AcWing 1068. 环形石子合并

Posted 2021-07-16 Jozky86

AcWing 1068. 环形石子合并

题意：

n堆石头围成一个圈，然后将相邻两堆合并成新的一堆，得分为新的一堆的石头数
问最高得分合最低得分

题解：

很简单，区间dp的模板题
和这个题一样
状态转移方程：
dpmax[i][j] = max(dp[i][k]+dp[k+1][j]+sum[j]-sum[i-1])
dpmin[i][j]=min(dp[i][k]+dp[k+1][j])+sum[j]-sum[i-1]
因为题目说的是环形，所以数组复制一倍
马上要java期末考试，所以用java练练

代码：

import java.io.*;
import java.util.*;

class Main{
    static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
    static int N = 410, INF = 0X3f3f3f3f;
    static int[] a = new int[N], sum = new int[N];
    static int[][] dpMax = new int[N][N];
    static int[][] dpMin = new int[N][N];
    public static void main(String[] args) throws Exception{

        int n = Integer.valueOf(read.readLine());

        String[] ss = read.readLine().split(" ");
        for(int i = 1; i <= ss.length; i++){
            a[i] = Integer.valueOf(ss[i - 1]);
            a[i + n] = Integer.valueOf(ss[i - 1]);
        }

        for(int i = 1; i <= 2 * n; i++){
            sum[i] = sum[i - 1] + a[i];
            Arrays.fill(dpMax[i], -INF);
            Arrays.fill(dpMin[i],  INF);
        }


        for(int len = 1; len <= n; len++){
            for(int i = 1; i + len - 1 <= 2 * n; i++){
                int j = i + len - 1;
                if(len == 1) {
                    dpMax[i][j] = dpMin[i][j] = 0;
                }else{
                    for(int k = i; k < j; k++){
                        dpMax[i][j] = Math.max(dpMax[i][j], dpMax[i][k] + dpMax[k + 1][j] + sum[j] - sum[i - 1]);
                        dpMin[i][j] = Math.min(dpMin[i][j], dpMin[i][k] + dpMin[k + 1][j] + sum[j] - sum[i - 1]);
                    }
                }
            }
        }

        int max = -INF, min = INF;
        for(int left = 1; left <= n; left++){
            max = Math.max(max, dpMax[left][left + n - 1]);
            min = Math.min(min, dpMin[left][left + n - 1]);
        }
        System.out.println(min);
        System.out.println(max);
    }

}