The Question

Jump Game Reachability

Given an array of non-negative integers where each element represents your maximum jump distance from that position, write a function to determine if you can successfully travel from the start of the array to the final index.

Java

Greedy

Array

Questions & Insights

Clarifying Questions

What is the maximum possible length of the nums array? (Assumption: up to

10^4

10^5

, requiring a linear or near-linear time complexity).

Are there any negative integers in the array? (Assumption: No, the problem states "maximum jump length", which implies non-negative values).

How should we handle an array with only one element? (Assumption: If the array has one element, we are already at the last index, so the result should be true).

Is there a time limit for the execution? (Assumption: Standard competitive programming limits, usually 1-2 seconds).

Thinking Process

Greedy Strategy: Instead of exploring all possible jump combinations (which would be exponential or

O(N^2)

with dynamic programming), we only need to track the furthest reachable index at any point in time.

Reachability Check: Iterate through the array. For every index

i

f s greater than the maximum index we have reached so far, it means we've hit a gap we cannot cross, and we should return false.

Updating Maximum: At each index

i

that is reachable, update the maximum reachable index to be the maximum of its current value and

i + nums[i]

Early Exit: If the maximum reachable index ever meets or exceeds the last index of the array, we can immediately return true.

Implementation Breakdown

Problem Set

Functional Requirement: Return a boolean indicating if the last index is reachable from the first index.

Constraints:

1 <= nums.length <= 10^4

0 <= nums[i] <= 10^5

Edge Cases:

nums.length == 1: Always true.

nums[0] == 0 and nums.length > 1: Always false.

Large jumps that skip most of the array.

Approach

Algorithm: Greedy Reachability

Data Structure: None (Scalar variables)

Complexity:

Time:

O(N)

where

N

is the length of the array.

Space:

O(1)

as we only store one integer variable.