Jump Game Problem in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Jump Game Reachability Check

What is the output of this TypeScript code that checks if you can jump to the last index?

DSA Typescript

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]));

A SyntaxError

B false

C true

D TypeError

💡 Hint

Think about whether the jumps allow reaching the last index.

The function tracks the furthest index reachable. Since the input allows jumps to the end, it returns true.

❓ Predict Output

intermediate

Output when jump is blocked early

What does this code print when the jump is blocked early?

DSA Typescript

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([3,2,1,0,4]));

A false

B true

C RangeError

D undefined

💡 Hint

Check if the zero blocks further progress.

The zero at index 3 blocks reaching index 4, so the function returns false.

🔧 Debug

advanced

Identify the error in jump game code

What error does this code produce when run?

DSA Typescript

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]));

A SyntaxError

B TypeError: Cannot read property 'undefined' of undefined

C RangeError: Maximum call stack size exceeded

D No error, outputs true

💡 Hint

Check the loop boundary and array access.

The loop goes one index too far (i <= nums.length), accessing nums[nums.length] which is undefined. This leads to NaN in the maxReach calculation (since Math.max with NaN returns NaN), and attempting to access nums[i] when i is out of bounds causes a TypeError.

🧠 Conceptual

advanced

Minimum jumps to reach the end

Given an array where each element represents max jump length at that position, what is the minimum number of jumps to reach the last index for [2,3,1,1,4]?

A 2

B 3

C 4

D 1

💡 Hint

Try to jump the farthest possible at each step.

Jump from index 0 to 1, then from 1 to 4, total 2 jumps.

🚀 Application

expert

Output of jump game with zero at start

What is the output of this code when the first element is zero?

DSA Typescript

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([0,1,2]));

A true

B IndexError

C SyntaxError

D false

💡 Hint

If you cannot move from the start, you cannot reach the end.

Since the first element is zero, you cannot move anywhere, so the function returns false.

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