mentioned to access a key.
The maps have an additional huge advantage. The have an index operator [], that will look very fast for a key value. If found, it will return a reference to the value associated with the key. If not found, it will create a key and initialize its value with the default (0 in our case). And then counting of any key is as simple as map[key]++.
But then, later, we here often hear: But it must be sorted by the count. That does of course not work, because the count my have duplicate values, and the map can only contain unique key values. So, impossible.
The solution is to use a second associative container a std::multiset which can have more of the same keys and a custome sort operator, where we can sort according to the value. In this we store the not a key and a value as 2 elements, but a std::pair with both values. And we sort by the 2nd part of the pair.
We cannot use a std::multi:set in the first place, because we need the unique key (in this case the letter).
The above described approach gives us extreme flexibility and ease of use. We can basically count anything with this algorithm
It could for example look the the below compact code:
#include <iostream>
#include <string>
#include <utility>
#include <set>
#include <unordered_map>
#include <type_traits>
#include <cctype>
// ------------------------------------------------------------
// Create aliases. Save typing work and make code more readable
using Pair = std::pair<char, unsigned int>;
// Standard approach for counter
using Counter = std::unordered_map<Pair::first_type, Pair::second_type>;
// Sorted values will be stored in a multiset
struct Comp { bool operator ()(const Pair& p1, const Pair& p2) const { return (p1.second == p2.second) ? p1.first<p2.first : p1.second>p2.second; } };
using Rank = std::multiset<Pair, Comp>;
// ------------------------------------------------------------
// --------------------------------------------------------------------------------------
// Compact function to calculate the frequency of charcters and then get their rank
Rank getRank(std::string& text) {
// Definition of our counter
Counter counter{};
// Iterate over all charcters in text and count their frequency
for (const char c : text) if (std::isalpha(c)) counter[char(std::tolower(c))]++;
// Return ranks,sorted by frequency and then sorted by character
return { counter.begin(), counter.end() };
}
// --------------------------------------------------------------------------------------
// Test, driver code
int main() {
// Get a string from the user
if (std::string text{}; std::getline(std::cin, text))
// Calculate rank and show result
for (const auto& [letter, count] : getRank(text))
std::cout << letter << " = " << count << '\n';
}
Please see the minimal statements used. Very elegant.
But often we do see that arrays are use as an associted container. They have also an index (a key) and a value. Disadvantage may be a tine space overhead for unsued keys. Additionally the will only work for something wit a know magnitude. For example for 26 letters. Other countries alphabets may have more or less letters. Then this kind of solution would be not that flexible. Anyway it is also often used and OK.
So, your solution maybe a littel bit more complex, but will of course still work.
Let me give you an additional example for getting the topmost value of any container. Here you will see, how flexible such a solution can be.
I am sorry, but it is a little bit advanced. . .
#include <iostream>
#include <utility>
#include <unordered_map>
#include <queue>
#include <vector>
#include <iterator>
#include <type_traits>
#include <string>
// Helper for type trait We want to identify an iterable container ----------------------------------------------------
template <typename Container>
auto isIterableHelper(int) -> decltype (
std::begin(std::declval<Container&>()) != std::end(std::declval<Container&>()), // begin/end and operator !=
++std::declval<decltype(std::begin(std::declval<Container&>()))&>(), // operator ++
void(*std::begin(std::declval<Container&>())), // operator*
void(), // Handle potential operator ,
std::true_type{});
template <typename T>
std::false_type isIterableHelper(...);
// The type trait -----------------------------------------------------------------------------------------------------
template <typename Container>
using is_iterable = decltype(isIterableHelper<Container>(0));
// Some Alias names for later easier reading --------------------------------------------------------------------------
template <typename Container>
using ValueType = std::decay_t<decltype(*std::begin(std::declval<Container&>()))>;
template <typename Container>
using Pair = std::pair<ValueType<Container>, size_t>;
template <typename Container>
using Counter = std::unordered_map<ValueType<Container>, size_t>;
template <typename Container>
using UnderlyingContainer = std::vector<Pair<Container>>;
// Predicate Functor
template <class Container> struct LessForSecondOfPair {
bool operator () (const Pair<Container>& p1, const Pair<Container>& p2) { return p1.second < p2.second; }
};
template <typename Container>
using MaxHeap = std::priority_queue<Pair<Container>, UnderlyingContainer<Container>, LessForSecondOfPair<Container>>;
// Function to get most frequent used number in any Container ---------------------------------------------------------
template <class Container>
auto topFrequent(const Container& data) {
if constexpr (is_iterable<Container>::value) {
// Count all occurences of data
Counter<Container> counter{};
for (const auto& d : data) counter[d]++;
// Build a Max-Heap
MaxHeap<Container> maxHeap(counter.begin(), counter.end());
// Return most frequent number
return maxHeap.top().first;
}
else
return data;
}
// Test
int main() {
std::vector testVector{ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,7 };
std::cout << "Most frequent is: " << topFrequent(testVector) << "\n";
double cStyleArray[] = { 1.1, 2.2, 2.2, 3.3, 3.3, 3.3 };
std::cout << "Most frequent is: " << topFrequent(cStyleArray) << "\n";
std::string s{ "abbcccddddeeeeeffffffggggggg" };
std::cout << "Most frequent is: " << topFrequent(s) << "\n";
double value = 12.34;
std::cout << "Most frequent is: " << topFrequent(value) << "\n";
return 0;
}
I've got a 3 by 3 grid of boolean values, and I'm interested in the number of ways I can have exactly three "living" cells (there's 56 permutations, by my count). Rotational symmetries don't matter, but the living cells are indistinguishable from each other.
