Implement a function which takes an array of numbers from 1 to 10 and returns the numbers from 1 to 10 which are missing. examples input: [5,2,6] output: [1,3,4,7,8,9,10]
C++ program for the above approach:
#include <bits/stdc++.h>
using namespace std;
// Function to find the missing elements
void printMissingElements(int arr[], int N)
{
// Initialize diff
int diff = arr[0] - 0;
for (int i = 0; i < N; i++) {
// Check if diff and arr[i]-i
// both are equal or not
if (arr[i] - i != diff) {
// Loop for consecutive
// missing elements
while (diff < arr[i] - i) {
cout << i + diff << " ";
diff++;
}
}
}
}
Driver Code
int main()
{
// Given array arr[]
int arr[] = { 5,2,6 };
int N = sizeof(arr) / sizeof(int);
// Function Call
printMissingElements(arr, N);
return 0;
}
How to solve this question for the given input?
First of all "plzz" is not an English world. Second, the question is already there, no need to keep writing in comments "if anyone knows try to help me".
Then learn standard headers: Why should I not #include <bits/stdc++.h>?
Then learn Why is "using namespace std;" considered bad practice?
Then read the text of the problem: "Implement a function which takes an array of numbers from 1 to 10 and returns the numbers from 1 to 10 which are missing. examples input: [5,2,6] output: [1,3,4,7,8,9,10]"
You need to "return the numbers from 1 to 10 which are missing."
I suggest that you really use C++ and get std::vector into your toolbox. Then you can leverage algorithms and std::find is ready for you.
#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>
std::vector<int> missingElements(const std::vector<int> v)
{
std::vector<int> missing;
for (int i = 1; i <= 10; ++i) {
if (find(v.begin(), v.end(), i) == v.end()) {
missing.push_back(i);
}
}
return missing;
}
int main()
{
std::vector<int> arr = { 5, 2, 6 };
std::vector<int> m = missingElements(arr);
copy(m.begin(), m.end(), std::ostream_iterator<int>(std::cout, " "));
std::cout << "\n";
return 0;
}
If you want to do something with lower computational complexity you can have an already filled vector and then mark for removal the elements found. Then it's a good chance to learn the erase–remove idiom:
std::vector<int> missingElements(const std::vector<int> v)
{
std::vector<int> m = { -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
for (const auto& x: v) {
m[x] = -1;
}
m.erase(remove(m.begin(), m.end(), -1), m.end());
return m;
}
By this approach we are using space to reduce execution time. Here the time complexity is O(N) where N is the no of elements given in the array and space complexity is O(1) i.e 10' .
#include<iostream>
void printMissingElements(int arr[], int n){
// Using 1D dp to solve this
int dp[11] = {0};
for(int i = 0; i < n; i++){
dp[arr[i]] = 1;
}
// Traverse through dp list and check for
// non set indexes
for(int i = 1; i <= 10; i++){
if (dp[i] != 1) std::cout << i << " ";
}
}
int main() {
int arr[] = {5,2,6};
int n = sizeof(arr) / sizeof(int);
printMissingElements(arr, n);
}
void printMissingElements(int arr[], int n,int low, int high)
{
bool range[high - low + 1] = { false };
for (int i = 0; i < n; i++) {
if (low <= arr[i] && arr[i] <= high)
range[arr[i] - low] = true;
}
for (int x = 0; x <= high - low; x++) {
if (range[x] == false)
std:: cout << low + x << " ";
}
}
int main()
{
int arr[] = { 5,2,6,6,6,6,8,10 };
int n = sizeof(arr) / sizeof(arr[0]);
int low = 1, high = 10;
printMissingElements(arr, n, low, high);
return 0;
}
I think this will work:
vector<int> missingnumbers(vector<int> A, int N)
{ vector<int> v;
for(int i=1;i<=10;i++)
v.push_back(i);
sort(A.begin(),A.end());
int j=0;
while(j<v.size()) {
if(binary_search(A.begin(),A.end(),v[j]))
v.erase(v.begin()+j);
else
j++;
}
return v;
}
Here is the program to find the pairs that sums up to 3.
For example:
INPUT : 0,3,5,1,2,4
OUTPUT: 0,3,1,2.
That means it should return all the pairs whose sum is equal to 3.
But I want to reduce the time complexity of this program. Right now I am using two nested for loops.
Can anyone suggest a better method to reduce the time complexity.
