Week Training: 486 Predict the Winner

动态规划解决博弈论问题

最新推荐文章于 2022-12-31 23:53:30 发布

原创最新推荐文章于 2022-12-31 23:53:30 发布 · 232 阅读

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本文介绍了一种使用动态规划解决两人轮流取数游戏中胜者预测的问题。通过定义状态dp[i][j]为玩家1在位置i到j区间内得分超过玩家2的分数，给出了具体的动态转移方程。

An another dp problem. The key to solve is still to find the dp state, here we chose the score player 1 get more than player 2. dp[i][j] means the score exceeded between position i and j in the array. So the initial state is dp[i][i] = nums[i], and the state transformation is dp[i][j] = max(nums[i]-dp[i+1][j],nums[j]-dp[i][j-1]), since whenever player 1 or player 2 chose a new number, the exceeding score will be the difference between the new number and the last dp state.

class Solution {
public:
    bool PredictTheWinner(vector<int>& nums) {
        int length = nums.size();
        int dp[25][25];
        for(int i=0;i<length;i++){
            dp[i][i]=nums[i];
        }
        for(int i=length-2;i>=0;i--){
            for(int j=i+1;j<length;j++){
                dp[i][j] = max(nums[i]-dp[i+1][j],nums[j]-dp[i][j-1]);
            }
        }
        if(dp[0][length-1]>=0) return true;
        return false;
    }
};