[LeetCode] Predict the Winner 预测得分最高的赢家

声明：原题目转载自LeetCode，解答部分为原创

Problem ：

        Given an array of scores that are non-negative integers. Player 1 picks one of the numbers from either end of the array followed by the player 2 and then player 1 and so on. Each time a player picks a number, that number will not be available for the next player. This continues until all the scores have been chosen. The player with the maximum score wins.

        Given an array of scores, predict whether player 1 is the winner. You can assume each player plays to maximize his score.

         Example 1:

Input: [1, 5, 2]Output: FalseExplanation: Initially, player 1 can choose between 1 and 2. 
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2). 
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5. 
Hence, player 1 will never be the winner and you need to return False.

        Example 2:

Input: [1, 5, 233, 7]Output: TrueExplanation: Player 1 first chooses 1. Then player 2 have to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.

Note:

1. 1 <= length of the array <= 20.
2. Any scores in the given array are non-negative integers and will not exceed 10,000,000.
3. If the scores of both players are equal, then player 1 is still the winner.

Solution：

        思路：动态规划的类型。双方博弈，假定本回合中我取数组头尾的其中一个分数，接下来的比赛中，你肯定会从剩余数组中尽可能取得最大的分数。设f（a，b）为从数组num【a，b】中获取最高的分数，动态转换方程为：

        f（a，b）=max{ num【a】 + sum_of_num【a + 1，b】- f（a + 1， b），num【b】 + sum_of_num【a， b - 1】- f（a， b - 1）}

        其中，每个比较项的后两项表示下一次轮到我时我能够获取的最大分数。

        代码如下：

#include<iostream>#include<vector>using namespace std;class Solution {public:    bool PredictTheWinner(vector<int>& nums) {    int size = nums.size();    vector<int> sum(size);        vector<vector<int> > max_score(size, vector<int>(size, 0));                for(int i = 0 ; i < size ; i ++)        {        max_score[i][i] = nums[i];}int temp = 0;for(int i = 0 ; i < size ; i ++){temp += nums[i];sum[i] = temp;}for(int i = 1 ; i < size ; i ++){for(int row = 0 ; row < size - i ; row ++){int get_left  = nums[row] + sum[row + i] - sum[row] - max_score[row + 1][row + i]; int get_right = nums[row + i] + sum[row + i - 1] - sum[row] + nums[row] - max_score[row][row + i - 1]; max_score[row][row + i] = max(get_left, get_right);}    }    return max_score[0][size - 1] >= sum[size - 1] - max_score[0][size - 1];    }};int main(){vector<int> nums(4);nums[0] = 1;nums[1] = 5;nums[2] = 233;nums[3] = 7;Solution text;cout << "max_score : " << text.PredictTheWinner(nums) << endl;return 0;}