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| Time Limit: 3000MS | Memory Limit: Unknown | 64bit IO Format: %lld & %llu |
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.
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.
For each of the input, print in a line the number of permutations which will take at least K swaps.
|
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[n][k]<<endl;
}
return 0;
}
UVA 11077 Find the Permutations DP
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原文地址：http://blog.csdn.net/ck_boss/article/details/45542591
