Algorithm for deleting multiple array elements and shifting array - c++

I have an array let's say with 5 items, if element[i] is less than 3 need to move element[i+1] in place of element[i].
int array[5] = {4, 2, 3, 5, 1};
int number = 3;
for (int i = 0; i < number; i++)
{
if (array[i] > number)
{
for (int j = 0; j < i - 1; j++)
{
array[j] = array[j + 1];
}
number = number - 1;
}
}
expected result is array = {2, 3, 1, anyNumber, anyNumber};

A O(n) working code for the above problem.. But as others pointed out in the comments.. You end up with an array that is using less space then allocated to it..
#include<stdio.h>
int main()
{
int arr[] = {4, 2, 3, 5, 1};
int* temp1 = arr;
int* temp2 = arr;
int i, n1 = 5, n2 = 5;
for(i = 0; i < n1; i++)
{
if(*temp2 >= 3)
{
*temp1 = *temp2;
temp1++;
temp2++;
}
else
{
n2--; //the number of elements left in the array is denoted by n2
temp2++;
}
}
}

Nested loops give you O(n2) complexity, and non-obvious code.
Better use std::remove_if:
int array[5] = {4, 2, 3, 5, 1};
int number = 3;
remove_if( begin( array ), end( array ), [=]( int x ) { return x>number; } );
Disclaimer: code untouched by compiler's hands.

Try this code. You should not decrease number at each step. Also, the second loop should start at i and stop at the end of array:
int array[5] = {4, 2, 3, 5, 1};
int number = 3;
for (int i = 0; i < number; i++)
{
if (array[i] > number)
{
for (int j = i; j < 5; j++)
{
array[j] = array[j + 1];
}
}
}

Here's a more compact and idiomatic (that's how I view it anyway) way to remove items from an array:
#include <iostream>
#include <algorithm>
#include <iterator>
int main()
{
int array[] = {4, 2, 3, 5, 1};
int* begin = array;
int* end = begin + sizeof(array)/sizeof(array[0]);
int number = 3;
end = std::remove_if(begin, end, [&number](int v) {return v > number;});
std::copy(begin, end, std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
return 0;
}
Just for comparison, here's a version using std::vector:
#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
int main()
{
std::vector<int> array = {4, 2, 3, 5, 1};
int number = 3;
auto end = std::remove_if(array.begin(), array.end(), [&number](int v) {return v > number;});
std::copy(array.begin(), end, std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
return 0;
}

As an alternative, if you want to keep your items, but denote what will be at some later time, "removed", the algorithm that can be used is stable_partition:
#include <algorithm>
#include <iostream>
#include <iterator>
#include <functional>
int main()
{
int vValues[] = {4,2,3,5,1};
// partition the values on left and right. The left side will have values
// <= 3, and on right >3. The return value is the partition point.
int *p = std::stable_partition(vValues, vValues + 5,
std::bind2nd(std::less_equal<int>(), 3));
// display information
std::cout << "Partition is located at vValues[" << std::distance(vValues, p) << "]\n";
std::copy(vValues, vValues + 5, std::ostream_iterator<int>(std::cout, " "));
}
Output:
Partition is located at vValues[3]
2 3 1 4 5
You will see that 2,3,1 are on the left of partition p, and 4,5 are on the right of the partition p. So the "removed" items start at where p points to. The std::partition ensures the elements are still in their relative order when done.

I created my own example, hope this helps people as a reference:
// Removing an element from the array. Thus, shifting to the left.
void remove(){
int a[] = {1, 2, 3, 4, 5, 6};
int size = sizeof(a)/sizeof(int); // gives the size
for(int i = 0; i < size; i++){
cout << "Value: " << a[i] << endl;
}
int index = 2; // desired index to be removed
for(int i = 0; i < size; i++){
if(i == index){
for(int j = i; j < size; j++){
a[j] = a[j+1];
}
}
}
size--; // decrease the size of the array
cout << "\nTesting output: " << endl;
for(int i = 0; i < size; i++){
cout << "Value: " << a[i] << endl;
}
}
int main(){
remove();
return 0;
}

Related

How can I put the indexs in descending order in C++ without using std?

