Jump Game Problem in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Jump Game Reachability Check

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

DSA C++

bool canJump(std::vector<int>& nums) {
    int maxReach = 0;
    for (int i = 0; i < nums.size(); ++i) {
        if (i > maxReach) return false;
        maxReach = std::max(maxReach, i + nums[i]);
    }
    return true;
}

int main() {
    std::vector<int> nums = {2,3,1,1,4};
    if (canJump(nums)) std::cout << "true" << std::endl;
    else std::cout << "false" << std::endl;
    return 0;
}

A true

B false

C Compilation error

D Runtime error

💡 Hint

Think about whether the jumps allow reaching the last index.

The code correctly tracks the maximum reachable index. Since the input allows reaching the end, it returns true.

❓ Predict Output

intermediate

Output for Unreachable Last Index

What will the output be for this input array when running the same jump game code?

DSA C++

int main() {
    std::vector<int> nums = {3,2,1,0,4};
    if (canJump(nums)) std::cout << "true" << std::endl;
    else std::cout << "false" << std::endl;
    return 0;
}

A false

B true

C Compilation error

D Runtime error

💡 Hint

Check if the zero blocks further progress.

The zero at index 3 blocks any further jumps, so the last index cannot be reached.

🧠 Conceptual

advanced

Understanding Greedy Approach in Jump Game

Why does the greedy approach work for the Jump Game problem instead of using backtracking or dynamic programming?

A Because it sorts the array to find the longest jump first.

B Because it tries all possible jumps recursively to find the path to the end.

C Because it uses memoization to store results of subproblems.

D Because tracking the maximum reachable index ensures we never revisit indices unnecessarily, making it efficient and correct.

💡 Hint

Think about how the algorithm avoids repeated work.

The greedy method keeps track of the furthest reachable index and stops early if progress is blocked, making it efficient.

❓ Predict Output

advanced

Output of Minimum Jumps Calculation

What is the output of this code that calculates the minimum number of jumps to reach the last index?

DSA C++

int jump(std::vector<int>& nums) {
    int jumps = 0, currentEnd = 0, farthest = 0;
    for (int i = 0; i < nums.size() - 1; ++i) {
        farthest = std::max(farthest, i + nums[i]);
        if (i == currentEnd) {
            jumps++;
            currentEnd = farthest;
        }
    }
    return jumps;
}

int main() {
    std::vector<int> nums = {2,3,1,1,4};
    std::cout << jump(nums) << std::endl;
    return 0;
}

A 4

B 3

C 2

D 1

💡 Hint

Count how many jumps are needed to cover the array.

The minimum jumps to reach the last index in this array is 2.

🔧 Debug

expert

Identify the Bug in Jump Game Code

What error will this code produce when trying to check if the last index is reachable?

DSA C++

bool canJump(std::vector<int>& nums) {
    int maxReach = 0;
    for (int i = 0; i < nums.size(); ++i) {
        if (i > maxReach) return false;
        maxReach = std::max(maxReach, i + nums.at(i));
    }
    return true;
}

int main() {
    std::vector<int> nums = {2,3,1,1,4};
    if (canJump(nums)) std::cout << "true" << std::endl;
    else std::cout << "false" << std::endl;
    return 0;
}

A Compilation error due to invalid syntax

B Runtime error: out_of_range exception

C Returns false incorrectly

D Returns true correctly

💡 Hint

Check the loop boundary condition carefully.

The loop runs until i <= nums.size(), which accesses nums[nums.size()] causing out_of_range error.

Practice

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

easy

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

B. Find the maximum jump length from the first index

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

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

Solution

1. Step 1: Understand the problem statement

   The Jump Game problem asks if it is possible to move from the first position of an array to the last position by jumping forward. Each array element represents the maximum jump length from that position.

2. Step 2: Identify the goal

   The goal is to check if the last index can be reached starting from the first index using the allowed jumps.

