Race Car — LeetCode 818 Python Solution

The problem

Your car starts at position 0 and speed +1 on an infinite number line. Your car can go into negative positions.

Example

Input

target = 3

Output

2

Explanation

The shortest instruction sequence is "AA".

Python solution

class Solution:
    def racecar(self, target: int) -> int:
        dp = [0] * (target + 1)
        for i in range(1, target + 1):
            k = i.bit_length()
            if i == 2**k - 1:
                dp[i] = k
                continue
            dp[i] = dp[2**k - 1 - i] + k + 1
            for j in range(k - 1):
                dp[i] = min(dp[i], dp[i - (2 ** (k - 1) - 2**j)] + k - 1 + j + 2)
        return dp[target]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 818. Race Car 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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