The results contain an index like 0,1,2,3,4,5,6,7 and these are the number of the players and I use cin to get their points like 10,0,2,0,9,0,23,0.
I would like to cout the number of the players in descending order when their point are not 0.
the result must be 6,0,4 2.
I only can make the points in descending order. How can I make this?
#include <iostream>
using namespace std;
int main ()
{ int results[8];
for (int i=0; i<N;i++)
{
cin >> results[i];
}
int change;
for( int i = 0; i < M-1; i++ )
{
for( int j = i+1; j < M; j++ )
{
if( results[i] < results[j] )
{
change = results[i];
results[i] = results[j];
results[j] = change;
}
}
}
return 0;
}
You make your life 10 times easier if you create a structure to hold the player id and score:
struct Player
{
int id;
int score;
};
Then all you need to do is sort and skip scores of 0 in the output:
int main()
{
std::vector<Player> players{
{0, 10},
{1, 0},
{2, 2},
{3, 0},
{4, 9},
{5, 0},
{6, 23},
{7, 0}
};
std::sort(players.begin(), players.end(),
[] (auto p1, auto p2) { return p1.score > p2.score; });
for (const auto& player : players)
{
if (player.score != 0)
std::cout << player.id << " ";
}
std::cout << std::endl;
}
6 0 4 2
If you can't use std (other than cin and cout) this turns pretty much into C code:
Read each input, filtering out zero values.
For non-zero inputs, walk the results array, use the index in the results array to access the value in the inputs array, and stop if that value is smaller than the current input.
Keep that results index, j, as it will be the position where you will have to place the current input's index.
Move all elements from that index until the end of the results array up one position (this is, towards the end of the array).
Write the current input's index, i, at results[j].
[Demo]
#include <iostream> // cin, cout
int main ()
{
int inputs[8];
int results[8];
size_t results_size{0};
for (int i = 0; i < 8; i++)
{
std::cin >> inputs[i];
int current_input{inputs[i]};
// Nothing to do with inputs equal to zero
if (current_input == 0)
{
continue;
}
// Kind of upper bound in results
int j{0};
for (; j < results_size and current_input <= inputs[results[j]]; j++);
// Make room for new index in results
for (int k = results_size; k > j; k--)
{
results[k] = results[k-1];
}
results[j] = i;
results_size++;
}
for (int i = 0; i < results_size; i++)
{
std::cout << results[i] << " ";
}
std::cout << "\n";
return 0;
}

C++ Selection Sort not Sorting Some Values of an Array

I am trying to sort an array of integers using a selection sort algorithm, but some of the numbers aren't sorting. Below is the isolated section of my code that does the sorting and the output. Any suggestions?
#include <iostream>
using namespace std;
int main()
{
int smallestIndex;
int temp;
int X[13] = {1, 19, 2, 18, 4, 12, 7, 8, 10, 3, 11, 17, 9};
for (int Index = 0; Index < 12; Index++) {
smallestIndex = Index;
for (int minIndex = Index+1; minIndex < 13; minIndex++) {
if (X[minIndex] < X[smallestIndex]) {
smallestIndex=minIndex;
}
if (smallestIndex != Index) {
temp = X[Index];
X[Index] = X[smallestIndex];
X[smallestIndex] = temp;
}
}
}
for (int i = 0; i < 13; i++) {
cout << X[i] << endl;
}
}
output:
1
2
4
7
9
3
10
8
11
12
17
18
19
There is an easier way to do this by using the swap() function, and using two more functions called, void selectionSort() and void printArray() to make the code look cleaner.
#include <iostream>
#include <algorithm>
void swap(int *xp, int *yp)
{
int temp = *xp;
*xp = *yp;
*yp = temp;
}
void selectionSort(int arr[], int n)
{
int i, j, min_idx;
// One by one move boundary of unsorted subarray
for (i = 0; i < n-1; i++)
{
// Find the minimum element in unsorted array
min_idx = i;
for (j = i+1; j < n; j++)
if (arr[j] < arr[min_idx])
min_idx = j;
swap(&arr[min_idx], &arr[i]);
}
}
void printArray(int arr[], int size)
{
int i;
for (i=0; i < size; i++)
std::cout << arr[i] << " ";
std::cout << std::endl;
}
int main()
{
int arr[] = {1, 19, 2, 18, 4, 12, 7, 8, 10, 3, 11, 17, 9};
int n = sizeof(arr)/sizeof(arr[0]);
selectionSort(arr, n);
std::cout << "The sorted array is: \n";
printArray(arr, n);
return 0;
}
Output:
The sorted array is:
1 2 3 4 7 8 9 10 11 12 17 18 19
Another way you could do this is by just strictly using std::swap without the use of pointers. Make sure to include the #include<algorithm> header file for std::swap. You will also need to include #include <iterator> for std::size.
#include <iostream>
#include <algorithm>
#include <iterator>
int main()
{
int arr[] = {1, 19, 2, 18, 4, 12, 7, 8, 10, 3, 11, 17, 9};
constexpr int length{ static_cast<int>(std::size(arr)) };
//constexpr means that value of a variable can appear in a constant expression.
// Step through each element of the array
for (int startIndex{ 0 }; startIndex < length - 1; ++startIndex)
{
int smallestIndex{ startIndex };
// Then look for a smaller element in the rest of the array
for (int currentIndex{ startIndex + 1 }; currentIndex < length; ++currentIndex)
{
if (arr[currentIndex] < arr[smallestIndex])
smallestIndex = currentIndex;
}
// swap our start element with our smallest element
std::swap(arr[startIndex], arr[smallestIndex]);
}
// Now that the whole array is sorted, print it.
for (int index{ 0 }; index < length; ++index)
std::cout << arr[index] << ' ';
std::cout << '\n';
return 0;
}
You could also just use std::sort instead. It is in the header file #include<algorithm> which just sorts in ascending order by default. You will also need the header file #include <iterator> for std::size
#include <iostream>
#include <algorithm>
#include <iterator>
int main()
{
int arr[] = {1, 19, 2, 18, 4, 12, 7, 8, 10, 3, 11, 17, 9};
std::sort(std::begin(arr), std::end(arr));
for (int i{ 0 }; i < static_cast<int>(std::size(arr)); ++i)
std::cout << array[i] << ' ';
std::cout << '\n';
return 0;
}

