guess-number-higher-or-lower-ii

// https://discuss.leetcode.com/topic/51353/simple-dp-solution-with-explanation
// https://en.wikipedia.org/wiki/Minimax
// 开始我的思路有问题，我是先选择区间，最后收敛到结果数
// 实际上work的思路是，先选择数字，再走向某个区间，然后取两个区间中的更大值

class Solution {
    int ** table;
    int DP(int s, int e) {
        if (s >= e) {
            return 0;
        }
        
        if (table[s][e] != INT_MAX) {
            return table[s][e];
        }
        int local_max = INT_MAX;
        for (int k=s; k<=e; ++k) {
            // 下面这个表达式很重要
            local_max = min(k + max(DP(s, k-1), DP(k+1, e)), local_max);
        }
        table[s][e] = local_max;
        return local_max;
    }
    
public:
    int getMoneyAmount(int n) {
        
        table = new int*[n+1];
        for (int i=0; i<n+1; ++i) {
            table[i] = new int[n+1];
            for (int j=0; j<n+1; ++j) {
                table[i][j] = INT_MAX;
            }
        }
        
        int ret = DP(1, n);
        
        for (int i=0; i<n+1; ++i) {
            delete[] table[i];
        }
        delete[] table;
        
        return ret;
    }
    
};