uva11077 Find the Permutations

Sorting is one of the most used operations in real life, where
Computer Science comes into act. It is well-known that the lower bound
of swap based sorting is nlog(n). It means that the best possible
sorting algorithm will take at least O(nlog(n)) swaps to sort a set of
n integers. However, to sort a particular array of n integers, you can
always nd a swapping sequence of at most ( n

可以把排列 P 看成一个置换，这样每个长度为 x 的循环都需要 x−1 次交换。
用 dp[i][j] 表示 i 个元素，交换 j 次的方案数。元素 i 要么单独成一个循环，这样交换次数不变，要么加入原来的一个循环，会使交换次数加一，总共有 i−1 种加入方法【加在任意一个元素的后面】。
所以

dp[i][j]=dp[i−1][j]+dp[i−1][j−1]∗(i−1)

#include
#include
#include
using namespace std;
const int maxn=21;
#define LL unsigned long long
LL dp[25][25];
int main()
{
    int i,j,n,k;
    dp[1][0]=1;
    for (i=2;i<=maxn;i++)
      for (j=0;j1][j-1]*(i-1):0)+dp[i-1][j];
    while (scanf("%d%d",&n,&k)&&n)
      printf("%llu\n",dp[n][k]);
}