Deleting an even number in an array and shift the elements

I'm trying to write a code where there is a research of even numbers and then it deletes the even numbers and then shifts all the other elements.
i is for offset and are the actual position of the elements in the array.
k is the position of the even number in the array.
int k;
for(i=0; i < N; i++)
{
if(Array[i] % 2 == 0)
{
for(k=i+1; k < N; k++)
{
Array[k-1] = Array[k];
}
N--;
}
}
Array=[2,10,3,5,8,7,3,3,7,10] the even numbers should be removed, but a 10
stays in the Array=[10,3,5,7,3,3,7].
Now is more than 3 hours that I'm trying to figure out what's wrong in my code.
This appears to be some sort of homework or school assignment. So what's the actual problem with the posted code?
It is that when you remove an even number at index i, you put the number that used to be at index i + 1 down into index i. Then you continue the outer loop iteration, which will check index i + 1, which is the number that was at the original i + 2 position in the array. So the number that started out at Array[i + 1], and is now in Array[i], is never checked.
A simple way to fix this is to decrement i when you decrement N.
Though already answered, I fail to see the reason people are driving this through a double for-loop, repetitively moving data over and over, with each reduction.
I completely concur with all the advice about using containers. Further, the algorithms solution doesn't require a container (you can use it on a native array), but containers still make it easier and cleaner. That said...
I described this algorithm in general-comment above. you don't need nested loops fr this. You need a read pointer and a write pointer. that's it.
#include <iostream>
size_t remove_even(int *arr, size_t n)
{
int *rptr = arr, *wptr = arr;
while (n-- > 0)
{
if (*rptr % 2 != 0)
*wptr++ = *rptr;
++rptr;
}
return (wptr - arr);
}
int main()
{
int arr[] = { 2,10,3,5,8,7,3,3,7,10 };
size_t n = remove_even(arr, sizeof arr / sizeof *arr);
for (size_t i=0; i<n; ++i)
std::cout << arr[i] << ' ';
std::cout << '\n';
}
Output
3 5 7 3 3 7
If you think it doesn't make a difference, I invite you to fill an array with a million random integers, then try both solutions (the nested-for-loop approach vs. what you see above).
Using std::remove_if on a native array.
Provided only for clarity, the code above basically does what the standard algorithm std::remove_if does. All we need do is provide iterators (the array offsets and size will work nicely), and know how to interpret the results.
#include <iostream>
#include <algorithm>
int main()
{
int arr[] = { 2,10,3,5,8,7,3,3,7,10 };
auto it = std::remove_if(std::begin(arr), std::end(arr),
[](int x){ return x%2 == 0; });
for (size_t i=0; i<(it - arr); ++i)
std::cout << arr[i] << ' ';
std::cout << '\n';
}
Same results.
The idiomatic solution in C++ would be to use a STL algorithm.
This example use a C-style array.
int Array[100] = {2,10,3,5,8,7,3,3,7,10};
int N = 10;
// our remove_if predicate
auto removeEvenExceptFirst10 = [first10 = true](int const& num) mutable {
if (num == 10 && first10) {
first10 = false;
return false;
}
return num % 2 == 0;
};
auto newN = std::remove_if(
std::begin(Array), std::begin(Array) + N,
removeEvenExceptFirst10
);
N = std::distance(std::begin(Array), newN);
Live demo
You could use a std::vector and the standard function std::erase_if + the vectors erase function to do this:
#include <iostream>
#include <vector>
#include <algorithm>
int main() {
std::vector<int> Array = {2, 10, 3, 5, 8, 7, 3, 3, 7, 10};
auto it = std::remove_if(
Array.begin(),
Array.end(),
[](int x) { return (x & 1) == 0 && x != 10; }
);
Array.erase(it, Array.end());
for(int x : Array) {
std::cout << x << "\n";
}
}
Output:
10
3
5
7
3
3
7
10
Edit: Doing it the hard way:
#include <iostream>
int main() {
int Array[] = {2, 10, 3, 5, 8, 7, 3, 3, 7, 10};
size_t N = sizeof(Array) / sizeof(int);
for(size_t i = 0; i < N;) {
if((Array[i] & 1) == 0 && Array[i] != 10) {
for(size_t k = i + 1; k < N; ++k) {
Array[k - 1] = Array[k];
}
--N;
} else
++i; // only step i if you didn't shift the other values down
}
for(size_t i = 0; i < N; ++i) {
std::cout << Array[i] << "\n";
}
}
Or simpler:
#include <iostream>
int main() {
int Array[] = {2, 10, 3, 5, 8, 7, 3, 3, 7, 10};
size_t N = sizeof(Array) / sizeof(int);
size_t k = 0;
for(size_t i = 0; i < N; ++i) {
if((Array[i] & 1) || Array[i] == 10) {
// step k after having saved this value
Array[k++] = Array[i];
}
}
N = k;
for(size_t i = 0; i < N; ++i) {
std::cout << Array[i] << "\n";
}
}

