题解 | 回文数组

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

vector<vector<int>> matrix;

int findMinSum(vector<int>& arr, int left, int right) {
    // 基础情况
    if (left == right) {
        return arr[left];
    }
    if (left > right) {
        return 0;
    }
    
    // 如果已经计算过
    if (matrix[left][right] != 0) {
        return matrix[left][right];
    }
    
    // 如果两端相等
    if (arr[left] == arr[right]) {
        matrix[left][right] = 2 * arr[left] + findMinSum(arr, left + 1, right - 1);
    } else {
        // 取两种方案的最小值
        int useLeft = findMinSum(arr, left + 1, right) + 2 * arr[left];
        int useRight = findMinSum(arr, left, right - 1) + 2 * arr[right];
        matrix[left][right] = min(useLeft, useRight);
    }
    
    return matrix[left][right];
}

int main() {
    // 读取输入
    int n;
    cin >> n;
    vector<int> arr(n);
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
    }
    
    // 初始化记忆数组
    matrix.resize(n, vector<int>(n, 0));
    
    // 计算结果
    int result = findMinSum(arr, 0, n-1);
    cout << result << endl;
    
    return 0;
}

import java.util.*;

public class Main {
    static int[][] matrix;
    
    static int findMinSum(int[] arr, int left, int right) {
        // 基础情况
        if (left == right) {
            return arr[left];
        }
        if (left > right) {
            return 0;
        }
        
        // 如果已经计算过
        if (matrix[left][right] != 0) {
            return matrix[left][right];
        }
        
        // 如果两端相等
        if (arr[left] == arr[right]) {
            matrix[left][right] = 2 * arr[left] + findMinSum(arr, left + 1, right - 1);
        } else {
            // 取两种方案的最小值
            int useLeft = findMinSum(arr, left + 1, right) + 2 * arr[left];
            int useRight = findMinSum(arr, left, right - 1) + 2 * arr[right];
            matrix[left][right] = Math.min(useLeft, useRight);
        }
        
        return matrix[left][right];
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        // 读取输入
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }
        
        // 初始化记忆数组
        matrix = new int[n][n];
        
        // 计算结果
        int result = findMinSum(arr, 0, n-1);
        System.out.println(result);
    }
}

def find_min_sum(arr, left, right, matrix):
    # 基础情况
    if left == right:
        return arr[left]
    if left > right:
        return 0
        
    # 如果已经计算过
    if matrix[left][right] != 0:
        return matrix[left][right]
    
    # 如果两端相等
    if arr[left] == arr[right]:
        matrix[left][right] = 2 * arr[left] + find_min_sum(arr, left + 1, right - 1, matrix)
    else:
        # 取两种方案的最小值
        use_left = find_min_sum(arr, left + 1, right, matrix) + 2 * arr[left]
        use_right = find_min_sum(arr, left, right - 1, matrix) + 2 * arr[right]
        matrix[left][right] = min(use_left, use_right)
    
    return matrix[left][right]

def solve():
    # 读取输入
    n = int(input())
    arr = list(map(int, input().split()))
    
    # 初始化记忆数组
    matrix = [[0] * n for _ in range(n)]
    
    # 计算结果
    result = find_min_sum(arr, 0, n-1, matrix)
    print(result)

if __name__ == "__main__":
    solve()