从C中的n生成k置换

std::next_permutation

n-k

std::reverse

next-permutation next_k_permutation k

std::reverse(); std::next_permutation();

#include <stddef.h>

/* Helper functions */
static void swap(int* elements, size_t a, size_t b) {
  int tmp = elements[a]; elements[a] = elements[b]; elements[b] = tmp;
}
static void flip(int* elements, size_t lo, size_t hi) {
  for (; lo + 1 < hi; ++lo, --hi) swap(elements, lo, hi - 1);
}

/* Given an array of n elements, finds the next permutation in
 * lexicographical order with a different k-prefix; in effect, it 
 * generates all k-permutations of the array.
 * It is required that the suffix be sorted in ascending order. This
 * invariant will be maintained by the function.
 * Before the first call, the array must be sorted in ascending order.
 * Returns true unless the input is the last k-permutation.
 */ 
int next_k_permutation(int* elements, size_t n, size_t k) {
  // Find the rightmost element which is strictly less than some element to its
  // right.
  int tailmax = elements[n - 1];
  size_t tail = k;
  while (tail && elements[tail - 1] >= tailmax)
    tailmax = elements[--tail];
  // If no pivot was found, the given permutation is the last one.
  if (tail) {
    size_t swap_in;
    int pivot = elements[tail - 1];
    // Find the smallest element strictly greater than the pivot, either
    // by searching forward from the pivot or backwards from the end.
    if (pivot >= elements[n - 1]) {
      for (swap_in = tail; swap_in + 1 < k && elements[swap_in + 1] > pivot; ++swap_in) {}
    } else {
      for (swap_in = n - 1; swap_in > k && elements[swap_in - 1] > pivot; --swap_in) {}
    }
    // Swap the pivots
    elements[tail - 1] = elements[swap_in];
    elements[swap_in] = pivot;
    // Flip the tail. 
    flip(elements, k, n);
    flip(elements, tail, n);
  }
  return tail;
}

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

int intcmp(const void* a, const void* b) {
  return *(int*)a < *(int*)b ? -1 : 
         *(int*)a > *(int*)b ?  1 :
                                0 ;
}

int main(int argc, char** argv) {
  size_t k = (argc > 1) ? atoi(argv[1]) : 0;
  if (argc < k + 2) {
    fprintf(stderr, "Usage: %s K element...\n"
                    "       where K <= number of elements\n",
                    argv[0]);
    return 1;
  }
  size_t n = argc - 2;
  int elements[n];
  for (int i = 0; i < n; ++i) elements[i] = atoi(argv[i + 2]);
  qsort(elements, n, sizeof *elements, intcmp);
  do {
    const char* delimiter = "";
    for (size_t i = 0; i < k; ++i) {
      printf("%s%2d ", delimiter, elements[i]);
      delimiter = " ";
    }
    putchar('\n');
  } while (next_k_permutation(elements, n, k));
  return 0;
}

$ ./k_next_permutation 2 7 3 4 4 5
 3   4 
 3   5 
 3   7 
 4   3 
 4   4 
 4   5 
 4   7 
 5   3 
 5   4 
 5   7 
 7   3 
 7   4 
 7   5 

n - k

#include <assert.h>
#include <stdbool.h>
#include <stddef.h>

/* Helper functions */
static void swap(int* elements, size_t a, size_t b) {
  int tmp = elements[a]; elements[a] = elements[b]; elements[b] = tmp;
}
static void flip(int* elements, size_t lo, size_t hi) {
  for (; lo + 1 < hi; ++lo, --hi) swap(elements, lo, hi - 1);
}
static void rotate_left(int* elements, size_t lo, size_t hi) {
  if (hi > lo) {
    int tmp = elements[lo];
    for (size_t i = lo + 1; i < hi; ++i) elements[i - 1] = elements[i];
    elements[hi - 1] = tmp;
  }
}

/* Recursive function; the main function will fill in the extra parameters */
/* Requires hi >= lo and hi >= k. Array must have size (at least) lo + k */    
static bool helper(int* array, size_t lo, size_t k, size_t hi,
                       bool(*process)(void*, int*, size_t), void* baton) {
  if (hi == lo) {
    if (!process(baton, array + lo, k)) return false;
    if (lo % 2)
      flip(array, 0, lo);
    else
      rotate_left(array, 0, lo);
  }
  else {
    for (size_t i = 0; i < hi - 1; ++i) {
      if (!helper(array, lo, k, hi - 1, process, baton))
        return false;
      swap(array, hi % 2 ? 0 : i, hi - 1);
    }
    if (!helper(array, lo, k, hi - 1, process, baton))
      return false;
  }
  return true;
}

/* Generate all k-permutations of the given array of size n.
 * The process function is called with each permutation; if it returns false,
 * generation of permutations is terminated.
 */ 
bool k_heap_permute(int* array, size_t n, size_t k,
                    bool(*process)(void*, int*, size_t), void* baton) {
  assert(k <= n);
  return helper(array, n - k, k, n, process, baton);
}

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

bool print_array(void* vf, int* elements, size_t n) {
  FILE* f = vf;
  const char* delim = "";
  for (size_t i = 0; i < n; ++i) {
    fprintf(f, "%s%2d", delim, elements[i]);
    delim = " ";
  }
  putc('\n', f);
  return true;
}

int main(int argc, char** argv) {
  size_t k = (argc > 1) ? atoi(argv[1]) : 0;
  if (argc < k + 2) {
    fprintf(stderr, "Usage: %s K element...\n"
                    "       where K <= number of elements\n",
                    argv[0]);
    return 1;
  }
  size_t n = argc - 2;
  int elements[n];
  for (int i = 0; i < n; ++i)
    elements[i] = atoi(argv[i + 2]);
  k_heap_permute(elements, n, k, print_array, stdout);
  return 0;
}

$ ./permut 2      1 5 9 7 3
 7  3
 9  3
 5  3
 1  3
 1  5
 7  5
 9  5
 3  5
 3  9
 1  9
 7  9
 5  9
 5  7
 3  7
 1  7
 9  7
 9  1
 5  1
 3  1
 7  1