Linear Search returning array with indices value is found at

I attempted a program to return an array with the indicies of the array where a specific inputed value is found, but every run results in an error, which seems to be an infinite run time. The error seems to be occuring right after printing out the last of the indicies found.
Can anyone help?
(Side note: I've seen multiple pages about deleting pointers when done with them; should I be doing that here?)
Forgot to mention - I want the first slot of the returned array to save the size of the array, so that it can be accessed easily later on in the program
#include <iostream>
#include <vector>
using namespace std;
int* linearSearch(int* n, int k, int f) {
// Input: Index 0 Address ; Size of Array; Element to Search
// Output: Array of Found Indicies
vector <int> a;
int* b;
for(int i = 0; i < k; i++)
if(n[i] == f)
a.push_back(i);
*b = a.size();
for(int i = 0; i < a.size(); i++)
b[i + 1] = a[i];
return b;
}
int main() {
int c[10] = {4, 4, 6, 3, 7, 7, 3, 6, 2, 0};
int* k = linearSearch(&c[0], sizeof(c)/sizeof(int), 4);
for(int i = 0; i < k[0]; i++) {
cout << "Found at index: " << k[i + 1] << endl;
}
return 0;
}
int* b;
....
*b = a.size();
b has to be allocated. Try following:
int* b = new int[a.size() + 1];
b[0] = a.size();
I see what you meant. b will have magically length in first element. This was in Pascal/Delphi but not the case in C/C++.
You are writing to heap memory that you never claimed.
int* b;
This pointer, having never been initialized, points to an undefined memory address. Then when you use the indexing operator to assign your matches, you are writing to the subsequent bytes following the undefined memory address.
You need to allocate space for storing the results using the 'new[]' operator. Additionally, if you had correctly claimed the memory, you would be assigning the number of match results to the first element in the result array - something that doesn't seem to be your intention.
Take a look at dynamic memory allocation in C++ using the new [] operator.
If you use std::vector anyway, why not to use it where it is needed the most? Also if you not suppose to modify array by that pointer express that by const pointer:
std::vector<int> linearSearch(const int* n, int k, int f)
{
std::vector<int> res;
for(int i = 0; i < k; i++)
if(n[i] == f) res.push_back(i);
return res;
}
int main() {
int c[10] = {4, 4, 6, 3, 7, 7, 3, 6, 2, 0};
std::vector<int> k = linearSearch(&c[0], sizeof(c)/sizeof(int), 4);
for(int i = 0; i < k.size(); i++) {
cout << "Found at index: " << k[i] << endl;
}
return 0;
}
This is not perfect but this is much closer to a correct implementation and you should be able to take it further with some work:
#include <iostream>
#include <vector>
using namespace std;
std::vector<int> linearSearch(int* n, int k, int f)
{
vector <int> a;
for(int i = 0; i < k; i++)
{
if(n[i] == f)
{
a.push_back(i);
}
}
return a ;
}
int main() {
int c[10] = {4, 4, 6, 3, 7, 7, 3, 6, 2, 0};
std::vector<int> result = linearSearch(&c[0], sizeof(c)/sizeof(int), 4);
for(unsigned int i = 0; i < result.size(); i++)
{
cout << "Found at index: " << result[i + 1] << endl;
}
return 0;
}