3. Final Answer:

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

4. Quick Check:

   Jump Game goal = Reach last index [OK]

Hint: Focus on reachability from start to end index [OK]

Common Mistakes:

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

2. Which of the following is the correct C++ syntax to declare a vector named nums initialized with values {2,3,1,1,4}?

easy

A. vector nums = [2,3,1,1,4];

B. std::vector nums = {2,3,1,1,4};

C. std::vector<int> nums = {2,3,1,1,4};

D. std::vector<int> nums(2,3,1,1,4);

Solution

1. Step 1: Understand vector declaration syntax

   In C++, to declare a vector of integers with initial values, use std::vector<int> nums = {values};.

2. Step 2: Check each option

   std::vector<int> nums = {2,3,1,1,4}; uses correct syntax with type and initializer list. Options A and C miss template type or use wrong brackets. std::vector<int> nums(2,3,1,1,4); uses constructor incorrectly.

3. Final Answer:

   std::vector<int> nums = {2,3,1,1,4}; -> Option C

4. Quick Check:

   Correct vector initialization syntax = std::vector<int> nums = {2,3,1,1,4}; [OK]

Hint: Use std::vector<int> with curly braces for initialization [OK]

Common Mistakes:

• Omitting <int> in vector declaration
• Using square brackets [] instead of curly braces {}
• Incorrect constructor parameters

3. What will be the output of the following C++ code snippet?

std::vector<int> nums = {2,3,1,1,4};
int maxReach = 0;
for (int i = 0; i <= maxReach; ++i) {
    maxReach = std::max(maxReach, i + nums[i]);
    if (maxReach >= nums.size() - 1) {
        std::cout << "true" << std::endl;
        break;
    }
}
if (maxReach < nums.size() - 1) std::cout << "false" << std::endl;

medium

A. false

B. true

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. At i=1, maxReach = max(2, 1+3) = 4. Since maxReach (4) >= last index (4), print "true" and break.

2. Step 2: Confirm output

   The loop breaks after printing "true". No further output.

3. Final Answer:

   true -> Option B

4. Quick Check:

   maxReach reaches last index, output = true [OK]

Hint: Track maxReach and break when it reaches last index [OK]

Common Mistakes:

• Not updating maxReach correctly
• Missing break causing extra output
• Confusing index bounds in loop

4. Identify the error in the following C++ code for the Jump Game problem:

bool canJump(std::vector<int>& nums) {
    int maxReach = 0;
    for (int i = 0; i < nums.size(); ++i) {
        if (i > maxReach) return false;
        maxReach = std::max(maxReach, i + nums[i]);
    }
    return true;
}

medium

A. No error, code works correctly

B. Return false should be after the loop, not inside

C. maxReach update is incorrect, should subtract 1

D. Loop condition should be i <= maxReach instead of i < nums.size()

Solution

1. Step 1: Analyze loop and conditions

   The loop iterates over all indices. If current index i is beyond maxReach, return false immediately. Otherwise, update maxReach.

2. Step 2: Verify correctness

   This logic correctly checks if the last index is reachable. Returning false inside loop is valid. maxReach update is correct.

3. Final Answer:

   No error, code works correctly -> Option A

4. Quick Check:

   Code logic matches Jump Game solution [OK]

Hint: Check if current index exceeds maxReach to return false early [OK]

Common Mistakes:

• Changing loop condition incorrectly
• Moving return false outside loop causing wrong result
• Incorrect maxReach calculation

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

hard

A. Because the zero at index 3 blocks any further jumps to the last index

B. Because the array length is less than 5

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

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

Solution

1. Step 1: Understand the array and jumps

   Starting at index 0 with jump length 3, you can reach indices 1, 2, or 3. At index 3, jump length is 0, so you cannot move forward from there.

2. Step 2: Identify why last index is unreachable

   Since index 4 is beyond index 3 and no jumps can be made from index 3, the last index cannot be reached, so the algorithm returns false.

3. Final Answer:

   Because the zero at index 3 blocks any further jumps to the last index -> Option A

4. Quick Check:

   Zero jump blocks path, output = false [OK]

Hint: Look for zero jump spots blocking progress [OK]

Common Mistakes:

• Ignoring zero jump blocking
• Assuming array length affects result
• Misunderstanding jump lengths