Jump Game Problem in DSA Java - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Jump Game Reachability Check

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

DSA Java

public class JumpGame {
    public static boolean canJump(int[] nums) {
        int maxReach = 0;
        for (int i = 0; i < nums.length; i++) {
            if (i > maxReach) return false;
            maxReach = Math.max(maxReach, i + nums[i]);
        }
        return true;
    }

    public static void main(String[] args) {
        int[] nums = {2,3,1,1,4};
        System.out.println(canJump(nums));
    }
}

A false

B true

C Compilation error

D Runtime exception

💡 Hint

Trace the maximum reachable index as you iterate through the array.

The code checks if the current index is reachable. Since maxReach updates to cover the last index, the output is true.

❓ Predict Output

intermediate

Output of Jump Game with Unreachable Last Index

What will the following Java code print when the last index is not reachable?

DSA Java

public class JumpGame {
    public static boolean canJump(int[] nums) {
        int maxReach = 0;
        for (int i = 0; i < nums.length; i++) {
            if (i > maxReach) return false;
            maxReach = Math.max(maxReach, i + nums[i]);
        }
        return true;
    }

    public static void main(String[] args) {
        int[] nums = {3,2,1,0,4};
        System.out.println(canJump(nums));
    }
}

A false

B Runtime exception

C Compilation error

D true

💡 Hint

Check if the loop breaks early due to an unreachable index.

At index 3, maxReach is 3 but nums[3] is 0, so maxReach does not advance beyond 3, making index 4 unreachable.

🔧 Debug

advanced

Identify the bug in Jump Game code

What error will the following Java code produce when run?

DSA Java

public class JumpGame {
    public static boolean canJump(int[] nums) {
        int maxReach = 0;
        for (int i = 0; i <= nums.length; i++) {
            if (i > maxReach) return false;
            maxReach = Math.max(maxReach, i + nums[i]);
        }
        return true;
    }

    public static void main(String[] args) {
        int[] nums = {2,3,1,1,4};
        System.out.println(canJump(nums));
    }
}

A true

B Compilation error

C false

D ArrayIndexOutOfBoundsException

💡 Hint

Check the loop condition and array access.

The loop runs with i <= nums.length causing access to nums[nums.length], which is out of bounds.

🧠 Conceptual

advanced

Minimum Jumps to Reach Last Index

Given an array where each element represents the max jump length at that position, which approach correctly finds the minimum number of jumps to reach the last index?

A Use a greedy approach tracking the current jump's max reach and increment jumps when passing it

B Use a depth-first search exploring all paths and pick the shortest

C Use a stack to store all indices and pop when jumps exceed max reach

D Use a queue to perform breadth-first search but ignore visited indices

💡 Hint

Think about how to jump as far as possible with each jump.

The greedy approach efficiently tracks the furthest reachable index within the current jump and increments jumps when moving beyond it.

🚀 Application

expert

Output of Modified Jump Game with Path Tracking

What is the output of the following Java code that returns the path of indices to reach the last index if possible, else returns an empty list?

DSA Java

import java.util.*;
public class JumpGame {
    public static List<Integer> jumpPath(int[] nums) {
        int n = nums.length;
        List<Integer> path = new ArrayList<>();
        int maxReach = 0, stepEnd = 0, lastPos = 0;
        for (int i = 0; i < n - 1; i++) {
            maxReach = Math.max(maxReach, i + nums[i]);
            if (i == stepEnd) {
                path.add(lastPos);
                lastPos = maxReach;
                stepEnd = maxReach;
                if (stepEnd >= n - 1) break;
            }
        }
        if (stepEnd < n - 1) return new ArrayList<>();
        path.add(n - 1);
        return path;
    }

    public static void main(String[] args) {
        int[] nums = {2,3,1,1,4};
        System.out.println(jumpPath(nums));
    }
}

A [0, 1, 4]

B [0, 4]

C [0, 2, 4]

D []

💡 Hint

Check how the path list is updated when stepEnd is reached.

The code adds lastPos to path when reaching stepEnd: adds 0 at i=0, adds 2 at i=2 (after maxReach updates to 4 at i=1), then adds 4, resulting in [0, 2, 4].

