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; } };
