LeetCode-in-All

55. Jump Game

Medium

You are given an integer array nums. You are initially positioned at the array’s first index, and each element in the array represents your maximum jump length at that position.

Return true if you can reach the last index, or false otherwise.

Example 1:

Input: nums = [2,3,1,1,4]

Output: true

Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 2:

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

Output: false

Explanation: You will always arrive at index 3 no matter what. Its maximum jump length is 0, which makes it impossible to reach the last index.

Constraints:

To solve the “Jump Game” problem, you can follow these steps:

  1. Initialize Variables: Start by initializing a variable max_reach to store the maximum reachable index. Initially, set max_reach to 0, as you are at the first index.

  2. Iterate through the Array: Traverse through the array nums starting from index 0 to n-1, where n is the length of the array.

  3. Update Maximum Reach: At each index i, update max_reach to be the maximum of max_reach and i + nums[i]. This indicates the farthest index you can reach from the current position i.

  4. Check for End Reachability: While traversing the array, if at any point max_reach becomes greater than or equal to the last index (i.e., n - 1), return True, indicating that you can reach the end of the array.

  5. Handle Zero Reach: If the current index i is greater than max_reach, it means you cannot progress further, and thus, return False.

  6. Return Result: After iterating through the entire array, if you haven’t reached the end of the array, return False, as you cannot reach the last index.

Here’s a Python function implementing the above steps:

from typing import List

class Solution:
    def canJump(self, nums: List[int]) -> bool:
        max_reach = 0
        n = len(nums)
        
        for i in range(n):
            if i > max_reach:
                return False
            max_reach = max(max_reach, i + nums[i])
            if max_reach >= n - 1:
                return True
        
        return False

# Example usage:
nums1 = [2, 3, 1, 1, 4]
nums2 = [3, 2, 1, 0, 4]

sol = Solution()
print(sol.canJump(nums1))  # Output: True
print(sol.canJump(nums2))  # Output: False

You can then test this function with different input arrays to verify its correctness.

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