Generate all sequences of bits within Hamming distance t

Question

Given a vector of bits v, compute the collection of bits that have Hamming distance 1 with v, then with distance 2, up to an input parameter t.

So for

011  I should get
~~~ 
111
001
010
~~~ -> 3 choose 1 in number
101
000
110
~~~ -> 3 choose 2
100
~~~ -> 3 choose 3

How to efficiently compute this? The vector won't be always of dimension 3, e.g. it could be 6. This will run numerous time in my real code, so some efficiency would be welcome as well (even by paying more memory).

---

My attempt:

#include <iostream>
#include <vector>

void print(const std::vector<char>& v, const int idx, const char new_bit)
{
    for(size_t i = 0; i < v.size(); ++i)
        if(i != idx)
            std::cout << (int)v[i] << " ";
        else
            std::cout << (int)new_bit << " ";
    std::cout << std::endl;
}

void find_near_hamming_dist(const std::vector<char>& v, const int t)
{
    // if t == 1
    for(size_t i = 0; i < v.size(); ++i)
    {
        print(v, i, v[i] ^ 1);
    }

    // I would like to produce t == 2
    // only after ALL the t == 1 results are reported
    /* how to? */
}

int main()
{
    std::vector<char> v = {0, 1, 1};
    find_near_hamming_dist(v, 1);
    return 0; 
}

Output:

MacBook-Pro:hammingDist gsamaras$ g++ -Wall -std=c++0x hammingDist.cpp -o ham
MacBook-Pro:hammingDist gsamaras$ ./ham
1 1 1 
0 0 1 
0 1 0 

Answer 1

#include <stdio.h>
#include <stdint.h>
#include <string.h>

void magic(char* str, int i, int changesLeft) {
        if (changesLeft == 0) {
                printf("%s\n", str);
                return;
        }
        if (i < 0) return;
        // flip current bit
        str[i] = str[i] == '0' ? '1' : '0';
        magic(str, i-1, changesLeft-1);
        // or don't flip it (flip it again to undo)
        str[i] = str[i] == '0' ? '1' : '0';
        magic(str, i-1, changesLeft);
}

int main(void) {
        char str[] = "011";
        printf("%s\n", str);
        size_t len = strlen(str);
        size_t maxDistance = len;
        for (size_t i = 1 ; i <= maxDistance ; ++i) {
                printf("Computing for distance %d\n", i);
                magic(str, len-1, i);
                printf("----------------\n");
        }
        return 0;
}

Output:

MacBook-Pro:hammingDist gsamaras$ nano kastrinis.cpp
MacBook-Pro:hammingDist gsamaras$ g++ -Wall kastrinis.cpp 
MacBook-Pro:hammingDist gsamaras$ ./a.out 
011
Computing for distance 1
010
001
111
----------------
Computing for distance 2
000
110
101
----------------
Computing for distance 3
100
----------------