Jump Game Problem in DSA C - 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 array represent?

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

intermediate

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

Keep track of the farthest index you can reach while iterating through the array. If at any point the current index is beyond the farthest reachable index, 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, it updates the farthest reachable position, ensuring that if the last index is reachable, it will be found without exploring all paths.

beginner

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

O(n), where n is the length of the 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 must jump backward

B You must jump exactly zero steps

C You can jump any number of steps

D You cannot jump forward from this position

A zero means you cannot jump forward from that position, which may block progress if you cannot jump over it.

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

A Continue iterating

B Reset the farthest reachable index

C Return false immediately

D Jump backward

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

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

A 0

B 1

C Length of the array

D -1

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

If the array is [2,3,1,1,4], can you reach the last index?

A Yes

B No

C Only if you jump backward

D Only if you jump exactly 1 step each time

You can jump from index 0 to 1 or 2, then from 1 to the last index, so yes.

What is the output of the greedy algorithm for the array [3,2,1,0,4]?

A True

B False

C Depends on jump choices

D Error

You get stuck at index 3 because it has zero jump length and cannot reach index 4.

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

Think about how you keep track of the best place you can jump to as you move forward.

Describe a scenario where the Jump Game problem returns false and why.

Consider when you get stuck and cannot move forward.

Practice

1. What is the main goal of the Jump Game problem?

easy

A. Calculate the minimum jump length required to reach the last index

B. Determine if you can reach the last index from the first index by jumping

C. Count the total number of jumps needed to reach the end

D. Find the maximum jump length from the first index

Solution

1. Step 1: Understand the problem statement

   The Jump Game problem asks if it is possible to move from the first index to 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 the last index is reachable, not to count jumps or find maximum jump length.

3. Final Answer:

   Determine if you can reach the last index from the first index by jumping -> Option B

4. Quick Check:

   Goal = Reach last index [OK]

Hint: Focus on reachability, not jump counts or lengths [OK]

Common Mistakes:

• Confusing maximum jump length with reachability
• Trying to count jumps instead of checking possibility
• Assuming jumps can go backward

2. Which of the following is the correct syntax to declare an integer array nums of size 5 in C for the Jump Game problem?

easy

A. int[] nums = new int[5];

B. int nums = [5];

C. int nums(5);

D. int nums[5];

Solution

1. Step 1: Recall C array declaration syntax

   In C, arrays are declared by specifying the type, name, and size in square brackets, like int nums[5];.

2. Step 2: Check each option

   int nums[5]; matches correct C syntax. int nums = [5]; uses invalid assignment. int nums(5); uses parentheses which is incorrect. int[] nums = new int[5]; is Java syntax.

3. Final Answer:

   int nums[5]; -> Option D

4. Quick Check:

   C array syntax = int nums[5]; [OK]

Hint: Use type name[size] for arrays in C [OK]

Common Mistakes:

• Using Java or C++ style array declarations
• Using parentheses instead of square brackets
• Assigning array size with equals sign

3. What will be the output of the following C code snippet for the Jump Game problem?

int nums[] = {2, 3, 1, 1, 4};
int n = 5;
int maxReach = 0;
for (int i = 0; i < n; i++) {
    if (i > maxReach) {
        printf("false\n");
        return 0;
    }
    if (i + nums[i] > maxReach) {
        maxReach = i + nums[i];
    }
}
printf("true\n");

medium

A. true

B. false

C. Compilation error

D. Runtime error

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 prints "true".

3. Final Answer:

   true -> Option A

4. Quick Check:

   maxReach covers all indices = true [OK]

Hint: Check if current index exceeds max reachable index [OK]

Common Mistakes:

• Stopping early without updating maxReach
• Confusing index with jump length
• Assuming false if maxReach equals index

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

int canJump(int* nums, int n) {
    int maxReach = 0;
    for (int i = 0; i <= n; i++) {
        if (i > maxReach) return 0;
        if (i + nums[i] > maxReach) maxReach = i + nums[i];
    }
    return 1;
}

medium

A. Return values should be swapped (1 for false, 0 for true)

B. maxReach should be initialized to -1

C. Loop condition should be i < n, not i <= n

D. nums array should be declared inside the function

Solution

1. Step 1: Analyze the loop condition

   The loop runs from i=0 to i<=n, which means it accesses nums[n], an out-of-bounds index causing undefined behavior.

2. Step 2: Correct the loop condition

   The loop should run while i < n to avoid accessing beyond the array.

3. Final Answer:

   Loop condition should be i < n, not i <= n -> Option C

4. Quick Check:

   Array index in bounds = i < n [OK]

Hint: Loop up to n-1 to avoid out-of-bounds access [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Ignoring array boundary checks
• Incorrect return values for boolean

5. Given the array nums = {3, 2, 1, 0, 4}, why does the standard greedy Jump Game algorithm return false for reachability?

hard

A. Because index 3 has a jump length of 0, blocking further progress

B. Because the array length is less than 5

C. Because the first element is too large

D. Because the last element is unreachable due to negative jumps

Solution

1. Step 1: Trace jumps from start

   Start at index 0 with jump length 3, maxReach = 3. Indices 1, 2, 3 are reachable. At index 3, jump length is 0, so maxReach stays 3.

2. Step 2: Check if last index is reachable

   Last index is 4, which is beyond maxReach 3, so it is unreachable, causing the algorithm to return false.

3. Final Answer:

   Because index 3 has a jump length of 0, blocking further progress -> Option A

4. Quick Check:

   Zero jump blocks path = false [OK]

Hint: Zero jump at reachable index blocks reaching the end [OK]

Common Mistakes:

• Ignoring zero jump blocking
• Assuming array length affects reachability
• Thinking negative jumps exist in problem