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;
}

};