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

Kadane's Algorithm Maximum Subarray

📖 Scenario: You are analyzing daily temperature changes to find the longest period of warming days. You have a list of temperature changes (positive or negative) for consecutive days. You want to find the maximum sum of any continuous sequence of days, which represents the strongest warming trend.

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

📋 What You'll Learn

Create a vector called temp_changes with the exact values: {-2, 1, -3, 4, -1, 2, 1, -5, 4}

Create an integer variable called max_sum initialized to 0

Use a for loop with index i to implement Kadane's Algorithm to find the maximum subarray sum

Print the value of max_sum as the final output

💡 Why This Matters

🌍 Real World

Finding the strongest warming trend in temperature changes helps meteorologists understand climate patterns and predict weather changes.

💼 Career

Kadane's Algorithm is a classic technique used in software engineering and data analysis roles to efficiently solve maximum subarray problems, common in financial data, signal processing, and more.

1

Create the temperature changes vector

Create a vector of integers called temp_changes with these exact values: {-2, 1, -3, 4, -1, 2, 1, -5, 4}

DSA C++

#include 
#include 

int main() {
    // Create vector temp_changes with values -2, 1, -3, 4, -1, 2, 1, -5, 4
    // Your code here

    return 0;
}

Hint

Use std::vector<int> and initialize it with the given values inside curly braces.

2

Initialize the max_sum variable

Create an integer variable called max_sum and set it to 0

DSA C++

#include 
#include 

int main() {
    std::vector temp_changes = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    // Create int max_sum and set to 0
    // Your code here

    return 0;
}

Hint

Declare an integer variable named max_sum and assign it the value 0.

3

Implement Kadane's Algorithm to find maximum subarray sum

Create an integer variable called current_sum and set it to 0. Then use a for loop with index i from 0 to temp_changes.size() to add temp_changes[i] to current_sum. If current_sum becomes less than 0, reset it to 0. Update max_sum to be the maximum of max_sum and current_sum inside the loop.

DSA C++

#include 
#include 

int main() {
    std::vector temp_changes = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    int max_sum = 0;
    // Implement Kadane's Algorithm using current_sum and for loop
    // Your code here

    return 0;
}

Hint

Use a variable current_sum to keep track of the current subarray sum. Reset it to 0 if it goes negative. Update max_sum whenever current_sum is bigger.

4

Print the maximum subarray sum

Write a std::cout statement to print the value of max_sum followed by a newline.

DSA C++

#include 
#include 

int main() {
    std::vector temp_changes = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    int max_sum = 0;
    int current_sum = 0;
    for (int i = 0; i  max_sum) {
            max_sum = current_sum;
        }
    }
    // Print max_sum
    // Your code here

    return 0;
}

Hint

Use std::cout << max_sum << std::endl; to print the result.

Practice

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

easy

A. The total sum of all elements

B. The minimum element in the array

C. The maximum product of any two 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 a contiguous subarray within a one-dimensional array of numbers.

2. Step 2: Compare options with the algorithm's purpose

   Options A, B, and D do not describe the main goal of Kadane's Algorithm. Only The maximum sum of a contiguous subarray correctly states it finds the maximum sum of a contiguous subarray.

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 finds max sum in a continuous slice [OK]

Common Mistakes:

• Confusing maximum sum with maximum product
• Thinking it finds minimum element
• Assuming it sums all elements

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

easy

A. int max_so_far = INT_MIN, max_ending_here = 0;

B. int max_so_far = INT_MAX, max_ending_here = INT_MAX;

C. int max_so_far = 0, max_ending_here = INT_MIN;

D. int max_so_far = 0, max_ending_here = 0;

Solution

1. Step 1: Understand variable roles in Kadane's Algorithm

   max_so_far stores the maximum sum found so far, so it should start very low (INT_MIN) to allow any sum to replace it. max_ending_here tracks the current subarray sum and starts at 0.

2. Step 2: Check each option's initialization

   int max_so_far = INT_MIN, max_ending_here = 0; correctly initializes max_so_far to INT_MIN and max_ending_here to 0. Other options either start max_so_far at 0 or INT_MAX, which can cause incorrect results.

