Jump Game

Problem

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.

Examples

The brute-force approach

Use DFS/BFS from index 0. Try all possible jump lengths from each reachable position. Mark positions visited to avoid infinite loops.

reachable = {0}
while reachable:
    pos = reachable.pop()
    for jump in range(1, nums[pos] + 1):
        next_pos = pos + jump
        if next_pos >= last_index: return True
        reachable.add(next_pos)
return False

O(n²) in the worst case — each position tries all jump lengths, potentially re-exploring many positions.

Spotting the pattern

This is a Greedy problem. The key question to ask yourself:

At each position, what's the only thing you need to know to decide whether you can keep going?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.