How do you solve the Jump Game? | Interview Question

Q: How do you solve the Jump Game?

**Target Audience:** Beginners preparing for coding interviews — you should know lists, loops and functions in Python; everything else is explained. **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged `📌 Interview term:` with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output in the **Verified** section is copied from that run. ## 1. Why This Even Matters — A Story First A row of stepping stones crosses a river. Painted on each stone is a number: the longest jump you can make from that stone (you may always jump shorter). You start on the first stone. Can you reach the last one? With stones `2 3 1 1 4` it is easy: jump 1 to the "3", then 3 to the end. With stones `3 2 1 0 4` you are stuck — every route lands on the "0" and the "4" is

The problem

Question presented to candidate: "You are given a list of non-negative integers. You start at index 0, and each value is the maximum jump length from that position. Write a Python function that returns whether you can reach the last index."

What a strong answer should cover:

The key observation: shorter jumps are allowed, so the reachable indices always form a prefix, and one number — the farthest reach — describes them.
The one-pass greedy: return false as soon as i > farthest, otherwise update farthest = max(farthest, i + nums[i]); O(n) time, O(1) space.
A correctness argument (the prefix / loop-invariant argument), not just the code.
The slower alternatives and why they lose: recursion (exponential) and the good[] DP (O(n²)).
Python details: enumerate(nums) for index and value together, an early return True once the end is covered, and avoiding recursion because of the default recursion limit.
The Jump Game II follow-up (fewest jumps) as BFS levels.

Clarifying questions expected:

Is each value the maximum jump (shorter jumps allowed)?
Do you want only yes/no, or the fewest jumps?

Code / implementation expected: Yes — can_jump(nums) -> bool in Python 3, one pass.

dsa
greedy
arrays

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Beginners preparing for coding interviews — you should know lists, loops and functions in Python; everything else is explained.
Difficulty: Medium
Language: Python 3

How to read this doc: every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged 📌 Interview term: with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output in the Verified section is copied from that run.

1. Why This Even Matters — A Story First

A row of stepping stones crosses a river. Painted on each stone is a number: the longest jump you can make from that stone (you may always jump shorter). You start on the first stone. Can you reach the last one?

With stones 2 3 1 1 4 it is easy: jump 1 to the "3", the

The solution is hidden so you can try first

14 min read · 12 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonGreedy farthest-reach check (9 inputs)

Practice

PythonGreedy vs DP vs backward greedy: 2,000 random arrays and work counts

Practice

PythonFollow-up: Jump Game II (fewest jumps)

Practice

Discussion

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