#include<iostream>
#include <vector>
using namespace std;
void main()
{
vector<int> v;
vector<int> r;
int x;
cout << "Enter the elements";
for(int i = 0; i < 6; i++)
{
cin >> x;
v.push_back(x);
}
for(int i = 0 ; i < v.size() - 1; i++)
{
for(int j = i + 1; j < v.size(); j++)
{
if(v[i] + v[j] == 3)
{
r.push_back(v[i]);
r.push_back(v[j]);
}
}
}
cout << "\noutput\n";
for(int i = 0 ; i < r.size(); i++)
{
cout<<r[i]<<"\n";
}
}
I'd do two preparation steps; First, eliminate all numbers > 3, as they will not be part of any valid pair. This reduces the complexity of the second step. Second, sort the remaining numbers such that a single walk through can then find all the results.
The walk through approaches the pairs from both ends of the sorted array; if a pair is found, both bounds can be narrowed down; if the current endings do sum up to a value > 3, only one boundary is narrowed.
Runtime complexity is O(N logN), where N is the count of elements <= 3; O(N logN) basically comes from sorting; the two single walk throughs will not count for large Ns.
int main(int argc, char* argv[]) {
const int N = 3;
std::vector<int> input{ 0,3,5,1,2,4};
std::vector<int>v(input.size());
int t=0;
for (auto i : input) {
if (i <= N) {
v[t++]=i;
}
}
std::sort (v.begin(), v.end());
long minIdx = 0;
long maxIdx = v.size()-1;
while (minIdx < maxIdx) {
int minv = v[minIdx];
int maxv = v[maxIdx];
if (minv+maxv == 3) {
cout << minv << '+' << maxv << endl;
minIdx++;maxIdx--;
}
else
minIdx++;
}
return 0;
}
You are searching for all the combinations between two numbers in n elements, more specifically, those that sum up to specific value. Which is a variation of the subset sum problem.
To make this happen you could generate all combinations without repetitions of the indexes of the vector holding the values. Here is an example of how to do this recursively and here is an example of how to do it iteratively, just to get an idea and possibly use it as a benchmark in your case.
Another approaches are dynamic programming and backtracking.
Late answer but works for negative integers too... For first, find the smallest number in the std::vector<int>, then like this answer says, remove all elements (or copy the opposite), which are higher than 3 + minimum. After sorting this std::vector<int> iterate through it from both ends with condition shown bellow:
#include <iostream>
#include <vector>
#include <algorithm>
#include <climits>
std::vector<int> findPairs(const std::vector<int>& input, const int sum) {
int minElem = INT_MAX;
for(auto lhs = input.begin(), rhs = input.end() - 1; lhs < rhs;
++lhs, --rhs) {
const int elem = (*lhs < *rhs ? *lhs : *rhs);
if(elem < minElem)
minElem = elem;
}
std::vector<int> temp(input.size());
const auto tempBegin = temp.begin();
const auto tempEnd = std::remove_copy_if(input.begin(), input.end(),
temp.begin(), [minElem, sum](int elem) {
return (elem + minElem) > sum;
});
std::sort(tempBegin, tempEnd);
std::vector<int> result;
auto leftIter = tempBegin;
auto rightIter = tempEnd - 1;
while(leftIter < rightIter) {
if(*leftIter + *rightIter == sum) {
result.push_back(*leftIter++);
result.push_back(*rightIter--);
}
else {
if(sum - *leftIter < *rightIter) rightIter--;
else leftIter++;
}
}
return result;
}
int main() {
auto pairs = findPairs({ 0, 3, 5, 1, 2, 4, 7, 0, 3, 2, -2, -4, -3 }, 3);
std::cout << "Pairs: { ";
for(auto it = pairs.begin(); it != pairs.end(); ++it)
std::cout << (it == pairs.begin() ? "" : ", ") << *it;
std::cout << " }" << std::endl;
}
The code above will results the following:
Pairs: { -4, 7, -2, 5, 0, 3, 0, 3, 1, 2 }
I think you can solve this in O(n) with a map.
public void printPairs(int[] a, int v)
{
map<int, int> counts = new map<int, int>();
for(int i = 0; i < a.length; i++)
{
if(map.count(a[i]) == 0)
{
map[a[i]] = 1;
}
else
{
map[a[i]] = map[a[i]] + 1;
}
}
map<int, int>::iterator it = map.begin();
while(it != map.end())
{
int v1 = it->second;
if (map.count(v - v1) > 0)
{
// Found pair v, v1
//will be found twice (once for v and once for v1)
}
}
}
Is it possible to sort a 2D Array using qsort or std::sort in C++ such that the elements are in increasing order when read from left to right in each row or from top to bottom in each column?
