UVA 11077 Find the Permutations DP

Find the Permutations

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

Description




Problem D

Find the Permutations

Input: Standard Input
Output: Standard Output
 

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 W(nlog(n)) swaps
to sort a set of n integers. However, to sort a particular array of n integers, you can always find a swapping sequence of at most (n-1) swaps, once you know the position of each element in the sorted sequence. For example – consider four
elements <1 2 3 4>. There are 24 possible permutations and for all elements you know the position in sorted sequence.

 

If the permutation is <2 1 4 3>, it will take minimum 2 swaps to make it sorted. If the sequence is <2 3 4 1>, at least 3 swaps are required. The sequence <4 2 3 1> requires only 1 and the sequence <1 2 3 4> requires none. In this way, we can find the permutations
of N distinct integers which will take at least K swaps to be sorted.

Input

Each input consists of two positive integers N (1≤N≤21) and K (0≤K<N) in a single line. Input is terminated by two zeros. There can be at most 250 test cases.

Output

For each of the input, print in a line the number of permutations which will take at least K swaps.

Sample Input                             Output for Sample Input

3 1 3 0 3 2 0 0

3 1 2

Problemsetter: Md. Kamruzzaman

Special Thanks: Abdullah-al-Mahmud

 

 

/* ***********************************************
Author        :CKboss
Created Time  :2015年05月06日 星期三 22时13分56秒
File Name     :UVA11077.cpp
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;

typedef unsigned long long int LL;

LL n,k;

LL dp[30][30];

void init()
{
dp[1][0]=1;
for(int i=2;i<=21;i++)
{
dp[i][0]=1;
for(int j=0;j<=i;j++)
{
dp[i][j]=dp[i-1][j]+dp[i-1][j-1]*(i-1);
}
}
}

int main()
{
//freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);

init();
while(cin>>n>>k)
{
if(n==0&&k==0) break;
cout<<dp
[k]<<endl;
}

return 0;
}