375. Guess Number Higher or Lower II
2016-08-07 13:18
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375. Guess Number Higher or Lower II
Question
Editorial Solution
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Difficulty: Medium
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.
这题求猜对数的最大花费的最小值。
通过模拟猜数过程得:在1-n个数里面,我们任意猜一个数(设为i),保证获胜所花的钱应该为 i +
max(w(1 ,i-1), w(i+1 ,n)),这里w(x,y))表示猜范围在(x,y)的数保证能赢应花的钱,则我们依次遍历 1-n作为猜的数,求出其中的最小值即为答案,即最小的最大值问题
class Solution { public: int cost(vector<vector<int> > &arr,int start,int end) { if (start>=end) return 0; if (arr[start][end]!=0) return arr[start][end]; int res=INT_MAX; for (int i=start;i<=end;++i) { int tmp=i+max(cost(arr,start,i-1),cost(arr,i+1,end)); if (tmp<res) res=tmp; } arr[start][end]=res; return res; } int getMoneyAmount(int n) { vector<vector<int> > arr(n+1,vector<int>(n+1,0)); return cost(arr,1,n); } };
非递归代码:
int getMoneyAmount(int n) { vector<vector<int> >cost(n+2,vector<int>(n+2,0));//下标0和n+1纯粹是为了计算方便而引入的,于是下面guess-1和guess+1无需判断是否越界 for(int diff=1;diff<=n;diff++){ //先循环距离,是因为刚开始的cost还没赋正确的值,你要先算完基本的。 for(int left=1;left+diff<=n;left++){ int right=left+diff; int minCostInThisRange=INT_MAX; for(int guess=left;guess<=right;guess++){ minCostInThisRange=min(minCostInThisRange,guess+max(cost[left][guess-1],cost[guess+1][right])); } cost[left][right]=minCostInThisRange; } } return cost[1] ; }
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