Generating combinations in C++

I have been searching for a source code for generating combinations using C++. I found some advanced codes for this but that is good for only specific number predefined data. Can anyone give me some hints, or perhaps, some ideas to generate a combination?
As an example, suppose the set S = { 1, 2, 3, ...., n} and we pick r= 2 out of it. The input would be n and r. In this case, the program will generate arrays of length two. So input of 5 2 would output 1 2, 1 3.
I had difficulty in constructing the algorithm. It took me a month to think about this.
A simple way using std::next_permutation:
#include <iostream>
#include <algorithm>
#include <vector>
int main() {
int n, r;
std::cin >> n;
std::cin >> r;
std::vector<bool> v(n);
std::fill(v.end() - r, v.end(), true);
do {
for (int i = 0; i < n; ++i) {
if (v[i]) {
std::cout << (i + 1) << " ";
}
}
std::cout << "\n";
} while (std::next_permutation(v.begin(), v.end()));
return 0;
}
or a slight variation that outputs the results in an easier to follow order:
#include <iostream>
#include <algorithm>
#include <vector>
int main() {
int n, r;
std::cin >> n;
std::cin >> r;
std::vector<bool> v(n);
std::fill(v.begin(), v.begin() + r, true);
do {
for (int i = 0; i < n; ++i) {
if (v[i]) {
std::cout << (i + 1) << " ";
}
}
std::cout << "\n";
} while (std::prev_permutation(v.begin(), v.end()));
return 0;
}
A bit of explanation:
It works by creating a "selection array" (v), where we place r selectors, then we create all permutations of these selectors, and print the corresponding set member if it is selected in in the current permutation of v.
You can implement it if you note that for each level r you select a number from 1 to n.
In C++, we need to 'manually' keep the state between calls that produces results (a combination): so, we build a class that on construction initialize the state, and has a member that on each call returns the combination while there are solutions: for instance
#include <iostream>
#include <iterator>
#include <vector>
#include <cstdlib>
using namespace std;
struct combinations
{
typedef vector<int> combination_t;
// initialize status
combinations(int N, int R) :
completed(N < 1 || R > N),
generated(0),
N(N), R(R)
{
for (int c = 1; c <= R; ++c)
curr.push_back(c);
}
// true while there are more solutions
bool completed;
// count how many generated
int generated;
// get current and compute next combination
combination_t next()
{
combination_t ret = curr;
// find what to increment
completed = true;
for (int i = R - 1; i >= 0; --i)
if (curr[i] < N - R + i + 1)
{
int j = curr[i] + 1;
while (i <= R-1)
curr[i++] = j++;
completed = false;
++generated;
break;
}
return ret;
}
private:
int N, R;
combination_t curr;
};
int main(int argc, char **argv)
{
int N = argc >= 2 ? atoi(argv[1]) : 5;
int R = argc >= 3 ? atoi(argv[2]) : 2;
combinations cs(N, R);
while (!cs.completed)
{
combinations::combination_t c = cs.next();
copy(c.begin(), c.end(), ostream_iterator<int>(cout, ","));
cout << endl;
}
return cs.generated;
}
test output:
1,2,
1,3,
1,4,
1,5,
2,3,
2,4,
2,5,
3,4,
3,5,
4,5,
my simple and efficient solution based on algorithms from Prof. Nathan Wodarz:
// n choose r combination
#include <vector>
#include <iostream>
#include <algorithm>
struct c_unique {
int current;
c_unique() {current=0;}
int operator()() {return ++current;}
} UniqueNumber;
void myfunction (int i) {
std::cout << i << ' ';
}
int main()
{
int n=5;
int r=3;
std::vector<int> myints(r);
std::vector<int>::iterator first = myints.begin(), last = myints.end();
std::generate(first, last, UniqueNumber);
std::for_each(first, last, myfunction);
std::cout << std::endl;
while((*first) != n-r+1){
std::vector<int>::iterator mt = last;
while (*(--mt) == n-(last-mt)+1);
(*mt)++;
while (++mt != last) *mt = *(mt-1)+1;
std::for_each(first, last, myfunction);
std::cout << std::endl;
}
}
then output is:
1 2 3
1 2 4
1 2 5
1 3 4
1 3 5
1 4 5
2 3 4
2 3 5
2 4 5
3 4 5
#include<iostream>
using namespace std;
for(int i=1;i<=5;i++)
for (int j=2;j<=5;j++)
if (i!=j)
cout<<i<<","<<j<<","<<endl;
