Guess Number Higher or Lower II

Guess Number Higher or Lower II

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I'll tell you whether the number I picked is higher or lower.

However, when you guess a particular number x, and you guess wrong, you pay $x. You win the game when you guess the number I picked.

Example:

n = 10, I pick 8.First round:  You guess 5, I tell you that it's higher. You pay $5.Second round: You guess 7, I tell you that it's higher. You pay $7.Third round:  You guess 9, I tell you that it's lower. You pay $9.Game over. 8 is the number I picked.You end up paying $5 + $7 + $9 = $21.

Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.

解析：

使用递归，对于每个值找到左右序列能保证的值，选取较小值加上当前值

代码：

class Solution {public:    int getMoneyAmount(int n) {        if (n==1)        return 0;        vector<vector<int>>table(n+1,vector<int>(n+1,0));        return DP(table,1,n);    }    int DP(vector<vector<int>>&table,int begin,int end)    {        if (begin>=end) return 0;        if ((end-begin)==1)        {            table[begin][end]=begin;            return begin;        }        if (table[begin][end]) return table[begin][end];        int ans=INT_MAX;        for (int i=begin; i<=end; i++)        {            int lefttable=DP(table,begin,i-1);            if ((i-1)>begin)            table[begin][i-1]=lefttable;            int righttable=DP(table,i+1,end);            if ((i+1)<end)            table[i+1][end]=righttable;            ans=min(ans,i+max(lefttable,righttable));        }        table[begin][end]=ans;        return ans;    }        };