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The Question
Coding

Jump Game I

You are given an integer array nums representing the maximum jump length from each position. Starting at the first index, determine if you can reach the last index of the array. Each element nums[i] indicates that from index i, you can jump to any index j where i <= j <= i + nums[i]. Return true if the last index is reachable, and false otherwise. Constraints: - 1 <= nums.length <= 10^4 - 0 <= nums[i] <= 10^5
Java
Greedy
Questions & Insights

Clarifying Questions

What is the maximum size of the input array? (Assumption: Up to 10^5, requiring a linear O(n) solution).
Can the values in `nums` be negative? (Assumption: No, jump lengths are non-negative integers).
What should be returned for an array of size 1? (Assumption: True, as you are already at the last index).
Are there any specific time or space complexity constraints? (Assumption: O(n) time and O(1) space are expected for an optimal solution).

Thinking Process

Greedy Strategy: Instead of exploring all possible jump paths (which would be exponential or O(n^2) with DP), we only need to track the furthest index reachable at any given point.
Reachability Check: As we iterate through the array, if the current index is greater than the maximum reachable index we have calculated so far, it means this point is unreachable, and thus the end is unreachable.
Update Logic: For every reachable index i, the new potential furthest reach is i + nums[i]. We update our global maxReach with this value if it's larger.
Early Exit: If at any point maxReach meets or exceeds the last index of the array, we can immediately return true.
Implementation Breakdown

Problem Set

Functional Requirement: Given an array of non-negative integers, determine if the last index is reachable starting from index 0.
Constraints:
Time Complexity: O(n)
Space Complexity: O(1)
Input size n up to 10^5.

Approach

Algorithm: Greedy
Data Structure: None (Scalar variables)
Complexity:
Time: O(n) where n is the length of the array.
Space: O(1) as we only store a single integer.

Implementation

Wrap Up

Advanced Topics

Dynamic Programming Perspective: This problem can be solved with DP in O(n^2) by marking reachable indices in a boolean array. The Greedy approach is an optimization of this DP where we realize we only care about the rightmost reachable boundary.
Backward Iteration: One could also solve this by starting from the last index and keeping track of the "last known position" that can reach the end. If at the end of the loop the last known position is 0, the answer is true.
Parallelization: While this specific problem is inherently sequential (each step depends on the reach of the previous), for massive datasets, one could partition the array and use a segment-tree like approach to find max jumps in ranges, though this would increase complexity to O(n \log n).