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 array values

B. The maximum jump length you can make from the first index

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 values at each index as maximum jump lengths.

2. Step 2: Identify the goal

   The goal is to check if reaching the last index is possible, 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 array values -> Option A

4. Quick Check:

   Jump Game = Reach last index? [OK]

Hint: Jump Game checks reachability, not jump count or sums [OK]

Common Mistakes:

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

2. Which of the following Java method signatures correctly represents a function to solve the Jump Game problem?

easy

A. public void canJump(int[] nums)

B. public int canJump(int[] nums)

C. public boolean canJump(int[] nums)

D. public String canJump(int[] nums)

Solution

1. Step 1: Determine the return type

   The Jump Game problem returns true or false depending on whether the last index is reachable, so the return type should be boolean.

2. Step 2: Check method signature correctness

   The method should accept an integer array and return a boolean, matching public boolean canJump(int[] nums).

3. Final Answer:

   public boolean canJump(int[] nums) -> Option C

4. Quick Check:

   Return type boolean for reachability [OK]

Hint: Jump Game method returns boolean for reachability [OK]

Common Mistakes:

• Using int return type instead of boolean
• Using void return type without returning result
• Returning String instead of boolean

3. What is the output of the following Java code snippet?

int[] nums = {2, 3, 1, 1, 4};
System.out.println(canJump(nums));

public static boolean canJump(int[] nums) {
    int maxReach = 0;
    for (int i = 0; i < nums.length; i++) {
        if (i > maxReach) return false;
        maxReach = Math.max(maxReach, i + nums[i]);
    }
    return true;
}

medium

A. Runtime exception

B. false

C. Compilation error

D. true

Solution

1. Step 1: Trace the loop and maxReach updates

   Start with maxReach=0. At i=0, maxReach=max(0,0+2)=2. i=1 ≤ 2, maxReach=max(2,1+3)=4. i=2 ≤ 4, maxReach=max(4,2+1)=4. i=3 ≤ 4, maxReach=max(4,3+1)=4. i=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:

   maxReach covers all indices, so true [OK]

Hint: Track maxReach; if index > maxReach, return false [OK]

Common Mistakes:

• Stopping early without updating maxReach
• Confusing maxReach with current index
• Ignoring the condition i > maxReach

4. Identify the bug in the following Java code for the Jump Game problem:

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

medium

A. The loop condition should be 'i < nums.length' instead of 'i <= nums.length' to avoid ArrayIndexOutOfBoundsException.

B. The maxReach update is incorrect; it should subtract 1 from i + nums[i].

C. The return type should be int, not boolean.

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

Solution

1. Step 1: Analyze the loop condition

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

2. Step 2: Correct the loop condition

   The loop should run while i < nums.length to stay within array bounds.

3. Final Answer:

   The loop condition should be 'i < nums.length' instead of 'i <= nums.length' to avoid ArrayIndexOutOfBoundsException. -> Option A

4. Quick Check:

   Array index must be less than length [OK]

Hint: Use i < nums.length to avoid array index errors [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Incorrect maxReach calculation
• Wrong return type for method

5. Given the array nums = {3, 2, 1, 0, 4}, why does the standard greedy Jump Game algorithm return false, and what does this imply about the array?

hard

A. Because the array length is too short to jump anywhere

B. Because index 3 has zero jump length blocking progress, making the last index unreachable

C. Because the first element is too large, causing an overflow error

D. Because the algorithm only works for arrays with all positive numbers

Solution

1. Step 1: Trace maxReach through the array

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

2. Step 2: Understand the implication

   Index 3 has zero jump length, blocking further progress, so the last index (4) is unreachable.

3. Final Answer:

   Because index 3 has zero jump length blocking progress, making the last index unreachable -> Option B

4. Quick Check:

   Zero jump blocks path, so false [OK]

Hint: Zero jump at blocking index means last index unreachable [OK]

Common Mistakes:

• Assuming large first element guarantees success
• Ignoring zero jump blocking
• Thinking algorithm fails on zeros always