Find Maximum Subarray Divide and Conquer in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the middle index of the array segment.

DSA C

int mid = (low + [1]) / 2;

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

Amid

Bhigh

Clow

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using low twice instead of high.

Using mid variable before assignment.

The middle index is calculated by adding low and high indices and dividing by 2.

2fill in blank

medium

Complete the code to return the maximum of two integers.

DSA C

int max = (a > [1]) ? a : b;

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

A0

Ba

Cmax

Db

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing a with itself.

Returning wrong variable.

We compare a and b, returning the greater value.

3fill in blank

hard

Fix the error in the loop that finds maximum crossing subarray sum.

DSA C

for (int i = mid; i >= [1]; i--) {
    sum += arr[i];
    if (sum > left_sum) left_sum = sum;
}

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

Alow

Bhigh

Cmid

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using high instead of low.

Loop direction incorrect.

The loop should run from mid down to low index to cover left half.

4fill in blank

hard

Fill both blanks to correctly compute the maximum crossing subarray sum.

DSA C

int right_sum = INT_MIN;
int sum = 0;
for (int j = mid + 1; j <= [1]; j++) {
    sum += arr[j];
    if (sum > [2]) right_sum = sum;
}

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

Ahigh

Bright_sum

Cleft_sum

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using left_sum instead of right_sum.

Comparing with wrong variable.

The loop runs from mid+1 to high. We compare sum with right_sum to update it.

5fill in blank

hard

Fill all three blanks to return the maximum subarray sum among left, right, and crossing sums.

DSA C

return [1](left_sum, [2](right_sum, [3]));

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

Amax

Bleft_sum

Cright_sum

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum instead of max.

Wrong order of arguments.

We use max function twice to find the maximum among three sums.

Practice

1. What is the main idea behind the Divide and Conquer approach to find the maximum subarray sum?

easy

A. Use a sliding window to find the maximum sum subarray in one pass

B. Sort the array and pick the largest element as max subarray sum

C. Divide the array into two halves, find max subarray in left, right, and crossing middle, then combine results

D. Calculate sum of all subarrays and pick the maximum

Solution

1. Step 1: Understand divide and conquer strategy

   The array is split into two halves recursively to simplify the problem.

2. Step 2: Combine results from left, right, and crossing subarrays

   We find max subarray sums in left half, right half, and subarrays crossing the middle, then take the maximum of these.

3. Final Answer:

   Divide the array into two halves, find max subarray in left, right, and crossing middle, then combine results -> Option C

4. Quick Check:

   Divide and conquer = split, solve, combine [OK]

Hint: Split array, solve halves, check crossing sum, combine [OK]

Common Mistakes:

• Thinking sorting helps find max subarray sum
• Ignoring subarrays crossing the middle
• Trying to sum all subarrays directly

2. Which of the following is the correct base case condition in the divide and conquer function for maximum subarray?

easy

A. if (low == high) return 0;

B. if (low > high) return 0;

C. if (low < high) return arr[low] + arr[high];

D. if (low == high) return arr[low];

Solution

1. Step 1: Identify base case meaning

   When the subarray has only one element (low equals high), the max subarray sum is that element itself.

2. Step 2: Match base case condition

   The condition if (low == high) return arr[low]; correctly returns the single element's value.

3. Final Answer:

   if (low == high) return arr[low]; -> Option D

4. Quick Check:

   Single element subarray returns element value [OK]

Hint: Base case: one element means return that element [OK]

Common Mistakes:

• Returning 0 when low == high
• Using incorrect comparison operators
• Returning sum of two elements instead of one

3. What is the output of the following C code snippet using divide and conquer to find max subarray sum?

int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
int result = maxSubArray(arr, 0, 8);
printf("%d", result);

Assume maxSubArray is correctly implemented divide and conquer function.

medium

A. 6

B. 7

C. 5

D. 4

Solution

1. Step 1: Identify max subarray in given array

   The maximum subarray is [4, -1, 2, 1] with sum 4 + (-1) + 2 + 1 = 6, but check if including more elements helps.

2. Step 2: Check if extending subarray increases sum

   Including the element before 4 is -3 (reduces sum), after 1 is -5 (reduces sum), so max sum is 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Max subarray sum = 6 [OK]

Hint: Find max sum of continuous elements [OK]

Common Mistakes:

• Counting non-continuous elements
• Miscomputing sums with negative numbers
• Assuming max element alone is answer

4. Identify the bug in this divide and conquer max subarray function snippet:

int maxCrossingSum(int arr[], int low, int mid, int high) {
    int left_sum = 0, sum = 0;
    for (int i = mid; i >= low; i--) {
        sum += arr[i];
        if (sum > left_sum)
            left_sum = sum;
    }
    int right_sum = 0;
    sum = 0;
    for (int i = mid + 1; i <= high; i++) {
        sum += arr[i];
        if (sum > right_sum)
            right_sum = sum;
    }
    return left_sum + right_sum;
}

medium

A. left_sum and right_sum should be initialized to INT_MIN, not 0

B. The loops should start from low and high, not mid

C. sum variable should not be reset between loops

D. Return statement should subtract left_sum from right_sum

Solution

1. Step 1: Understand initialization of sums

   Initializing left_sum and right_sum to 0 causes errors if all numbers are negative, as max sum could be less than 0.

2. Step 2: Correct initialization

   They should be initialized to the smallest integer (INT_MIN) to correctly track max sums even if negative.

3. Final Answer:

   left_sum and right_sum should be initialized to INT_MIN, not 0 -> Option A

4. Quick Check:

   Initialize max sums to INT_MIN to handle negatives [OK]

Hint: Use INT_MIN for max sums to handle negative arrays [OK]

Common Mistakes:

• Initializing max sums to zero causes wrong results
• Not resetting sum variable properly
• Incorrect loop ranges

5. Given an array arr = [-1, -2, -3, -4], what will the divide and conquer max subarray function return and why?

hard

A. 0 because empty subarray sum is considered

B. -1 because the max subarray is the single largest element

C. -10 because sum of all elements is max

D. -4 because last element is max

Solution

1. Step 1: Analyze array with all negative numbers

   All elements are negative, so the max subarray is the one with the least negative value (largest number).

2. Step 2: Identify max element

   The largest element is -1, so max subarray sum is -1 (single element subarray).

3. Final Answer:

   -1 because the max subarray is the single largest element -> Option B

4. Quick Check:

   Max subarray in negatives = max single element [OK]

Hint: Max subarray in all negatives is max single element [OK]

Common Mistakes:

• Assuming sum of all negatives is max
• Considering empty subarray sum as zero incorrectly
• Picking last element without comparison