Jump Game Problem in DSA Typescript - Build from Scratch

Jump Game Problem

📖 Scenario: Imagine you are playing a video game where you need to jump across platforms to reach the end. Each platform lets you jump a certain maximum number of steps forward. You want to check if it is possible to reach the last platform starting from the first one.

🎯 Goal: Build a program that checks if you can jump from the first platform to the last platform using the maximum jump lengths given for each platform.

📋 What You'll Learn

Create an array called platforms with exact values representing maximum jump lengths.

Create a variable called maxReach to track the farthest platform reachable.

Use a for loop with variable i to iterate over platforms and update maxReach.

Print "Can reach the last platform" if the last platform is reachable, otherwise print "Cannot reach the last platform".

💡 Why This Matters

🌍 Real World

This problem models situations where you need to check if a path or sequence of steps is possible given constraints, such as in games, robotics, or network routing.

💼 Career

Understanding this problem helps in software engineering roles that involve algorithmic thinking, problem solving, and optimization.

1

Create the platforms array

Create an array called platforms with these exact values: [3, 2, 1, 0, 4] representing the maximum jump lengths from each platform.

DSA Typescript

# Your code here

Hint

Use const platforms = [3, 2, 1, 0, 4]; to create the array.

2

Create maxReach variable

Create a variable called maxReach and set it to 0 to track the farthest platform reachable.

DSA Typescript

const platforms = [3, 2, 1, 0, 4];
# Your code here

Hint

Use let maxReach = 0; to create the variable.

3

Implement the jump logic

Use a for loop with variable i to iterate over platforms. Inside the loop, check if i is greater than maxReach. If yes, break the loop. Otherwise, update maxReach to the maximum of maxReach and i + platforms[i].

DSA Typescript

const platforms = [3, 2, 1, 0, 4];
let maxReach = 0;
# Your code here

Hint

Use a for loop and update maxReach inside it. Stop if current index is beyond maxReach.

4

Print if last platform is reachable

Print "Can reach the last platform" if maxReach is greater than or equal to platforms.length - 1. Otherwise, print "Cannot reach the last platform".

DSA Typescript

const platforms = [3, 2, 1, 0, 4];
let maxReach = 0;
for (let i = 0; i  maxReach) {
        break;
    }
    maxReach = Math.max(maxReach, i + platforms[i]);
}
# Your code here

Hint

Use an if statement to compare maxReach with platforms.length - 1 and print the correct message.

Practice

1. What does the Jump Game problem ask you to determine given an array of non-negative integers?

easy

A. If you can reach the last index starting from the first index by jumping according to the values.

B. The maximum jump length you can make from any position in the array.

C. The minimum number of jumps needed to reach the last index.

D. The sum of all jump lengths in the array.

Solution

1. Step 1: Understand the problem statement

   The Jump Game problem asks if you can start at the first index and reach the last index by jumping forward using the numbers in the array as maximum jump lengths.

2. Step 2: Identify the key goal

   The goal is to check if the last index is reachable, not the number of jumps or sums.

3. Final Answer:

   If you can reach the last index starting from the first index by jumping according to the values. -> Option A

4. Quick Check:

   Jump Game = Reach last index? [OK]

Hint: Focus on reachability, not jump counts or sums [OK]

Common Mistakes:

• Confusing reachability with minimum jumps needed
• Thinking the problem asks for maximum jump length
• Assuming sum of jumps is the answer

2. Which of the following TypeScript function signatures correctly represents a function solving the Jump Game problem?

easy

A. function canJump(nums: number[]): boolean

B. function canJump(nums: number): number[]

C. function canJump(nums: string[]): boolean

D. function canJump(nums: number[][]): boolean

Solution

1. Step 1: Analyze the input and output types

   The input is an array of numbers representing jump lengths, so type is number[]. The output is a boolean indicating if last index is reachable.

