Jump Game Problem in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Rust

if i + nums[i] >= [1] {
    return true;
}

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

Anums.len() - 1

B0

Cnums[0]

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 instead of the last index.

Using nums[0] which is the first element, not the last index.

Using i which is the current index, not the last.

We compare the current index plus its jump length to the last index, which is nums.len() - 1.

2fill in blank

medium

Complete the code to update the farthest reachable index.

DSA Rust

let farthest = farthest.max(i + [1]);

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

Ai

Bfarthest

Cnums[i]

Dnums.len()

Attempts:

3 left

💡 Hint

Common Mistakes

Using i instead of nums[i] for jump length.

Using farthest instead of nums[i].

Using nums.len() which is unrelated here.

We update farthest with the maximum of current farthest and i plus nums[i], the jump length at i.

3fill in blank

hard

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

DSA Rust

for i in 0..[1] {

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

Anums.len() / 2

Bnums.len()

Cnums.len() - 1

Dnums.len() + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using nums.len() - 1 which excludes the last index.

Using nums.len() + 1 which is invalid.

Using nums.len() / 2 which skips many indices.

We loop from 0 to nums.len() because Rust ranges exclude the upper bound, so this iterates over all indices.

4fill in blank

hard

Fill both blanks to check if the current index is reachable and update farthest.

DSA Rust

if i <= [1] {
    farthest = farthest.max(i + [2]);
}

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

Afarthest

Bnums.len()

Cnums[i]

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Checking i <= nums.len() which is unrelated.

Using i instead of farthest in the condition.

Using nums.len() instead of nums[i] for jump length.

We check if i is reachable by comparing it to farthest, then update farthest using nums[i] jump length.

5fill in blank

hard

Fill all three blanks to return if the last index is reachable after the loop.

DSA Rust

return farthest [1] [2] - 1;

// where [3] is the length of nums

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

A>=

B<

Cnums.len()

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of >=

Comparing to nums.len() instead of nums.len() - 1.

Using == which is too strict.

We return true if farthest is greater than or equal to the last index (nums.len() - 1).

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