Kadane's Algorithm Maximum Subarray in DSA Java - Build from Scratch

Kadane's Algorithm Maximum Subarray

📖 Scenario: You are analyzing daily temperature changes to find the longest warm streak. Each day's temperature change is recorded as a number (positive for warmer, negative for colder). You want to find the maximum sum of consecutive days' temperature changes to identify the warmest period.

🎯 Goal: Build a Java program that uses Kadane's Algorithm to find the maximum sum of a contiguous subarray from a list of integers representing daily temperature changes.

📋 What You'll Learn

Create an integer array called tempChanges with exact values

Create an integer variable called maxSoFar to track the maximum sum found

Create an integer variable called maxEndingHere to track the current subarray sum

Use a for loop with variable i to iterate over tempChanges

Update maxEndingHere and maxSoFar inside the loop using Kadane's logic

Print the value of maxSoFar as the final output

💡 Why This Matters

🌍 Real World

Finding the warmest period in temperature changes helps meteorologists and farmers plan better.

💼 Career

Kadane's Algorithm is a classic technique used in software engineering interviews and real-world problems involving maximum sums in arrays.

1

Create the temperature changes array

Create an integer array called tempChanges with these exact values: {-2, 3, 2, -1, 4, -5, 4}

DSA Java

# Create the integer array tempChanges with the given values
// Your code here

Hint

Use int[] tempChanges = { ... }; to create the array with the exact numbers.

2

Initialize variables for Kadane's Algorithm

Create two integer variables called maxSoFar and maxEndingHere, both initialized to the first element of tempChanges

DSA Java

int[] tempChanges = {-2, 3, 2, -1, 4, -5, 4};
// Initialize maxSoFar and maxEndingHere to tempChanges[0]
// Your code here

Hint

Set both variables equal to tempChanges[0] to start tracking sums.

3

Implement Kadane's Algorithm loop

Use a for loop with variable i starting from 1 to iterate over tempChanges. Inside the loop, update maxEndingHere to the maximum of tempChanges[i] and maxEndingHere + tempChanges[i]. Then update maxSoFar to the maximum of maxSoFar and maxEndingHere.

DSA Java

int[] tempChanges = {-2, 3, 2, -1, 4, -5, 4};
int maxSoFar = tempChanges[0];
int maxEndingHere = tempChanges[0];
// Add a for loop from i = 1 to tempChanges.length - 1
// Update maxEndingHere and maxSoFar inside the loop
// Your code here

Hint

Use Math.max to update maxEndingHere and maxSoFar inside the loop.

4

Print the maximum subarray sum

Print the value of maxSoFar using System.out.println(maxSoFar);

DSA Java

int[] tempChanges = {-2, 3, 2, -1, 4, -5, 4};
int maxSoFar = tempChanges[0];
int maxEndingHere = tempChanges[0];
for (int i = 1; i < tempChanges.length; i++) {
    maxEndingHere = Math.max(tempChanges[i], maxEndingHere + tempChanges[i]);
    maxSoFar = Math.max(maxSoFar, maxEndingHere);
}
// Print maxSoFar
// Your code here

Hint

Use System.out.println(maxSoFar); to show the result.

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