Kadane's Algorithm Maximum Subarray in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the variable that stores the maximum sum found so far.

DSA Java

int maxSoFar = [1];

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

A0

BInteger.MAX_VALUE

CInteger.MIN_VALUE

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing maxSoFar to 0 causes errors when all numbers are negative.

Using Integer.MAX_VALUE will prevent updates to maxSoFar.

We initialize maxSoFar to Integer.MIN_VALUE to ensure any subarray sum will be larger initially.

2fill in blank

medium

Complete the code to update the current subarray sum by adding the current element.

DSA Java

currentSum = currentSum [1] nums[i];

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication changes the logic incorrectly.

Division is not applicable here.

We add the current element to currentSum to extend the subarray.

3fill in blank

hard

Fix the error in the condition to reset currentSum when it becomes negative.

DSA Java

if (currentSum [1] 0) {
    currentSum = 0;
}

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

A>

B==

C>=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using > or >= will reset incorrectly when sum is positive.

Using == only resets when sum is exactly zero, missing negatives.

We reset currentSum to 0 when it is less than 0 to start a new subarray.

4fill in blank

hard

Complete the code to update maxSoFar with the larger of maxSoFar and currentSum.

DSA Java

maxSoFar = Math.[1](maxSoFar, currentSum);

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

Amax

Bmin

C)

D(

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.min will select the smaller value incorrectly.

Missing the closing parenthesis causes syntax errors.

Use Math.max to get the larger value and close the method call with a parenthesis.

5fill in blank

hard

Fill all three blanks to complete the for-loop iterating over the array.

DSA Java

for (int [1] = 0; [2] < nums[3]; [1]++) {
    // loop body
}

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

Ai

B.length

C[i]

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'n' instead of 'i' inconsistently.

Using nums[i] in the condition instead of nums.length.

Forgetting to increment the loop variable.

Use 'i' as the loop variable, compare i with nums.length, and access elements with nums[i].

Practice

1. What does Kadane's Algorithm primarily help to find in an array of integers?

easy

A. The minimum element in the array

B. The number of positive elements

C. The total sum of all elements

D. The maximum sum of a contiguous subarray

Solution

1. Step 1: Understand the problem Kadane's Algorithm solves

   Kadane's Algorithm is designed to find the maximum sum of any contiguous subarray within a given array.

2. Step 2: Differentiate from other array operations

   It does not find minimum elements, total sum, or count positives, but specifically the maximum sum of a continuous segment.

3. Final Answer:

   The maximum sum of a contiguous subarray -> Option D

4. Quick Check:

   Maximum subarray sum = maximum sum of contiguous elements [OK]

Hint: Kadane's finds max sum of continuous elements fast [OK]

Common Mistakes:

• Confusing maximum subarray sum with total array sum
• Thinking it finds minimum or count of elements
• Assuming it works on non-contiguous elements

2. Which of the following is the correct initialization for Kadane's Algorithm variables in Java?

easy

A. int maxSoFar = 0, maxEndingHere = 0;

B. int maxSoFar = 0, maxEndingHere = Integer.MAX_VALUE;

C. int maxSoFar = Integer.MIN_VALUE, maxEndingHere = 0;

D. int maxSoFar = Integer.MAX_VALUE, maxEndingHere = Integer.MIN_VALUE;

Solution

1. Step 1: Identify correct initial values for Kadane's variables

   maxSoFar should start at the smallest integer to handle all negative arrays; maxEndingHere starts at 0 to accumulate sums.

2. Step 2: Check each option's initialization

   int maxSoFar = Integer.MIN_VALUE, maxEndingHere = 0; correctly sets maxSoFar to Integer.MIN_VALUE and maxEndingHere to 0, which is standard practice.

3. Final Answer:

   int maxSoFar = Integer.MIN_VALUE, maxEndingHere = 0; -> Option C

4. Quick Check:

   Initialize maxSoFar low, maxEndingHere zero [OK]

Hint: Start maxSoFar at smallest int, maxEndingHere at zero [OK]

Common Mistakes:

• Initializing maxSoFar to 0 causes errors with all negative arrays
• Swapping maxSoFar and maxEndingHere initial values
• Using Integer.MAX_VALUE incorrectly

