Coin Path — LeetCode 656 Python Solution

The problem

You are given an integer array coins (1-indexed) of length n and an integer maxJump. You can jump to any index i of the array coins if coins[i] != -1 and you have to pay coins[i] when you visit index i.

Example

Input

coins = [1,2,4,-1,2], maxJump = 2

Output

[1,3,5]

Python solution

class Solution:
    def cheapestJump(self, coins: List[int], maxJump: int) -> List[int]:
        if coins[-1] == -1:
            return []
        n = len(coins)
        f = [inf] * n
        f[-1] = coins[-1]
        for i in range(n - 2, -1, -1):
            if coins[i] != -1:
                for j in range(i + 1, min(n, i + maxJump + 1)):
                    if f[i] > f[j] + coins[i]:
                        f[i] = f[j] + coins[i]
        if f[0] == inf:
            return []
        ans = []
        s = f[0]
        for i in range(n):
            if f[i] == s:
                s -= coins[i]
                ans.append(i + 1)
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 656. Coin Path 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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