For example,
13, 14, 15, 16
1, 4, 3, 2
7, 5, 7, 6
9, 10, 11, 12
Becomes:
{ 1, 2, 3, 4 }
{ 5, 6, 7, 8 }
{ 9, 10, 11, 12 }
{ 13, 14, 15, 16 }
I know you can do it by creating two comparison functions and then first sorting each row then comparing the first elements of each row to establish the columns, but is there a way to do it in one function itself?
# include <iostream>
using namespace std ;
void swap (int &x , int &y)
{
int temp = x ;
x = y ;
y = temp ;
}
void main ()
{
int arr [3][3] = {{90,80,70},{60,50,40},{30,100,10}} ;
int x ;
for (int k = 0; k < 3; k++)
{
for (int m = 0; m < 3; m++)
{
x = m+1;
for (int i = k; i < 3 ; i++)
{
for (int j = x; j < 3; j++)
{
if (arr [k][m] > arr [i][j])
swap(arr [k][m] ,arr [i][j]);
}
x=0;
}
}
}
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
cout << arr [i][j] << " ";
}
}
system("pause");
}
C++ Sorting 2-D array ascendingly
Yes. C++ STL library is built with separation of algorithms and containers. What links them together is iterators. Raw pointer is iterator, therefore it is possible to initialize vector with raw pointers and then sort that vector as usual.
std::vector<int> v(arr2d, arr2d + N); // create a vector based on pointers
// This assumes array is contiguous range
// in memory, N=number of elemnts in arr2d
// using default comparison (operator <):
std::sort (v.begin(), v.end());
// cout by 4 elements in a row
In theory you should be able to input the 16 numbers into an array. Use a for loop, maybe even a nested one, to sort the numbers. Then as for output you want the ascending numbers in four groups of four?
cout<<Vector[0]<<Vector[1]<<Vector[2]<<Vector[3]<<endl;
cout<<Vector[4]<<Vector[5]<<Vector[6]<<Vector[7]<<endl;
cout<<Vector[8]<<Vector[9]<<Vector[10]<<Vector[11]<<endl;
cout<<Vector[12]<<Vector[13]<<Vector[14]<<Vector[15]<<endl;
very arbitrary but I'm not quite sure of the question.
First Make a 2D vector .
Sort each vector in this 2D vector
Sort the whole vector
Code :
#include <iostream>
#include <vector>
#include <algorithm>
template <class T>
void Sort2dArray(std::vector<std::vector<T>> & numbers)
{
for(auto & i : numbers){//sort each vector<T> in numbers
std::sort(i.begin(),i.end());
}
std::sort(numbers.begin(),numbers.end(),[](//sort numbers by defining custom compare
const std::vector<T>& a,const std::vector<T>&b){
for(int i=0;i<a.size()&&i<b.size();i++)
{
if(a[i]>b[i])
return false;
else if(a[i]<b[i])
return true;
}
return a.size()<b.size() ? true : false;
});
}
int main()
{
std::vector<std::vector<int>> numbers={ {13, 14, 15, 16},
{1, 4, 3, 2},
{8, 5, 7, 6},
{9, 10, 12,11}};
Sort2dArray(numbers);//sort array
//write sorted array
for(auto i:numbers)
{
for(auto j:i)
std::cout<<j<<" ";
std::cout<<"\n";
}
}
**Sorting 2D array in c++**
#include <iostream>
using namespace std;
int main()
{
int i,j,k,m,temp,n,limit;
int** p;
cout<<"Enter the limit:";
cin>>limit;
p=new int*[limit];
//inputing
for(i=0;i<limit;i++)
{
p[i] = new int[limit];
for(j=0;j<limit;j++)
{
cin>>p[i][j];
}
}
//sorting
for(i=0;i<limit;i++)
{
for(j=0;j<limit;j++)
{
if (j==limit-1 && i<limit-1)
{
n =-1;
m=i+1;
}
else
{
m=i;
n=j;
}
for(k=n+1;k<limit;k++)
{
if(p[i][j] > p[m][k] )
{
temp = p[i][j];
p[i][j] = p[m][k];
p[m][k] = temp;
}
if(k==limit-1 && m<limit-1) { m++; k=-1; }
}
}
}
//displaying
for(i=0;i<limit;i++)
{
for(j=0;j<limit;j++)
{
cout<<p[i][j]<<endl;
}
}
return 0;
}
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;
}
}