Jump Game Problem in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the array is empty and return true.

DSA Typescript

function canJump(nums: number[]): boolean {
  if (nums.length [1] 0) return true;
  // rest of the code
}

Drag options to blanks, or click blank then click option'

A===

B==

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using assignment operator '=' instead of comparison.

Using '<' or '>' which do not check for equality.

We use strict equality === to check if the length is exactly zero.

2fill in blank

medium

Complete the code to initialize the farthest reachable index.

DSA Typescript

function canJump(nums: number[]): boolean {
  let farthest = [1];
  // rest of the code
}

Drag options to blanks, or click blank then click option'

A1

B-1

Cnums[0]

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing farthest to nums[0] which is a jump length, not an index.

Starting farthest at 1 which skips the first index.

We start from index 0, so the farthest reachable index initially is 0.

3fill in blank

hard

Fix the error in the loop condition to iterate through the array correctly.

DSA Typescript

for (let i = 0; i [1] nums.length; i++) {
  // loop body
}

Drag options to blanks, or click blank then click option'

A<

B>=

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<=' causes index out of bounds error.

Using '>' or '>=' causes the loop to never run.

The loop should run while i is less than nums.length to avoid going out of bounds.

4fill in blank

hard

Fill both blanks to update the farthest reachable index and check if current index is reachable.

DSA Typescript

if (i [1] farthest) {
  farthest = Math.max(farthest, i [2] nums[i]);
}

Drag options to blanks, or click blank then click option'

A<=

B<

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '<=' causes skipping reachable positions.

Using '-' instead of '+' causes wrong farthest calculation.

We check if i is less than or equal to farthest to ensure the position is reachable. Then update farthest by adding nums[i] to i.

5fill in blank

hard

Fill all three blanks to return true if the last index is reachable, otherwise false.

DSA Typescript

return farthest [1]= nums.length [2] 1;

// or

return farthest [3] nums.length - 1;

Drag options to blanks, or click blank then click option'

A>

B>=

C==

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using == which only works if exactly at last index.

Using > which misses the case when farthest equals last index.

We return true if farthest is greater than or equal to the last index (nums.length - 1). The second return uses less than to return false if not reachable.

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