Assuming that I'm indexing the values in the grid relative to the centroid:
-------------------
|-1,-1| 0,-1| 1,-1|
-------------------
|-1,0 | | 1,0 |
-------------------
|-1,1 | 0,1 | 1,1 |
-------------------
is there a nice loop that I could use to calculate the 56 permutations? (I've just finished typing it all out, and I'd love to know if I could have been slightly smarter).
I'm using C++, but a basic algorithm would be wonderful in any language or pseudo-language, if it's clear.
You can use next_permutation.
For example, assume string each character in x below represents the a cell in the grid (except centroid cell) starting at top left and going to bottom right. You could run this code to find all the possible arrangements, and inside the loop, string x will represent a possible arrangement, where 1 is a live cell, and 0 is a dead one.
int main() {
string x = "00000111";
int cnt = 0;
do {
++cnt;
// do something useful with this configuration...
} while(next_permutation(x.begin(),x.end()));
cout<<cnt<<endl;
return 0;
}
Try this procedure from Wikipedia.
The following algorithm generates the next permutation lexicographically after a given permutation. It changes the given permutation in-place.
Find the largest index k such that a[k] < a[k + 1]. If no such index exists, the permutation is the last permutation.
Find the largest index l such that a[k] < a[l]. Since k + 1 is such an index, l is well defined and satisfies k < l.
Swap a[k] with a[l].
Reverse the sequence from a[k + 1] up to and including the final element a[n].
you could use this method:
assume you represent your grid with an array, where your elements are
[(-1,-1), (0,-1),(1,-1)...]
and so on, you basically take element in the first line, then second line, then third line.
So now, you just have to take all the available numbers you have, that is to say:
[1,1,1,0,0,0,0,0,0]
as you said you only want 3 living cells.
now that we decided wha tdifferent strings mean, you can simply take a code which performs permutation, like the xcellnt one at this link How To Generate Permutation In C?
hich does exactly what you want, or any ohte equivalent code like std::next_permutation which is in the algorithm library.
Do you prefer "smarter" looping or "saner"?
//c++ --std=c++11 test.cc
#include <iostream>
#include <string>
#include <list>
#include <vector>
#include <algorithm>
#include <utility>
using std::string;
using std::list;
using std::vector;
const string show[8] = { "(-1,-1)","( 0,-1)","( 1,-1)"
, "(-1, 0)", "( 1, 0)"
, "(-1, 1)","( 0, 1)","( 1, 1)"
};
auto permutations_of_living_cells =
[] (int number_of_living_cells) -> list<vector<string>>
{
typedef list<vector<string>> (*recT)( void*
, int
, int
, vector<string> &&
, list<vector<string>> &&
);
recT rec = []( void*r
, int n
, int i
, vector<string> && prefix
, list<vector<string>> && l
) -> list<vector<string>>
{
if( n==0 )
{
l.push_back(std::move(prefix));
return std::move(l);
}
if( i>8-n ) return std::move(l);
vector<string> psi(prefix);
psi.push_back(show[i]);
return ((recT)r)(r,n ,i+1,std::move(prefix),
((recT)r)(r,n-1,i+1,std::move(psi ),
std::move(l)
)
);
};
return rec( (void*)rec
, number_of_living_cells
, 0
, vector<string>()
, list<vector<string>>()
);
};
template<class T>
std::ostream& operator<<( std::ostream & out,const vector<T> & v )
{
if( v.empty() ) return out << "[]";
out << "[ " << *v.begin();
std::for_each( v.begin()+1, v.end(), [&](T x){out<<", "<<x;} );
return out << " ]";
}
int main()
{
for( auto v : permutations_of_living_cells(3) )
std::cout << v << "\n";
std::cout << std::flush;
return 0;
}