0045-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].

Solution(Python)¶

class Solution:
    def jump(self, nums: List[int]) -> int:
        #  nums = [2,3,1,1,4]
        #     i : jump  i +j ; o<= j <= nums[i] i + j <=n
        #    Goal minimum number of jumps to reach index n-1 
        #   
        # nums =  [2,3,1,1,4]
        #    i =   0 1 2 3 4
        #  
        #  i = 0  possible ->  0 1 2 
        #    Can index 4 be reached directly from index 0?
        #  
        #  fathest possible jump from current location and current end
        #   jumpss =0
        #    farthest = 0
        #  curEnd = 0
        #
        jumps = 0
        farthest = 0
        currentEnd = 0
        n = len(nums)

        for i in range(n-1):
            farthest = max(farthest, i + nums[i])
            
            if i == currentEnd:
                jumps+=1
                currentEnd = farthest
        return jumps
        