foj Problem 2282 Wand
Accept: 432 Submit: 1537
Time Limit: 1000 mSec Memory Limit :
262144 KB
Problem Description
N wizards are attending a meeting. Everyone has his own magic wand. N magic
wands was put in a line, numbered from 1 to n(Wand_i owned by wizard_i). After
the meeting, n wizards will take a wand one by one in the order of 1 to n. A
boring wizard decided to reorder the wands. He is wondering how many ways to
reorder the wands so that at least k wizards can get his own wand.
For example, n=3. Initially, the wands are w1 w2 w3. After reordering, the
wands become w2 w1 w3. So, wizard 1 will take w2, wizard 2 will take w1, wizard
3 will take w3, only wizard 3 get his own wand.
Input
First line contains an integer T (1 ≤ T ≤ 10), represents there are T test
cases.
For each test case: Two number n and k.
1<=n <=10000.1<=k<=100. k<=n.
Output
For each test case, output the answer mod 1000000007(10^9 + 7).
Sample Input
1 1
3 1
Sample Output
4
Source
第八届福建省大学生程序设计竞赛-重现赛(感谢承办方厦门理工学院)
#define _CRT_SECURE_NO_DEPRECATE
#include <iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<bitset>
#include<set>
#include<map>
#include<cmath>
#include<queue>
using namespace std;
#define N_MAX 10000+4
#define MOD 1000000007
#define INF 0x3f3f3f3f
typedef long long ll;
int n, k;
ll dp[N_MAX];//错排数
ll C[N_MAX][ + ];
void init() {
dp[] = ; dp[] = ; dp[] = ;
for (int i = ; i < N_MAX; i++) {
dp[i] = ((i - )*(dp[i - ] + dp[i - ]) + MOD) % MOD;
}
}
void C_table() {
for (int i = ; i < N_MAX; i++) {
C[i][] = ;
for (int j = ; j <= min(, i); j++) {//!!!j<=i并且数组中j不能超过100
C[i][j] = (C[i - ][j] + C[i - ][j - ]) % MOD;
}
}
} int main() {
init(); C_table();
int t; scanf("%d", &t);
while (t--) {
scanf("%d%d", &n, &k);
ll num = , ans = ;
for (ll i = ; i <= n; i++) {
ans = ans*i%MOD;
}
for (int i = ; i <= k - ; i++) {
num = (num + C[n][i] * dp[n - i]) % MOD;
}
printf("%lld\n", (ans - num + MOD) % MOD);
}
return ;
}
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