ブルートフォースなしでn番目の順列を効率的に見つけるにはどうすればよいでしょうか?

void ithPermutation(const int n, int i) {
    int *fact = (int *)calloc(n, sizeof(int));
    int *perm = (int *)calloc(n, sizeof(int));

    // Compute factorial numbers
    fact[0] = 1;
    for (int k = 1; k < n; k++) {
        fact[k] = fact[k - 1] * k;
    }

    // Compute factorial code
    for (int k = 0; k < n; k++) {
        perm[k] = i / fact[n - 1 - k];
        i = i % fact[n - 1 - k];
    }

    // Readjust values to obtain the permutation
    for (int k = n - 1; k > 0; k--) {
        for (int j = k - 1; j >= 0; j--) {
            if (perm[j] <= perm[k]) {
                perm[k]++;
            }
        }
    }

    // Print permutation
    for (int k = 0; k < n; k++) {
        printf("%d ", perm[k]);
    }
    printf("\n");

    free(fact);
    free(perm);
}

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