algorithm-in-python/math/permute/permute_cantor.c

/* mbinary
#########################################################################
# File : permute_cantor.c
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-11-17  11:25
# Description:
#########################################################################
*/
#include<stdio.h>

//使用康托展开计算全排列, 下面存储的是0!,1!,2!...(n-1)!
long long int fac[100] = {};
void calFac(int n)
{
    int i;
    fac[0] = 1;

    for (i = 1; i <= n; i++) {
        fac[i] = i * fac[i - 1];
    }
}

void permute(int *arr, int n, int sum)
{
    /*sum表示全排列由小到大排序后的名次,从0 开始计数, 由名次求出 n位的排列存储到 arr 中*/
    int i, j, ct = 0, k, ct2;
    int flag[n];

    for (i = 0; i < n; i++)flag[i] = 1;

    for (i = n - 1; i >= 0; i--) {
        for (j = i; j >= 0; j--) {
            if (j * fac[i] <= sum) {
                ct2 = 0;

                for (k = 0; k < n; ++k) {
                    //printf("i%d  j%d  k%d\n",i,j,k);
                    if (flag[k] == 1)ct2++;

                    if (ct2 > j)break;
                }

                arr[ct++] = k;
                flag[k] = 0;
                sum -= j * fac[i];
                break;
            }
        }
    }
}

void printArr(int *p, int n)
{
    for (int i = 0; i < n; ++i)printf("%d, ", p[i]);

    printf("\n");
}

int main()
{
    int n = 5, arr[n];
    calFac(n);

    for (int i = 0; i < 5; ++i)arr[i] = i;

    for (int i = 0; i < fac[n]; ++i) {
        printArr(arr, n);
        permute(arr, n, i);
    }

    return 0;
}