45-jump-game-ii.py

"""
45. Jump Game II
Medium - 42.0%

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]
- 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
"""

from typing import List

class Solution:
    def jump(self, nums: List[int]) -> int:
        n = len(nums)
        if n <= 1:
            return 0
        
        jumps = 0
        current_end = 0
        farthest = 0
        
        # We don't need to jump from the last index
        for i in range(n - 1):
            # Update the farthest point we can reach
            farthest = max(farthest, i + nums[i])
            
            # If we've reached the end of current jump range
            if i == current_end:
                jumps += 1
                current_end = farthest
                
                # If we can already reach the end, break
                if current_end >= n - 1:
                    break
        
        return jumps