3. Final Answer:

   int max_so_far = INT_MIN, max_ending_here = 0; -> Option A

4. Quick Check:

   max_so_far = INT_MIN, max_ending_here = 0 [OK]

Hint: Start max_so_far at INT_MIN to handle negatives [OK]

Common Mistakes:

• Initializing max_so_far to 0 causes wrong results with negatives
• Setting max_ending_here to INT_MIN breaks logic
• Using INT_MAX causes overflow issues

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

int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
int n = 9;
int max_so_far = INT_MIN, max_ending_here = 0;
for (int i = 0; i < n; i++) {
    max_ending_here += arr[i];
    if (max_so_far < max_ending_here)
        max_so_far = max_ending_here;
    if (max_ending_here < 0)
        max_ending_here = 0;
}
std::cout << max_so_far << std::endl;

medium

A. 6

B. 7

C. 5

D. 4

Solution

1. Step 1: Trace Kadane's Algorithm on the array

   Iterate through arr: max_ending_here and max_so_far update as follows:
   - i=0: max_ending_here=-2, max_so_far=-2, reset max_ending_here=0
   - i=1: max_ending_here=1, max_so_far=1
   - i=2: max_ending_here=-2, max_so_far=1, reset max_ending_here=0
   - i=3: max_ending_here=4, max_so_far=4
   - i=4: max_ending_here=3, max_so_far=4
   - i=5: max_ending_here=5, max_so_far=5
   - i=6: max_ending_here=6, max_so_far=6
   - i=7: max_ending_here=1, max_so_far=6
   - i=8: max_ending_here=5, max_so_far=6

2. Step 2: Identify maximum subarray sum

   The maximum sum found is 6, which corresponds to subarray [4, -1, 2, 1].

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Max subarray sum = 6 [OK]

Hint: Add elements, reset sum if negative, track max [OK]

Common Mistakes:

• Not resetting max_ending_here when negative
• Confusing max_so_far with current sum
• Miscounting subarray sums

4. Identify the bug in this Kadane's Algorithm implementation and select the fix:

int maxSubArraySum(int arr[], int n) {
    int max_so_far = 0, max_ending_here = 0;
    for (int i = 0; i < n; i++) {
        max_ending_here += arr[i];
        if (max_so_far < max_ending_here)
            max_so_far = max_ending_here;
        if (max_ending_here < 0)
            max_ending_here = 0;
    }
    return max_so_far;
}

medium

A. Remove resetting max_ending_here to 0

B. Initialize max_ending_here to INT_MIN instead of 0

C. Initialize max_so_far to INT_MIN instead of 0

D. Change loop to start from i = 1

Solution

1. Step 1: Analyze initialization impact on negative arrays

   Starting max_so_far at 0 causes incorrect results if all array elements are negative, as max_so_far will never update to a negative sum.

2. Step 2: Fix initialization to handle all negative values

   Setting max_so_far to INT_MIN allows it to update correctly even if all elements are negative, ensuring the maximum subarray sum is found.

3. Final Answer:

   Initialize max_so_far to INT_MIN instead of 0 -> Option C

4. Quick Check:

   max_so_far = INT_MIN fixes negative-only arrays [OK]

Hint: Use INT_MIN for max_so_far to handle negatives [OK]

Common Mistakes:

• Leaving max_so_far at 0 causes wrong max for negatives
• Removing reset breaks algorithm logic
• Changing loop start misses first element

5. Given an array with all negative numbers: int arr[] = {-8, -3, -6, -2, -5, -4}; What is the maximum subarray sum using Kadane's Algorithm?

hard

A. 0

B. -2

C. -3

D. -8

Solution

1. Step 1: Understand Kadane's behavior with all negative numbers

   When all numbers are negative, resetting max_ending_here to 0 causes the algorithm to miss the largest (least negative) number. Proper initialization with max_so_far = INT_MIN helps track the max single element.

2. Step 2: Identify the maximum single element

   The largest number in the array is -2, which is the maximum subarray sum since any longer subarray sum will be smaller.

3. Final Answer:

   -2 -> Option B

4. Quick Check:

   Max single negative element = -2 [OK]

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

Common Mistakes:

• Assuming max sum is 0 by resetting sums
• Ignoring single element max in negative arrays
• Confusing minimum with maximum