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Jump Game LC #55 Medium Greedy · Max Reach
Problem

You are given an integer array nums. You start at index 0, and each element represents your maximum jump length from 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 from index 0→1, then 3 steps to the end.
Example 2
Input: nums = [3,2,1,0,4]
Output: false
Explanation: Always stuck at index 3 (nums[3]=0, can't move forward).
Constraints: 1 ≤ nums.length ≤ 10⁴  |  0 ≤ nums[i] ≤ 10⁵
Try Examples
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Approach
Greedy — Track the Farthest Reachable Index
Scan left→right: at each index, extend maxReach. If you ever stand beyond maxReach, you're permanently stuck — return false.
Jump Arena
Variables
Index i
—
nums[i]
—
i + nums[i]
—
maxReach
0
Step Logic
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Algorithm
1
Init maxReach = 0 (furthest index reachable so far)
2
If i > maxReach: index unreachable → return false
3
Update maxReach = max(maxReach, i + nums[i])
4
Processed all indices without getting stuck → return true
Time
O(n)
Space
O(1)
Why Greedy Works

We never need to track exact jump paths. All we care about is the farthest index reachable from any position visited so far. If index i is within that range, we can reach it — and from it, potentially push the frontier further. The moment i exceeds our frontier, no combination of earlier jumps can save us.

How to solve Jump Game

LeetCode 55 · Medium · Greedy · Pattern: Greedy Reach

Why the obvious approach is slow

Trying every possible jump from every index explodes, and even dynamic programming is O(n²). We only need to know the farthest index we can reach.

The key idea

Keep a variable, far, for the farthest reachable index so far. At each index, if i is beyond far, we are stuck, so return false. Otherwise update far with i plus the jump length, and return true once far reaches the end.

Remember

Track only the farthest reachable index. If you ever stand beyond it, you are stuck.

Run the animation above on your own input, or watch the 1:18 video explanation of Jump Game with a dry run and Java code.

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