Jump Game Problem in DSA C++ - Build from Scratch

Jump Game Problem

📖 Scenario: Imagine you are playing a video game where you need to jump across platforms to reach the end. Each platform lets you jump forward a certain number of steps. You want to check if you can reach the last platform starting from the first one.

🎯 Goal: Build a program that checks if it is possible to jump from the first platform to the last platform using the jump lengths given for each platform.

📋 What You'll Learn

Create a vector called jumps with exact values representing jump lengths on each platform

Create an integer variable called maxReach to track the farthest platform reachable

Use a for loop with variable i to iterate over the jumps vector

Inside the loop, update maxReach to the maximum of current maxReach and i + jumps[i]

If maxReach is less than or equal to i before reaching the last platform, break the loop

After the loop, print "true" if maxReach is greater than or equal to the last index, otherwise print "false"

💡 Why This Matters

🌍 Real World

This problem models situations where you need to check if a path or sequence of steps is possible given constraints, such as in games, navigation, or network routing.

💼 Career

Understanding this problem helps in software development roles that involve algorithmic thinking, problem solving, and optimization, which are common in technical interviews.

1

Create the jumps vector

Create a std::vector<int> called jumps with these exact values: 2, 3, 1, 1, 4

DSA C++

#include 
#include 

int main() {
    // Create the jumps vector with values 2, 3, 1, 1, 4
    // Your code here

    return 0;
}

Hint

Use std::vector<int> jumps = {2, 3, 1, 1, 4}; to create the vector.

2

Create maxReach variable

Create an integer variable called maxReach and set it to 0

DSA C++

#include 
#include 

int main() {
    std::vector jumps = {2, 3, 1, 1, 4};
    // Create maxReach variable and set to 0
    // Your code here

    return 0;
}

Hint

Use int maxReach = 0; to create the variable.

3

Implement the jump logic loop

Use a for loop with variable i to iterate over the jumps vector from 0 to jumps.size() - 1. Inside the loop, update maxReach to the maximum of maxReach and i + jumps[i]. If maxReach is less than or equal to i, break the loop.

DSA C++

#include 
#include 

int main() {
    std::vector jumps = {2, 3, 1, 1, 4};
    int maxReach = 0;

    // Use a for loop to update maxReach and check if jump is possible
    // Your code here

    return 0;
}

Hint

Use for (int i = 0; i < (int)jumps.size(); i++) and update maxReach inside the loop. Break if i > maxReach.

4

Print the result

After the loop, print "true" if maxReach is greater than or equal to jumps.size() - 1, otherwise print "false"

DSA C++

#include 
#include 

int main() {
    std::vector jumps = {2, 3, 1, 1, 4};
    int maxReach = 0;

    for (int i = 0; i  maxReach) {
            break;
        }
        if (i + jumps[i] > maxReach) {
            maxReach = i + jumps[i];
        }
    }

    // Print "true" if last platform is reachable, else "false"
    // Your code here

    return 0;
}

Hint

Use if (maxReach >= jumps.size() - 1) to decide what to print.

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