//or instead of cout... you can put them in a matrix n x 2 and use the solution
Code is similar to generating binary digits. Keep an extra data structure, an array perm[], whose value at index i will tell if ith array element is included or not. And also keep a count variable. Whenever count == length of combination, print elements based on perm[].
#include<stdio.h>
// a[] : given array of chars
// perm[] : perm[i] is 1 if a[i] is considered, else 0
// index : subscript of perm which is to be 0ed and 1ed
// n : length of the given input array
// k : length of the permuted string
void combinate(char a[], int perm[],int index, int n, int k)
{
static int count = 0;
if( count == k )
{
for(int i=0; i<n; i++)
if( perm[i]==1)
printf("%c",a[i]);
printf("\n");
} else if( (n-index)>= (k-count) ){
perm[index]=1;
count++;
combinate(a,perm,index+1,n,k);
perm[index]=0;
count--;
combinate(a,perm,index+1,n,k);
}
}
int main()
{
char a[] ={'a','b','c','d'};
int perm[4] = {0};
combinate(a,perm,0,4,3);
return 0;
}
this is a recursive method, which you can use on any type. you can iterate on an instance of Combinations class (e.g. or get() vector with all combinations, each combination is a vector of objects. This is written in C++11.
//combinations.hpp
#include <vector>
template<typename T> class Combinations {
// Combinations(std::vector<T> s, int m) iterate all Combinations without repetition
// from set s of size m s = {0,1,2,3,4,5} all permuations are: {0, 1, 2}, {0, 1,3},
// {0, 1, 4}, {0, 1, 5}, {0, 2, 3}, {0, 2, 4}, {0, 2, 5}, {0, 3, 4}, {0, 3, 5},
// {0, 4, 5}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5},
// {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}
public:
Combinations(std::vector<T> s, int m) : M(m), set(s), partial(std::vector<T>(M))
{
N = s.size(); // unsigned long can't be casted to int in initialization
out = std::vector<std::vector<T>>(comb(N,M), std::vector<T>(M)); // allocate space
generate(0, N-1, M-1);
};
typedef typename std::vector<std::vector<T>>::const_iterator const_iterator;
typedef typename std::vector<std::vector<T>>::iterator iterator;
iterator begin() { return out.begin(); }
iterator end() { return out.end(); }
std::vector<std::vector<T>> get() { return out; }
private:
void generate(int i, int j, int m);
unsigned long long comb(unsigned long long n, unsigned long long k); // C(n, k) = n! / (n-k)!
int N;
int M;
std::vector<T> set;
std::vector<T> partial;
std::vector<std::vector<T>> out;
int count (0);
};
template<typename T>
void Combinations<T>::generate(int i, int j, int m) {
// combination of size m (number of slots) out of set[i..j]
if (m > 0) {
for (int z=i; z<j-m+1; z++) {
partial[M-m-1]=set[z]; // add element to permutation
generate(z+1, j, m-1);
}
} else {
// last position
for (int z=i; z<j-m+1; z++) {
partial[M-m-1] = set[z];
out[count++] = std::vector<T>(partial); // add to output vector
}
}
}
template<typename T>
unsigned long long
Combinations<T>::comb(unsigned long long n, unsigned long long k) {
// this is from Knuth vol 3
if (k > n) {
return 0;
}
unsigned long long r = 1;
for (unsigned long long d = 1; d <= k; ++d) {
r *= n--;
r /= d;
}
return r;
}
Test file:
// test.cpp
// compile with: gcc -O3 -Wall -std=c++11 -lstdc++ -o test test.cpp
#include <iostream>
#include "combinations.hpp"
struct Bla{
float x, y, z;
};
int main() {
std::vector<int> s{0,1,2,3,4,5};
std::vector<Bla> ss{{1, .4, 5.0},{2, .7, 5.0},{3, .1, 2.0},{4, .66, 99.0}};
Combinations<int> c(s,3);
// iterate over all combinations
for (auto x : c) { for (auto ii : x) std::cout << ii << ", "; std::cout << "\n"; }
// or get a vector back
std::vector<std::vector<int>> z = c.get();
std::cout << "\n\n";
Combinations<Bla> cc(ss, 2);
// combinations of arbitrary objects
for (auto x : cc) { for (auto b : x) std::cout << "(" << b.x << ", " << b.y << ", " << b.z << "), "; std::cout << "\n"; }
}
output is :
0, 1, 2,
0, 1, 3,
0, 1, 4,
0, 1, 5,
0, 2, 3,
0, 2, 4,
0, 2, 5,
0, 3, 4,
0, 3, 5,
0, 4, 5,
1, 2, 3,
1, 2, 4,
1, 2, 5,
1, 3, 4,
1, 3, 5,
1, 4, 5,
2, 3, 4,
2, 3, 5,
2, 4, 5,
3, 4, 5,
(1, 0.4, 5), (2, 0.7, 5),
(1, 0.4, 5), (3, 0.1, 2),
(1, 0.4, 5), (4, 0.66, 99),
