Jump Game Problem in DSA Rust - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Jump Game Reachability Check

What is the output of this Rust code that checks if you can jump to the last index?

DSA Rust

fn can_jump(nums: Vec<i32>) -> bool {
    let mut max_reach = 0;
    for i in 0..nums.len() {
        if i > max_reach {
            return false;
        }
        max_reach = max_reach.max(i + nums[i] as usize);
    }
    true
}

fn main() {
    let nums = vec![2,3,1,1,4];
    println!("{}", can_jump(nums));
}

A Runtime panic

B false

C Compilation error

D true

💡 Hint

Think about whether the jumps allow reaching the last index.

The code checks if the maximum reachable index covers the last index. Here, it does, so output is true.

❓ Predict Output

intermediate

Output for Unreachable Last Index

What will this Rust code print when the last index is not reachable?

DSA Rust

fn can_jump(nums: Vec<i32>) -> bool {
    let mut max_reach = 0;
    for i in 0..nums.len() {
        if i > max_reach {
            return false;
        }
        max_reach = max_reach.max(i + nums[i] as usize);
    }
    true
}

fn main() {
    let nums = vec![3,2,1,0,4];
    println!("{}", can_jump(nums));
}

A true

B false

C Runtime panic

D Compilation error

💡 Hint

Check if the zero blocks progress to the last index.

The zero at index 3 blocks any jump to index 4, so the function returns false.

🔧 Debug

advanced

Identify the bug in Jump Game code

What error will this Rust code produce when compiled and run?

DSA Rust

fn can_jump(nums: Vec<i32>) -> bool {
    let mut max_reach = 0;
    for i in 0..nums.len() {
        if i >= max_reach {
            return false;
        }
        max_reach = max_reach.max(i + nums[i] as usize);
    }
    true
}

fn main() {
    let nums = vec![2,3,1,1,4];
    println!("{}", can_jump(nums));
}

A Always returns false

B Compilation error

C Always returns true

D Runtime panic

💡 Hint

Check the condition that returns false inside the loop.

The condition 'i >= max_reach' causes the function to return false even when i == max_reach, which is incorrect. It should be 'i > max_reach'.

❓ Predict Output

advanced

Output of Minimum Jumps Calculation

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

DSA Rust

fn jump(nums: Vec<i32>) -> i32 {
    let mut jumps = 0;
    let mut current_end = 0;
    let mut farthest = 0;
    for i in 0..nums.len() - 1 {
        farthest = farthest.max(i + nums[i] as usize);
        if i == current_end {
            jumps += 1;
            current_end = farthest;
        }
    }
    jumps
}

fn main() {
    let nums = vec![2,3,1,1,4];
    println!("{}", jump(nums));
}

A 2

B 3

C 4

D 1

💡 Hint

Count how many jumps are needed to cover the array.

The minimum jumps to reach the last index is 2: jump from index 0 to 1, then from 1 to 4.

🧠 Conceptual

expert

Why Greedy Works for Jump Game

Why does the greedy approach correctly solve the Jump Game problem?

A Because it uses dynamic programming to store intermediate results for all indices.

B Because it tries all possible jump sequences recursively to find the best path.

C Because it always chooses the jump that covers the farthest index, ensuring minimum jumps and reachability.

D Because it sorts the array first to optimize jump choices.

💡 Hint

Think about how the algorithm updates the farthest reachable index.

The greedy method updates the farthest reachable index at each step, ensuring that the jumps cover the maximum distance possible, which leads to a correct and efficient solution.

Practice

1. What does the Jump Game problem ask you to determine given an array of non-negative integers?

easy

A. The minimum number of jumps to reach the last index

B. The maximum jump length from the first index

C. If you can reach the last index starting from the first 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 it is possible to move from the first index to the last index by jumping according to the values in the array.

2. Step 2: Identify the goal

   The goal is to check if the last index is reachable, not the number of jumps or sums.

3. Final Answer:

   If you can reach the last index starting from the first index -> Option C

4. Quick Check:

   Jump Game = Reach last index [OK]

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

Common Mistakes:

• Confusing reachability with minimum jumps
• Thinking about total jump sums
• Assuming jumps can be backward

2. Which of the following Rust code snippets correctly declares a vector representing jump lengths for the Jump Game problem?

easy

A. let jumps = vec![2, 3, 1, 1, 4];

B. let jumps = [2, 3, 1, 1, 4];

C. let jumps = (2, 3, 1, 1, 4);

D. let jumps = {2, 3, 1, 1, 4};

Solution

1. Step 1: Identify Rust vector syntax

   In Rust, vectors are declared using vec![elements], which creates a growable array.

