Guess Number Higher or Lower

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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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

// https://code.dennyzhang.com/guess-number-higher-or-lower-ii // Basic Ideas: Dynamic Programming // // f(i, j) -> money we need to gurantee a win for the range of [i, j] // We will have to start by picking one, let's say it's k. // Then the cost is: k + max(f(i, k-1), f(k+1, j)) // // From bottom to up, from left to right, we can get f(1, n) // Complexity: Time O(n*n*n), Space O(n^2) func getMoneyAmount(n int) int { dp := make([][]int, n+1) for i:=0; i<n+1; i++ { dp[i] = make([]int, n+1) } for i:=n-1; i>=1; i-- { // Range of i:j for j := i+1; j<=n; j++ { cost, mincost := 0, 1<<31 - 1 for k:=i; k<=j; k++ { cost = k r1, r2 := 0, 0 if k!=i { r1 = dp[i][k-1] } if k!=j { r2 = dp[k+1][j] } if r1 > r2 { cost += r1 } else { cost += r2 } if mincost > cost { mincost = cost } } dp[i][j] = mincost } } return dp[1][n] }