3. What is the output of the following Java code using Kadane's Algorithm?

int[] arr = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
int maxSoFar = Integer.MIN_VALUE, maxEndingHere = 0;
for (int num : arr) {
    maxEndingHere += num;
    if (maxSoFar < maxEndingHere) maxSoFar = maxEndingHere;
    if (maxEndingHere < 0) maxEndingHere = 0;
}
System.out.println(maxSoFar);

medium

A. 6

B. 7

C. 5

D. 4

Solution

1. Step 1: Trace the loop and update sums

   Iterate through arr, updating maxEndingHere and maxSoFar:
   - Start: maxSoFar = -∞, maxEndingHere = 0
   - Add -2: maxEndingHere = -2 (reset to 0)
   - Add 1: maxEndingHere = 1, maxSoFar = 1
   - Add -3: maxEndingHere = -2 (reset to 0)
   - Add 4: maxEndingHere = 4, maxSoFar = 4
   - Add -1: maxEndingHere = 3
   - Add 2: maxEndingHere = 5, maxSoFar = 5
   - Add 1: maxEndingHere = 6, maxSoFar = 6
   - Add -5: maxEndingHere = 1
   - Add 4: maxEndingHere = 5

2. Step 2: Identify maximum sum found

   The maximum sum recorded is 6, but check carefully:
   At step adding 1 after 2, maxEndingHere = 6, maxSoFar = 6
   At last step, maxEndingHere = 5, maxSoFar remains 6
   Wait, re-check:
   Actually, after adding 1 (step 7), maxEndingHere = 6
   Then adding -5 (step 8), maxEndingHere = 1
   Then adding 4 (step 9), maxEndingHere = 5
   So maxSoFar = 6

3. Correction:

   Re-examining the sums, the maximum subarray is [4, -1, 2, 1] which sums to 6, but the subarray [4, -1, 2, 1] sums to 6, so 6 is correct.
   However, the standard Kadane's algorithm for this array returns 6, but the known maximum subarray sum is 6.
   But the options include 7, which is incorrect.
   Therefore, the original answer C (6) is correct.

4. Final Answer:

   6 -> Option A

5. Quick Check:

   Max subarray sum = 6 [OK]

Hint: Add and reset sum; track max sum found [OK]

Common Mistakes:

• Forgetting to reset maxEndingHere when negative
• Miscounting sums during iteration
• Confusing maxSoFar with maxEndingHere

4. Identify the bug in this Kadane's Algorithm Java code snippet:

int maxSoFar = 0, maxEndingHere = 0;
for (int num : arr) {
    maxEndingHere = Math.max(num, maxEndingHere + num);
    maxSoFar = Math.max(maxSoFar, maxEndingHere);
}
System.out.println(maxSoFar);

medium

A. maxEndingHere should be initialized to Integer.MAX_VALUE

B. maxSoFar should start at Integer.MIN_VALUE, not 0

C. The loop should start from index 1, not 0

D. Using Math.max is incorrect for Kadane's Algorithm

Solution

1. Step 1: Analyze initialization of maxSoFar

   Starting maxSoFar at 0 causes incorrect results if all numbers are negative, as maxSoFar will never update to a negative max subarray.

2. Step 2: Correct initialization for negative arrays

   maxSoFar should be initialized to Integer.MIN_VALUE to correctly track maximum sums even if all are negative.

3. Final Answer:

   maxSoFar should start at Integer.MIN_VALUE, not 0 -> Option B

4. Quick Check:

   Initialize maxSoFar low to handle negatives [OK]

Hint: Initialize maxSoFar to smallest int to handle negatives [OK]

Common Mistakes:

• Initializing maxSoFar to 0 causes wrong max for negative arrays
• Misunderstanding Math.max usage in Kadane's
• Incorrect loop indexing assumptions

5. Given an array int[] arr = {-1, -2, -3, -4}, what will Kadane's Algorithm return as the maximum subarray sum if initialized with maxSoFar = Integer.MIN_VALUE and maxEndingHere = 0?

hard

A. -1

B. 0

C. -10

D. 4

Solution

1. Step 1: Trace Kadane's Algorithm on all negative array

   maxEndingHere resets to 0 when negative, but maxSoFar tracks max subarray sum:
   - Add -1: maxEndingHere = -1 (reset to 0), maxSoFar = -1
   - Add -2: maxEndingHere = -2 (reset to 0), maxSoFar = -1
   - Add -3: maxEndingHere = -3 (reset to 0), maxSoFar = -1
   - Add -4: maxEndingHere = -4 (reset to 0), maxSoFar = -1

2. Step 2: Identify maximum subarray sum

   The maximum subarray sum is -1, the largest single element in the array.

3. Final Answer:

   -1 -> Option A

4. Quick Check:

   Max subarray sum in negatives = max single element [OK]

Hint: Max sum in all negatives is largest single element [OK]

Common Mistakes:

• Assuming max sum is 0 due to resets
• Summing all negatives incorrectly
• Ignoring initialization of maxSoFar