区间DP HDU2476 区间染色升级版

最新推荐文章于 2022-03-01 11:37:36 发布

Y_is_sunshine

最新推荐文章于 2022-03-01 11:37:36 发布

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分类专栏： DP

本文链接：https://blog.youkuaiyun.com/qq_43676357/article/details/98874381

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本文介绍了一种基于区间动态规划的升级版区间染色算法，通过两次区间DP解决复杂的问题。首先进行字符串匹配预处理，然后利用动态规划求解最小染色次数。该算法适用于处理字符串比对与编辑距离相关问题。

区间染色的升级版
相当于两次区间DP
HDU 2476

//MADE BY Y_is_sunshine;
//#include <bits/stdc++.h>
//#include <memory.h>
#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <cstdio>
#include <vector>
#include <string>
#include <cmath>
#include <queue>
#include <stack>
#include <map>
#include <set>

#define INF 0x3f3f3f3f
#define MAXN 105

const int mod = 1e9 + 7;
const double PI = acos(-1);

using namespace std;

int dp[MAXN][MAXN];

int main()
{
	freopen("data.txt", "r", stdin);

	string s1, s2;
	while (cin >> s1 >> s2) {
		int N = s1.size();
		s1.insert(s1.begin(), ' ');
		s2.insert(s2.begin(), ' ');

		for (int i = 1; i <= N; i++)
			dp[i][i] = 1;

		for (int len = 2; len <= N; len++) {
			for (int i = 1; i + len - 1 <= N; i++) {
				int j = i + len - 1;
				dp[i][j] = INF;
				if (s2[i] == s2[j])
					dp[i][j] = dp[i][j - 1];
				for (int k = i; k < j; k++)
					dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]);
			}
		}
		int ans[MAXN];
		ans[0] = 0;
		for (int i = 1; i <= N; i++)
			ans[i] = dp[1][i];
		for (int i = 1; i <= N; i++) {
			if (s1[i] == s2[i])
				ans[i] = ans[i - 1];
			else
				for (int j = 1; j < i; j++)
					ans[i] = min(ans[i], ans[j] + dp[j + 1][i]);
		}

		cout << ans[N] << endl;
	}

	

	freopen("CON", "r", stdin);
	system("pause");
	return 0;
}