2. Step 2: Match the function signature

   function canJump(nums: number[]): boolean matches input type number[] and output boolean, which fits the problem.

3. Final Answer:

   function canJump(nums: number[]): boolean -> Option A

4. Quick Check:

   Input array, output boolean = function canJump(nums: number[]): boolean [OK]

Hint: Input array of numbers, output boolean for reachability [OK]

Common Mistakes:

• Using wrong input types like string or 2D arrays
• Returning array instead of boolean
• Incorrect function parameter types

3. What is the output of the following TypeScript code?

function canJump(nums: number[]): boolean {
  let maxReach = 0;
  for (let i = 0; i < nums.length; i++) {
    if (i > maxReach) return false;
    maxReach = Math.max(maxReach, i + nums[i]);
  }
  return true;
}

console.log(canJump([2,3,1,1,4]));

medium

A. Runtime error

B. false

C. undefined

D. true

Solution

1. Step 1: Trace the loop and maxReach updates

   Start maxReach=0. i=0: maxReach=max(0,0+2)=2; i=1: 1<=2, maxReach=max(2,1+3)=4; i=2: 2<=4, maxReach=max(4,2+1)=4; i=3: 3<=4, maxReach=max(4,3+1)=4; i=4: 4<=4, maxReach=max(4,4+4)=8.

2. Step 2: Check if loop completes without returning false

   Since i never exceeds maxReach, loop completes and returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   All indices reachable, so true [OK]

Hint: Check if current index exceeds max reachable index [OK]

Common Mistakes:

• Not updating maxReach correctly
• Returning false too early
• Confusing output with minimum jumps

4. Identify the bug in this TypeScript code for the Jump Game problem:

function canJump(nums: number[]): boolean {
  let maxReach = 0;
  for (let i = 0; i <= nums.length; i++) {
    if (i > maxReach) return false;
    maxReach = Math.max(maxReach, i + nums[i]);
  }
  return true;
}

medium

A. The return type should be number, not boolean.

B. The loop condition should be i < nums.length, not i <= nums.length.

C. maxReach should be initialized to 1 instead of 0.

D. The function should return false at the end instead of true.

Solution

1. Step 1: Check loop boundary conditions

   The loop runs from i=0 to i <= nums.length, which means it accesses nums[nums.length] causing undefined access.

2. Step 2: Correct the loop condition

   Changing to i < nums.length prevents out-of-bounds access and fixes the bug.

3. Final Answer:

   The loop condition should be i < nums.length, not i <= nums.length. -> Option B

4. Quick Check:

   Loop index must stay within array bounds [OK]

Hint: Loop index must be less than array length [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Ignoring out-of-bounds array access
• Incorrect initialization of maxReach

5. Given the array [3,2,1,0,4], why does the standard greedy Jump Game algorithm return false?

hard

A. Because the array length is less than 5, so it always returns false.

B. Because the maximum jump length at index 0 is too large.

C. Because the zero at index 3 blocks any further jumps, making the last index unreachable.

D. Because the algorithm only checks the first two elements.

Solution

1. Step 1: Analyze jump reachability step-by-step

   Start maxReach=0. i=0: maxReach=max(0,0+3)=3; i=1: 1<=3, maxReach=max(3,1+2)=3; i=2: 2<=3, maxReach=max(3,2+1)=3; i=3: 3<=3, maxReach=max(3,3+0)=3; i=4: 4>3, return false.

2. Step 2: Understand why last index is unreachable

   The zero at index 3 prevents extending maxReach beyond 3, so index 4 cannot be reached.

3. Final Answer:

   Because the zero at index 3 blocks any further jumps, making the last index unreachable. -> Option C

4. Quick Check:

   Zero jump blocks progress = false [OK]

Hint: Zeros can block progress if maxReach can't pass them [OK]

Common Mistakes:

• Ignoring zeros that block jumps
• Assuming array length affects result
• Misunderstanding maxReach updates