Jump Game Problem in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the current index can jump to or beyond the last index.

DSA C++

if (i + nums[i] [1] n - 1) return true;

Drag options to blanks, or click blank then click option'

A<

B<=

C==

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<=' instead of '>=' causes wrong logic.

Using '==' misses jumps that go beyond the last index.

We check if the current position plus its jump length reaches or passes the last index, so '>=' is correct.

2fill in blank

medium

Complete the code to update the farthest reachable index from the current position.

DSA C++

farthest = std::max(farthest, i [1] nums[i]);

Drag options to blanks, or click blank then click option'

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' subtracts jump length, which is incorrect.

Using '*' or '/' does not represent jump distance.

We add the current index and its jump length to find the farthest reachable index.

3fill in blank

hard

Fix the error in the loop condition to iterate over all indices correctly.

DSA C++

for (int i = 0; i [1] n; ++i) {

Drag options to blanks, or click blank then click option'

A>

B<

C<=

D>=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<=' causes out-of-bounds access.

Using '>' or '>=' prevents the loop from running.

The loop should run while i is less than n to cover all indices from 0 to n-1.

4fill in blank

hard

Fill both blanks to complete the condition that checks if the current index is reachable.

DSA C++

if (i [1] farthest) {
    farthest = std::max(farthest, i [2] nums[i]);
}

Drag options to blanks, or click blank then click option'

A<

B<=

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' in the first blank skips reachable indices.

Using '<' in the second blank causes wrong calculation.

We check if i is less than or equal to farthest to ensure it's reachable, then update farthest with max of current farthest and i + nums[i].

5fill in blank

hard

Fill all three blanks to complete the function that returns true if the last index is reachable.

DSA C++

bool canJump(std::vector<int>& nums) {
    int n = nums.size();
    int farthest = 0;
    for (int i = 0; i [1] n; ++i) {
        if (i [2] farthest) {
            farthest = std::max(farthest, i [3] nums[i]);
        } else {
            return false;
        }
    }
    return true;
}

Drag options to blanks, or click blank then click option'

A<

B<=

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' in the loop condition causes infinite loops.

Using '>' in reachability check skips valid indices.

Using '-' instead of '+' miscalculates farthest.

The loop runs while i < n; we check if i <= farthest to confirm reachability; then update farthest with i + nums[i].

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