Guess Number Higher or Lower II — LeetCode 375 Python Solution

The problem

We are playing the Guessing Game. The game will work as follows: I pick a number between 1 and n.

Example

Input

n = 10

Output

16

Explanation

The winning strategy is as follows:

Python solution

class Solution:
    def getMoneyAmount(self, n: int) -> int:
        f = [[0] * (n + 1) for _ in range(n + 1)]
        for i in range(n - 1, 0, -1):
            for j in range(i + 1, n + 1):
                f[i][j] = j + f[i][j - 1]
                for k in range(i, j):
                    f[i][j] = min(f[i][j], max(f[i][k - 1], f[k + 1][j]) + k)
        return f[1][n]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 375. Guess Number Higher or Lower II is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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