Permutations with some fixed numbers

Question

How to effectively generate permutations of a number (or chars in word), if i need some char/digit on specified place?

e.g. Generate all numbers with digit 3 at second place from the beginning and digit 1 at second place from the end of the number. Each digit in number has to be unique and you can choose only from digits 1-5.

4 3 2 1 5
4 3 5 1 2
2 3 4 1 5
2 3 5 1 4
5 3 2 1 4
5 3 4 1 2

I know there's a next_permutation function, so i can prepare an array with numbers {4, 2, 5} and post this in cycle to this function, but how to handle the fixed positions?

Answer 1

Generate all permutations of 2 4 5 and insert 3 and 1 in your output routine. Just remember the positions were they have to be:

int perm[3] = {2, 4, 5};
const int N = sizeof(perm) / sizeof(int);

std::map<int,int> fixed;  // note: zero-indexed
fixed[1] = 3;
fixed[3] = 1;

do {
    for (int i=0, j=0; i<5; i++)
        if (fixed.find(i) != fixed.end())
            std::cout << " " << fixed[i];
        else
            std::cout << " " << perm[j++];
    std::cout << std::endl;
} while (std::next_permutation(perm, perm + N));

outputs

 2 3 4 1 5
 2 3 5 1 4
 4 3 2 1 5
 4 3 5 1 2
 5 3 2 1 4
 5 3 4 1 2