Jump Game Problem in DSA Java - Execution Trace

Concept Flow - Jump Game Problem

Start at index 0

↓

Check if current index can reach end

↓

From current index, check all reachable next indices

↓

If any next index can reach end, mark current as reachable

↓

Move to previous index

↓

Repeat until index 0 is checked

↓

If index 0 is reachable, return True else False

Start from the last index and move backward, marking indices that can reach the end until you check if the start can reach the end.

Execution Sample

DSA Java

int[] nums = {2,3,1,1,4};
boolean canJump = true;
// Check if start can reach end
for (int i = nums.length - 2; i >= 0; i--) {
  // Check reachable indices
}

This code checks if you can jump from the start to the end of the array.

Execution Table

Step	Operation	Current Index	Reachable Indices Checked	Can Reach End from Current?	Reachable Indices Set	Visual State
1	Initialize	N/A	N/A	True (last index)	Reachable = {4}	[2,3,1,1,4] Reachable: {4}
2	Check index 3	3	Indices 4	Yes (3 + nums[3] = 4 >= 4)	Reachable = {3,4}	[2,3,1,1,4] Reachable: {3,4}
3	Check index 2	2	Indices 3	Yes (2 + nums[2] = 3 >= 3 reachable)	Reachable = {2,3,4}	[2,3,1,1,4] Reachable: {2,3,4}
4	Check index 1	1	Indices 2,3,4	Yes (1 + nums[1] = 4 >= 2 reachable)	Reachable = {1,2,3,4}	[2,3,1,1,4] Reachable: {1,2,3,4}
5	Check index 0	0	Indices 1,2	Yes (0 + nums[0] = 2 >= 1 reachable)	Reachable = {0,1,2,3,4}	[2,3,1,1,4] Reachable: {0,1,2,3,4}
6	Result	0	N/A	True (start can reach end)	Reachable = {0,1,2,3,4}	[2,3,1,1,4] Reachable: {0,1,2,3,4}

💡 Checked all indices backward; start index 0 can reach the end.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
currentIndex	N/A	3	2	1	0	0
reachableIndicesSet	{}	{3,4}	{2,3,4}	{1,2,3,4}	{0,1,2,3,4}	{0,1,2,3,4}
canReachEnd	False	True	True	True	True	True

Key Moments - 3 Insights

Why do we start checking from the last index backwards?

Because the last index is always reachable from itself (see Step 1 in execution_table). We then check if previous indices can reach any index already marked reachable.

How do we know if the current index can reach the end?

If from the current index, you can jump to any index already marked reachable (see Steps 2-5 in execution_table), then current index is also reachable.

Why do we keep a set of reachable indices?

The set helps us quickly check if a jump from current index can land on an index that can reach the end (see reachableIndicesSet column).

Visual Quiz - 3 Questions

Look at the execution_table, at Step 4, which indices are reachable?

A {1,2,3,4}

B {2,3,4}

C {3,4}

D {0,1,2,3,4}

💡 Hint

Check the 'Reachable Indices Set' column at Step 4 in execution_table.

At which step does the start index 0 become reachable?

A Step 3

B Step 5

C Step 2

D Step 6

💡 Hint

Look at the 'Current Index' and 'Reachable Indices Set' columns in execution_table.

If nums[0] was 1 instead of 2, how would the reachable set change at Step 5?

A Reachable would exclude 0

B Reachable would be empty

C Reachable would include 0

D Reachable would only include 4

💡 Hint

Check if index 0 can jump to any reachable index with nums[0] = 1 in execution_table logic.

Concept Snapshot

Jump Game Problem:
- Given array nums, each value is max jump length.
- Goal: Can start index reach last index?
- Start from last index, move backward.
- Mark indices that can reach end.
- If index 0 marked reachable, return True.

Full Transcript

The Jump Game problem asks if you can jump from the start of an array to the end, where each element tells you the max jump length from that position. We solve it by starting from the last index, which is always reachable from itself. Then we move backward checking if each index can jump to any index already known to reach the end. We keep a set of reachable indices and update it as we go. If the start index 0 becomes reachable, we return True. The execution table shows each step checking indices backward, updating reachable sets, and finally confirming the start can reach the end.

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