Jump Game: Can You Reach the End?
You are given a list of non-negative integers representing jump lengths. Starting at the first index, your goal is to determine if you can reach the last index of the list. This problem is a classic example of greedy algorithms and dynamic programming, frequently encountered in coding interviews to assess problem-solving and algorithmic thinking.
Problem Description
You are provided with an array, nums, where each element nums[i] represents the maximum jump length from index i. You begin at the first index (index 0). The task is to determine whether it's possible to reach the very last index of the array.
Key Requirements:
- You must start at index 0.
- From index
i, you can jump to any indexjsuch thati <= j <= i + nums[i]. - The objective is to reach the last index.
Expected Behavior:
- If you can reach the last index, return
true. - If you cannot reach the last index, return
false.
Edge Cases to Consider:
- An array with only one element.
- An array where the first element is 0, and the array has more than one element.
- Cases where you can jump beyond the last index.
Examples
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.
Example 3:
Input: nums = [0]
Output: true
Explanation: The array has only one element, so you are already at the last index.
Example 4:
Input: nums = [1, 0, 1, 0, 1]
Output: false
Explanation: From index 0, you can reach index 1. From index 1, you can only reach index 1 (max jump 0). You cannot progress further.
Constraints
1 <= nums.length <= 10^40 <= nums[i] <= 10^5- The problem should ideally be solved with a time complexity of O(n) and a space complexity of O(1).
Notes
Consider how you can keep track of the furthest index you can reach. This greedy approach can be very efficient. Think about what information you need to maintain as you iterate through the array.