leetcode 1246

问题

Given an integer array arr, in one move you can select a palindromic subarray arr[i], arr[i+1], ..., arr[j] where i <= j, and remove that subarray from the given array. Note that after removing a subarray, the elements on the left and on the right of that subarray move to fill the gap left by the removal.

Return the minimum number of moves needed to remove all numbers from the array.

Example 1:

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Input: arr = [1,2]
Output: 2

Example 2:

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Input: arr = [1,3,4,1,5]
Output: 3
Explanation: Remove [4] then remove [1,3,1] then remove [5].

Constraints:

  • 1 <= arr.length <= 100
  • 1 <= arr[i] <= 20

分析

每个字段 $arr[i] … arr[j]$ 要么 $arr[i]$ 和 $arr[j]$ 一起“带走”，要么分两次以上带走。

代码

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class Solution {
public:
    int minimumMoves(vector<int>& arr) {
        int n = arr.size();
        vector<vector<int>> dp(n, vector<int>(n, INT_MAX/2));
        
        for (int i = 0; i < n; ++i) {
            dp[i][i] = 1;
            if (i < n-1) {
                dp[i][i+1] = arr[i]==arr[i+1]? 1: 2;
            }
        }
        for (int len = 3; len <= n; ++len) {
            for (int i = 0, j = i+len-1; j < n; ++i, ++j) {
                if (arr[i] == arr[j])
                    dp[i][j] = dp[i+1][j-1];
                
                for (int k = i; k < j; ++k) {
                    dp[i][j] = min(dp[i][j], dp[i][k]+dp[k+1][j]);
                }
            }
        }
        return dp[0][n-1];
    }
};