45. Jump Game II

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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

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

  • 0 <= j <= nums[i] and
  • i + j < n

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

🧠 Thuật Toán & Kỹ Thuật

Dynamic Programming (Quy hoạch động)
⏱️ Thời gian O(n)
💾 Không gian O(n)

💻 Lời Giải

Python 0045-jump-game-ii.py 
class Solution:
    def jump(self, nums: List[int]) -> int:
        n = len(nums)
        
        @cache
        def dp(i: int) -> int:
            if i >= n - 1:
                return 0
            minJump = 10001
            for j in range(1, nums[i] + 1):
                minJump = min(minJump, 1 + dp(i + j))
            return minJump
            
        return dp(0)