How Do You Solve the Jump Game?

When preparing for a tech interview, understanding classic problems like the Jump Game is essential. Many interviewers ask about this problem because it tests your ability to handle greedy algorithms, dynamic programming, and array traversal techniques. In this article, I will explain what the Jump Game problem is, how to approach it, and will include clear code examples for solving it efficiently.

What Is the Jump Game?

The Jump Game is a common coding problem that appears in coding interviews. The problem usually states something like this: You are given an array of non-negative integers, where each element represents your maximum jump length from that position. Your goal is to determine if you can reach the last index starting from the first index.

Example

Imagine the array: [2, 3, 1, 1, 4]

• Starting at index 0 with value 2, you can jump to either index 1 or index 2.
• If you jump to index 1 (value 3), you can reach index 4 (value 4).
• Since index 4 is the last position, you can reach the end.

In this case, the answer is true. But for the array [3, 2, 1, 0, 4], no matter how you jump, you will get stuck at index 3 because its value is 0, preventing further moves. The answer here is false.

Approaches to Solve Jump Game

There are several ways to determine whether you can reach the last index. Two common approaches are:

1. Greedy Approach

This approach is efficient and easy to implement. It involves keeping track of the furthest index you can reach as you traverse the array. If at any step, the current index exceeds the maximum reachable index so far, it means you cannot progress further.

2. Dynamic Programming

This method uses bottom-up or top-down strategies to remember whether specific positions are reachable. While it’s easier to understand, it can be less efficient compared to the greedy approach for large arrays.

Below, I will focus on the greedy approach, which is commonly used in interviews because of its simplicity and performance.

Greedy Solution - Step By Step

The core idea is to start from the first position, keep updating the maximum reachable index, and verify if you can reach or surpass the last index.

Implementation

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Explanation of the Code

• We initialize max_reachable to 0 because the furthest position we can reach initially is the first element.
• We iterate through each position in the array.
• For each position i, we check if i exceeds max_reachable. If it does, it means we cannot reach the current position, and thus can't reach the end.
• If we can reach i, we update max_reachable to be the furthest position we can reach from the current position, which is i + nums[i].
• If at any point max_reachable is at or beyond the last index (n - 1), we conclude it's possible to reach the end and return True.

How It Works

This approach effectively simulates the process of jumping through the array, always extending the furthest point we can reach so far. It stops early if it finds it’s impossible to progress further.

Test the Example

PythonCopy code

The Jump Game problem is straightforward once you understand the greedy technique: track the furthest index reachable, update it at each step, and determine if you can make it to the last position. This solution runs in linear time (O(n)) and only requires constant space (O(1)), making it ideal for large input arrays often encountered in interviews.