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.
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題目鏈接:https://leetcode.com/problems/guess-number-higher-or-lower-ii/
題目大意:求出保證能猜出結果的最小花費。
思路:使用動態規劃。dp[i][j]表示從i到j的最小花費。則:
int ans = INT_MAX ;
for ( int i = begin ; i <= end ; i ++ )
{
ans = min ( ans , i + max ( compute ( dp , begin , i - 1 ) , compute ( dp , i + 1 , end ) ) ) ;
}
dp[begin][end] = ans ;
參考代碼:
class Solution {
public:
int getMoneyAmount(int n) {
if ( n <= 1 )
return 0 ;
int miner = 1 , maxer = n ;
vector < vector <int> > dp ( n + 1 , vector <int> ( n + 1 , 0 ) ) ;
return compute ( dp , 1 , n ) ;
}
int compute ( vector < vector <int> > & dp , int begin , int end )
{
if ( begin >= end )
return 0 ;
if ( dp[begin][end] )
return dp[begin][end] ;
int ans = INT_MAX ;
for ( int i = begin ; i <= end ; i ++ )
{
ans = min ( ans , i + max ( compute ( dp , begin , i - 1 ) , compute ( dp , i + 1 , end ) ) ) ;
}
dp[begin][end] = ans ;
return ans ;
}
};