[c++] Creating all possible k combinations of n items in C++

If the number of the set would be within 32, 64 or a machine native primitive size, then you can do it with a simple bit manipulation.

template<typename T>
void combo(const T& c, int k)
{
    int n = c.size();
    int combo = (1 << k) - 1;       // k bit sets
    while (combo < 1<<n) {

        pretty_print(c, combo);

        int x = combo & -combo;
        int y = combo + x;
        int z = (combo & ~y);
        combo = z / x;
        combo >>= 1;
        combo |= y;
    }
}

this example calls pretty_print() function by the dictionary order.

For example. You want to have 6C3 and assuming the current 'combo' is 010110. Obviously the next combo MUST be 011001. 011001 is : 010000 | 001000 | 000001

010000 : deleted continuously 1s of LSB side. 001000 : set 1 on the next of continuously 1s of LSB side. 000001 : shifted continuously 1s of LSB to the right and remove LSB bit.

int x = combo & -combo;

this obtains the lowest 1.

int y = combo + x;

this eliminates continuously 1s of LSB side and set 1 on the next of it (in the above case, 010000 | 001000)

int z = (combo & ~y)

this gives you the continuously 1s of LSB side (000110).

combo = z / x;
combo >> =1;

this is for 'shifted continuously 1s of LSB to the right and remove LSB bit'.

So the final job is to OR y to the above.

combo |= y;

Some simple concrete example :

#include <bits/stdc++.h>

using namespace std;

template<typename T>
void pretty_print(const T& c, int combo)
{
    int n = c.size();
    for (int i = 0; i < n; ++i) {
        if ((combo >> i) & 1)
            cout << c[i] << ' ';
    }
    cout << endl;
}

template<typename T>
void combo(const T& c, int k)
{
    int n = c.size();
    int combo = (1 << k) - 1;       // k bit sets
    while (combo < 1<<n) {

        pretty_print(c, combo);

        int x = combo & -combo;
        int y = combo + x;
        int z = (combo & ~y);
        combo = z / x;
        combo >>= 1;
        combo |= y;
    }
}

int main()
{
    vector<char> c0 = {'1', '2', '3', '4', '5'};
    combo(c0, 3);

    vector<char> c1 = {'a', 'b', 'c', 'd', 'e', 'f', 'g'};
    combo(c1, 4);
    return 0;
}

result :

1 2 3 
1 2 4 
1 3 4 
2 3 4 
1 2 5 
1 3 5 
2 3 5 
1 4 5 
2 4 5 
3 4 5 
a b c d 
a b c e 
a b d e 
a c d e 
b c d e 
a b c f 
a b d f 
a c d f 
b c d f 
a b e f 
a c e f 
b c e f 
a d e f 
b d e f 
c d e f 
a b c g 
a b d g 
a c d g 
b c d g 
a b e g 
a c e g 
b c e g 
a d e g 
b d e g 
c d e g 
a b f g 
a c f g 
b c f g 
a d f g 
b d f g 
c d f g 
a e f g 
b e f g 
c e f g 
d e f g 

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