2. Step 2: Check each option

   let jumps = vec![2, 3, 1, 1, 4]; uses vec![], which is correct. let jumps = [2, 3, 1, 1, 4]; is an array, not a vector. let jumps = (2, 3, 1, 1, 4); is a tuple. let jumps = {2, 3, 1, 1, 4}; uses braces which is invalid syntax.

3. Final Answer:

   let jumps = vec![2, 3, 1, 1, 4]; -> Option A

4. Quick Check:

   vec! macro creates vectors [OK]

Hint: Use vec![] for vectors, not [] or () [OK]

Common Mistakes:

• Using array syntax instead of vec! macro
• Confusing tuples with vectors
• Using braces {} which is invalid

3. What is the output of the following Rust code snippet for the Jump Game problem?

fn can_jump(nums: Vec<usize>) -> bool {
    let mut max_reach = 0;
    for i in 0..nums.len() {
        if i > max_reach {
            return false;
        }
        max_reach = max_reach.max(i + nums[i]);
    }
    true
}

fn main() {
    let jumps = vec![2, 3, 1, 1, 4];
    println!("{}", can_jump(jumps));
}

medium

A. Runtime panic

B. false

C. Compilation error

D. true

Solution

1. Step 1: Trace the loop and max_reach updates

   Start with max_reach = 0. For i=0, max_reach = max(0, 0+2) = 2. For i=1, max_reach = max(2, 1+3) = 4. For i=2, max_reach = max(4, 2+1) = 4. For i=3, max_reach = max(4, 3+1) = 4. For i=4, max_reach = max(4, 4+4) = 8.

2. Step 2: Check if any index is unreachable

   At each i, i <= max_reach, so no false return. Loop completes and returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Max reach covers all indices [OK]

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

Common Mistakes:

• Not updating max_reach correctly
• Returning false too early
• Confusing max_reach with jump count

4. Identify the bug in the following Rust function for the Jump Game problem and select the fix.

fn can_jump(nums: Vec<usize>) -> bool {
    let mut max_reach = 0;
    for i in 0..nums.len() {
        if i >= max_reach {
            return false;
        }
        max_reach = max_reach.max(i + nums[i]);
    }
    true
}

medium

A. Change 'max_reach.max(i + nums[i])' to 'max_reach.min(i + nums[i])'

B. Change 'if i >= max_reach' to 'if i > max_reach'

C. Change 'for i in 0..nums.len()' to 'for i in 1..nums.len()'

D. Add 'max_reach += nums[i]' inside the loop

Solution

1. Step 1: Analyze the condition for unreachable index

   The condition 'if i >= max_reach' returns false even when i equals max_reach, which is incorrect because reaching exactly max_reach is allowed.

2. Step 2: Correct the condition

   Changing it to 'if i > max_reach' allows reaching max_reach index and only returns false if i is beyond max_reach.

3. Final Answer:

   Change 'if i >= max_reach' to 'if i > max_reach' -> Option B

4. Quick Check:

   Allow index equal to max_reach [OK]

Hint: Use strict greater than to check unreachable index [OK]

Common Mistakes:

• Using >= instead of > causes early false
• Using min instead of max for max_reach
• Skipping index 0 in loop

5. Given the array vec![3, 2, 1, 0, 4], what is the correct output of the Jump Game problem using the standard greedy approach in Rust?

hard

A. false

B. true

C. Compilation error

D. Runtime panic

Solution

1. Step 1: Trace max_reach for each index

   Start max_reach=0. i=0: max_reach=max(0,0+3)=3. i=1: max_reach=max(3,1+2)=3. i=2: max_reach=max(3,2+1)=3. i=3: max_reach=max(3,3+0)=3. i=4: i=4 > max_reach=3, so return false.

2. Step 2: Understand why last index is unreachable

   Index 4 cannot be reached because max_reach never extends beyond 3 due to zero jump at index 3.

3. Final Answer:

   false -> Option A

4. Quick Check:

   Zero jump blocks progress [OK]

Hint: Zero jump can block reaching the end [OK]

Common Mistakes:

• Assuming always true if first jump > 0
• Ignoring zero jump blocking path
• Confusing max_reach with jump count