45. Jump Game II

Description

You are given a 0-indexed array of integers nums of length n. You are initially positioned at index 0.

Each element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at index i, you can jump to any index (i + j) where:

• 0 <= j <= nums[i] and
• i + j < n

Return the minimum number of jumps to reach index n - 1. The test cases are generated such that you can reach index n - 1.

Example 1:

• Input: nums = [2,3,1,1,4]
• Output: 2
• Explanation: The minimum number of jumps to reach the last index is 2. Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 2:

• Input: nums = [2,3,0,1,4]
• Output: 2

Constraints:

• 1 <= nums.length <= 10⁴
• 0 <= nums[i] <= 1000
• It’s guaranteed that you can reach nums[n - 1].

Submitted Code

class Solution:
    def jump(self, nums: List[int]) -> int:
        n = len(nums)
        jumps, curr_end, max_dist = 0, 0, 0

        for i in range(n-1):
            max_dist = max(max_dist, (i + nums[i])) # 다음 범위에서 갈 수 있는 최대 거리 갱신
            if i == curr_end:                       # 현재 범위를 넘어갈 때 점프 횟수 +1
                jumps += 1
                curr_end = max_dist

        return jumps

Runtime: 3 ms | Beats 88.70%
Memory: 20.11 MB | Beats 49.61%

현재 범위 안에 있는 노드들로 다음 범위에서 갈 수 있는 최대 거리를 계산하는 방법이다.

Other Solutions

1st

class Solution:
    def jump(self, nums: List[int]) -> int:
        near = far = jumps = 0

        while far < len(nums) - 1:
            farthest = 0
            for i in range(near, far + 1):
                farthest = max(farthest, i + nums[i])
            
            near = far + 1
            far = farthest
            jumps += 1
        
        return jumps

time complexity: 𝑂(𝑛)
space complexity: 𝑂(1)

2nd

class Solution:
    def jump(self, nums):
        if len(nums) <= 1: return 0
        l, r = 0, nums[0]
        times = 1
        while r < len(nums) - 1:
            times += 1
            nxt = max(i + nums[i] for i in range(l, r + 1))
            l, r = r, nxt
        return times