Jump Game Problem in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Jump Game problem?

To determine if you can reach the last index of an array starting from the first index, where each element represents the maximum jump length from that position.

beginner

In the Jump Game problem, what does each element in the input array represent?

Each element represents the maximum number of steps you can jump forward from that position.

intermediate

What is a greedy approach to solve the Jump Game problem?

Keep track of the farthest reachable index while iterating through the array. If at any point the current index is beyond the farthest reachable, return false. If you can reach or pass the last index, return true.

intermediate

Why does the greedy approach work for the Jump Game problem?

Because at each step, choosing the farthest reachable position ensures you don't miss any possible path to the end, making it efficient and correct.

beginner

What is the time complexity of the greedy solution for the Jump Game problem?

O(n), where n is the length of the input array, because it requires a single pass through the array.

In the Jump Game problem, what does a zero in the array mean?

A You cannot jump forward from that position

B You must jump exactly zero steps

C You can jump any number of steps

D You must jump backward

A zero means you cannot move forward from that position, which might block progress if you land there.

What should you do if the current index is greater than the farthest reachable index in the greedy approach?

A Return true immediately

B Continue iterating

C Return false immediately

D Reset the farthest reachable index

If the current index is beyond the farthest reachable, it means you cannot move forward to this position, so return false.

What is the initial value of the farthest reachable index in the greedy solution?

A -1

B 1

C Length of the array

D 0

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

Which of these arrays can you reach the last index from the first index? [2,3,1,1,4]

A Only if you jump backward

B Yes

C No

D Only if you skip elements

You can jump from index 0 to 1 (max 2 steps), then from 1 to the last index.

What is the space complexity of the greedy solution for the Jump Game problem?

A O(1)

B O(n)

C O(log n)

D O(n^2)

The greedy solution uses only a few variables, so space complexity is constant O(1).

Explain how the greedy algorithm solves the Jump Game problem step-by-step.

Think about tracking the farthest point you can jump to as you move forward.

Describe a scenario where you cannot reach the last index in the Jump Game problem.

Imagine landing on a spot where you cannot jump forward anymore.

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