(2, 0.7, 5), (3, 0.1, 2),
(2, 0.7, 5), (4, 0.66, 99),
(3, 0.1, 2), (4, 0.66, 99),
Below is an iterative algorithm in C++ that does not use the STL nor recursion nor conditional nested loops. It is faster that way, it does not perform any element swaps and it does not burden the stack with recursion and it can also be easily ported to ANSI C by substituting mallloc(), free() and printf() for new, delete and std::cout, respectively.
If you want the displayed elements to start from 1 then change the OutputArray() function. Namely: cout << ka[i]+1... instead of cout << ka[i]....
Note that I use K instead of r.
void OutputArray(unsigned int* ka, size_t n) {
for (int i = 0; i < n; i++)
std::cout << ka[i] << ",";
std::cout << endl;
}
void GenCombinations(const unsigned int N, const unsigned int K) {
unsigned int *ka = new unsigned int [K]; //dynamically allocate an array of UINTs
unsigned int ki = K-1; //Point ki to the last elemet of the array
ka[ki] = N-1; //Prime the last elemet of the array.
while (true) {
unsigned int tmp = ka[ki]; //Optimization to prevent reading ka[ki] repeatedly
while (ki) //Fill to the left with consecutive descending values (blue squares)
ka[--ki] = --tmp;
OutputArray(ka, K);
while (--ka[ki] == ki) { //Decrement and check if the resulting value equals the index (bright green squares)
OutputArray(ka, K);
if (++ki == K) { //Exit condition (all of the values in the array are flush to the left)
delete[] ka;
return;
}
}
}
}
int main(int argc, char *argv[])
{
GenCombinations(7, 4);
return 0;
}
Combinations: Out of "7 Choose 4".
I'd suggest figuring out how you would do it on paper yourself and infer pseudocode from that. After that, you only need to decide the way to encode and store the manipulated data.
For ex:
For each result item in result array // 0, 1, ... r
For each item possible // 0, 1, 2, ... n
if current item does not exist in the result array
place item in result array
exit the inner for
end if
end for
end for
You can use recursion whereby to pick N+1 combinations you pick N combinations then add 1 to it. The 1 you add must always be after the last one of your N, so if your N includes the last element there are no N+1 combinations associated with it.
Perhaps not the most efficient solution but it should work.
Base case would be picking 0 or 1. You could pick 0 and get an empty set. From an empty set you can assume that iterators work between the elements and not at them.
Here are my attempt:
Function (ready for copy/paste) without any dependency
template<class _Tnumber, class _Titerator >
bool next_combination
(
_Titerator const& _First
, _Titerator const& _Last
, _Tnumber const& _Max //!< Upper bound. Not reachable
)
{
_Titerator _Current = _First;
if( _Current == _Last )
{
return false;
}
*_Current += 1;
if( *_Current < _Max )
{
return true;
}
_Titerator _Next = _Current + 1;
if( _Next == _Last )
{
return false;
}
if( false == next_combination( _Next, _Last, _Max - 1 ) )
{
return false;
}
*_Current = *_Next + 1;
return *_Current < _Max;
}
Test:
vector<int> vec({3,2,1}); // In descending order and different
do
{
copy( vec.begin(), vec.end(), ostream_iterator<int>(cout, ", " ) ); cout << endl;
}while( ::math::algorithm::next_combination( vec.begin(), vec.end(), 6 ) );
And output:
3, 2, 1,
4, 2, 1,
5, 2, 1,
4, 3, 1,
5, 3, 1,
5, 4, 1,
4, 3, 2,
5, 3, 2,
5, 4, 2,
5, 4, 3,
void print(int *a, int* s, int ls)
{
for(int i = 0; i < ls; i++)
{
cout << a[s[i]] << " ";
}
cout << endl;
}
void PrintCombinations(int *a, int l, int k, int *s, int ls, int sp)
{
if(k == 0)
{
print(a,s,ls);
return;
}
for(int i = sp; i < l; i++)
{
s[k-1] = i;
PrintCombinations(a,l,k-1,s,ls,i+1);
s[k-1] = -1;
}
}
int main()
{
int e[] = {1,2,3,4,5,6,7,8,9};
int s[] = {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1};
PrintCombinations(e,9,6,s,6,0);
}
For the special case of (n choose r), where r is a fixed constant, we can write r nested loops to arrive at the situation. Sometimes when r is not fixed, we may have another special case (n choose n-r), where r is again a fixed constant. The idea is that every such combination is the inverse of the combinations of (n choose r). So we can again use r nested loops, but invert the solution:
