hdu5362 Just A String(dp)
转载请注明出处: http://www.cnblogs.com/fraud/ ——by fraud
Just A String
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 320 Accepted Submission(s): 62
For a string s, if we can reorder the letters in string s so as to get a palindrome, then we call s a good string.
soda wants to know the expected number of good substrings in the random string.
The first line contains two integers n and m (1≤n,m≤2000).
当时状态真是见鬼,其实这题还是比较容易的一个dp
dp[i][j]表示长度为i时,j种字符是奇数个的字符串种数
从而dp[i][j] = dp[i-1][j+1]*(j+1) + dp[i-1][j-1]*(m-j+1)
最后Σdp[i][i&1]*(n-i+1)*(m^(n-i))
/**
* code generated by JHelper
* More info: https://github.com/AlexeyDmitriev/JHelper
* @author xyiyy @https://github.com/xyiyy
*/ #include <iostream>
#include <fstream> //#####################
//Author:fraud
//Blog: http://www.cnblogs.com/fraud/
//#####################
//#pragma comment(linker, "/STACK:102400000,102400000")
#include <iostream>
#include <sstream>
#include <ios>
#include <iomanip>
#include <functional>
#include <algorithm>
#include <vector>
#include <string>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <climits>
#include <cctype> using namespace std;
#define rep2(X, L, R) for(int X=L;X<=R;X++)
typedef long long ll; int dp[][];
int dp2[];
const int mod = ; class hdu5362 {
public:
void solve(std::istream &in, std::ostream &out) {
int n, m;
in >> n >> m;
dp[][] = ;
rep2(i, , n) {
for (int j = (i & ); j <= m && j <= i; j++) {
if (!j)dp[i][j] = dp[i - ][j + ];
else if (j == i || j == m)dp[i][j] = (ll) dp[i - ][j - ] * (m - j + ) % mod;
else dp[i][j] = ((ll) dp[i - ][j - ] * (m - j + ) + (ll) dp[i - ][j + ] * (j + )) % mod;
}
}
dp2[] = ;
rep2(i, , n) {
dp2[i] = (ll) dp2[i - ] * m % mod;
}
int ans = ;
rep2(i, , n) {
ans = (ans + (ll) dp[i][i & ] * (n - i + ) % mod * dp2[n - i]) % mod;
}
out << ans << endl;
}
}; int main() {
std::ios::sync_with_stdio(false);
std::cin.tie();
hdu5362 solver;
std::istream &in(std::cin);
std::ostream &out(std::cout);
int n;
in >> n;
for (int i = ; i < n; ++i) {
solver.solve(in, out);
} return ;
}
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