Leetcode 1340. Jump Game V

文章作者：Tyan
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1. Description

Jump Game V

2. Solution

解析：Version 1，采用深度优先搜索，使用visited记录遍历过的索引及对应的跳跃次数，如果当前索引遍历过，直接返回对应的跳跃次数，分别遍历其左右两侧，取左右两侧最大的跳跃次数，返回最大跳跃次数加上当前元素的跳跃次数1。Version 2对数组先排序，获得排序后的索引，然后从最小值的索引开始寻找左右两侧最大跳跃次数，这样每个数左右两侧比其小的数的跳跃次数都已计算出来，所有元素的初始默认跳跃次数为1，依次更新dp[current]，最后返回最大跳跃次数。

• Version 1

class Solution:
    def maxJumps(self, arr: List[int], d: int) -> int:
        stat = {}
        n = len(arr)
        visited = {}
        nums = 0
        for i in range(n):
            nums = max(nums, self.dfs(arr, i, visited, d))
        return nums


    def dfs(self, arr, current, visited, d):
        if current in visited:
            return visited[current]
        n = len(arr)
        count = 0
        i = current - 1
        thres = max(-1, current - d - 1)
        while i > thres and arr[i] < arr[current]:
            temp = self.dfs(arr, i, visited, d)
            visited[i] = temp
            count = max(count, temp)
            i -= 1
        i = current + 1
        thres = min(n, current + d + 1)
        while i <  thres and arr[i] < arr[current]:
            temp = self.dfs(arr, i, visited, d)
            visited[i] = temp
            count = max(count, temp)
            i += 1
        return count + 1

• Version 2

class Solution:
    def maxJumps(self, arr: List[int], d: int) -> int:
        indexes = sorted(range(len(arr)), key=lambda i: arr[i])
        n = len(arr)
        dp = [1] * n
        nums = 0
        for current in indexes:
            i = current - 1
            thres = max(-1, current - d - 1)
            count = 0
            while i > thres and arr[i] < arr[current]:
                count = max(count, dp[i])
                i -= 1
            i = current + 1
            thres = min(n, current + d + 1)
            while i < thres and arr[i] < arr[current]:
                count = max(count, dp[i])
                i += 1
            dp[current] += count
            nums = max(nums, dp[current])
        return nums

Reference

1. https://leetcode.com/problems/jump-game-v/