// example 1: choose each 2 from given vector and apply 'doSomething'
void doOnCombinationsOfTwo(const std::vector<T> vector) {
for (int i1 = 0; i1 < vector.size() - 1; i1++) {
for (int i2 = i1 + 1; i2 < vector.size(); i2++) {
doSomething( { vector[i1], vector[i2] });
}
}
}
// example 2: choose each n-2 from given vector and apply 'doSomethingElse'
void doOnCombinationsOfNMinusTwo(const std::vector<T> vector) {
std::vector<T> combination(vector.size() - 2); // let's reuse our combination vector
for (int i1 = 0; i1 < vector.size() - 1; i1++) {
for (int i2 = i1 + 1; i2 < vector.size(); i2++) {
auto combinationEntry = combination.begin(); // use iterator to fill combination
for (int i = 0; i < vector.size(); i++) {
if (i != i1 && i != i2) {
*combinationEntry++ = i;
}
}
doSomethingElse(combinationVector);
}
}
}
This seems readable and also it works for std::vector, std::list, std::deque or even static declared int intArray[]
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <list>
#include <set>
#include <iterator>
template<typename InputIt, typename T>
bool nextCombination(InputIt begin,
InputIt end,
T toElement) {
/*
Given sequence: 1 2 3 4 5
Final sequence: 6 7 8 9 10
-- Formally --
Given sequence: 1 2 ... k-1 k
Final sequence: (n-k+1) (n-k+2) ... (n-1) n
lengthOfSubsequence = positionOf(5) - positionOf(1) = 5
We look for an element that satisfies:
seqeunce[pos] < n - k + pos
*/
const auto lengthOfSubsequence = std::distance(begin, end);
auto viewed_element_it = std::make_reverse_iterator(end);
auto reversed_begin = std::make_reverse_iterator(begin);
/*Looking for this element here*/
while ((viewed_element_it != reversed_begin) &&
(*viewed_element_it >= toElement -
lengthOfSubsequence +
std::distance(viewed_element_it, reversed_begin))) {
//std::distance shows position of element in subsequence here
viewed_element_it++;
}
if (viewed_element_it == reversed_begin)
return false;
auto it = std::prev(viewed_element_it.base());
/*
Increment the found element.
The rest following elements we set as seqeunce[pos] = seqeunce[pos-1] + 1
*/
std::iota(it, end, *it + 1);
return true;
}
int main()
{
std::list<int> vec = { 1, 2, 3 };
do {
std::copy(vec.begin(), vec.end(), std::ostream_iterator<int>(std::cout, " "));
std::cout << std::endl;
} while (nextCombination(vec.begin(), vec.end(), 10));
}
One can directly compute all combinations indices in lexicographical order, like I did in following code.
These indices can be used for direct output or as pointers to any combined items as "abcde" string in second example of main() function, see output example after code.
Try it online!
#include <vector>
#include <iostream>
template <typename F>
void Combinations(size_t n, size_t k, F && out) {
if (k > n)
return;
std::vector<size_t> a(k);
for (size_t i = 0; i < k; ++i)
a[i] = i;
while (true) {
out(a);
int i = int(k) - 1;
while (i >= 0 && a[i] >= n - 1 - (k - 1 - i))
--i;
if (i < 0)
break;
for (size_t j = a[i] + 1; i < k; ++j, ++i)
a[i] = j;
}
}
int main() {
Combinations(5, 3, [](auto const & a){
for (auto i: a)
std::cout << i << " ";
std::cout << std::endl;
});
std::string s = "abcde";
Combinations(5, 3, [&](auto const & a){
for (auto i: a)
std::cout << s[i] << " ";
std::cout << std::endl;
});
}
Output:
0 1 2
0 1 3
0 1 4
0 2 3
0 2 4
0 3 4
1 2 3
1 2 4
1 3 4
2 3 4
a b c
a b d
a b e
a c d
a c e
a d e
b c d
b c e
b d e
c d e
vector<list<int>> generate(int N, int K, int& count) {
vector<list<int>> output;
if(K == 1) {
count = N;
for(int i = 1; i <= N; i++) {
list<int> l = {i};
output.push_back(l);
}
} else {
count = 0;
int n;
vector<list<int>> l = generate(N, K - 1, n);
for(auto iter = l.begin(); iter != l.end(); iter++) {
int last = iter->back();
for (int i = last + 1; i <= N; ++i) {
list<int> value = *iter;
value.push_back(i);
output.push_back(value);
count++;
}
}
}
return output;
}
You can just use for loops if r is small, here r = 2, so two for loops:
unsigned int i, j, max=0;
for(i=1; i<=n; i++){
for(j=i+1; j<=n; j++){
int ans = (i & j);
cout << i << " " << j << endl;
}
}