Kadane's Algorithm Explained: Optimal Approach for Maximum Subarray Sum (DSA Guide)

Welcome to our Data Structures and Algorithms (DSA) Series by Drag Coder In this tutorial, we’ll deep-dive into Kadane's Algorithm, one of the most important and frequently asked topics in coding interviews and competitive programming.

Kadane’s Algorithm offers an efficient solution to the Maximum Subarray Sum problem using dynamic programming principles. We’ll start from the basics, explore brute force and optimized approaches, and finally break down Kadane's Algorithm step-by-step with examples and code. Let’s begin!

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📌 What is a Subarray in DSA?

Before diving into the maximum subarray sum, it’s essential to understand what a subarray is.

A subarray is a contiguous portion of an array. For instance, given an array [1, 2, 3, 4, 5], valid subarrays include:

• Single elements like [1], [3]

• Multiple elements like [1, 2, 3], [4, 5]

• The entire array [1, 2, 3, 4, 5]

💡 Total Subarrays Formula: For an array of size n, the number of subarrays = n * (n + 1) / 2.

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🔍 Problem Statement: Maximum Subarray Sum

Given an array of integers, the task is to find the contiguous subarray with the largest sum.

Example:

Input: [3, -4, 5, 7, -1, 8, -8]
Output: 19 (Subarray: [5, 7, -1, 8])

This is a classic array problem in DSA, often solved using Kadane's Algorithm for optimal performance.

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🐌 Brute Force Approach – Time Complexity: O(n³)

The naive solution involves:

1. Generating all possible subarrays

2. Calculating the sum of each

3. Tracking the maximum sum encountered

This method is inefficient for large arrays due to its cubic time complexity, making it unsuitable for competitive programming or interviews.

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🔧 Improved Brute Force – Time Complexity: O(n²)

By storing intermediate results and avoiding redundant computations, we can optimize to O(n²). This approach:

• Fixes the start index

• Iterates through possible end indices

• Updates a running sum instead of recalculating

Still, this isn’t scalable for very large arrays or real-time systems.

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⚡ Kadane’s Algorithm – Optimal Linear Time Solution (O(n))

Now, let’s explore the most efficient way to solve the maximum subarray sum problem: Kadane’s Algorithm.

✅ Key Idea:

Kadane’s Algorithm uses a single pass through the array and tracks:

• currSum: the current subarray sum

• maxSum: the highest subarray sum found so far

If currSum becomes negative, we reset it to zero—because any negative subarray will reduce the total sum going forward.

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💡 Kadane’s Algorithm Example Walkthrough

Input: [3, -4, 5, 7, -1, 8, -8]

Step	currSum	maxSum
+3	3	3
-4	-1 → 0	3
+5	5	5
+7	12	12
-1	11	12
+8	19	19
-8	11	19

Result: Maximum Subarray Sum = 19

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🚫 Handling Edge Cases: All Negative Numbers

For arrays like [-1, -2, -3, -4], resetting currSum to 0 won’t work correctly.

Fix:
Initialize maxSum with the smallest possible integer (INT_MIN) and only reset currSum after updating maxSum.

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🧑‍💻 Kadane's Algorithm Code (C++ Style Pseudocode)

cpp

int maxSubArraySum(vector<int> &nums) {
    int currSum = 0;
    int maxSum = INT_MIN;

    for (int num : nums) {
        currSum += num;
        maxSum = max(maxSum, currSum);
        if (currSum < 0) currSum = 0;
    }
    return maxSum;
}

⚙️ Time Complexity: O(n)
📦 Space Complexity: O(1)

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🧠 Why Kadane’s Algorithm Works (Dynamic Programming Insight)

Kadane’s Algorithm leverages the optimal substructure property of dynamic programming:

• For each element, decide whether to:

  • Extend the current subarray

  • Start a new subarray from the current index

This bottom-up approach builds the solution using previously solved subproblems.

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📚 Practice Problems & Further Learning

To master Kadane's Algorithm, solve similar problems on coding platforms like:

• Codeforces, GFG, HackerRank — under topics: Arrays, Kadane's Algorithm, Dynamic Programming

Also, understanding Kadane’s Algorithm helps tackle advanced DSA problems like:

• Maximum circular subarray sum

• Subarrays with given sum

• Longest subarray problems

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🏁 Conclusion: Mastering Kadane’s Algorithm for Interviews

The Maximum Subarray Sum problem is fundamental to understanding how to optimize array traversal problems using Kadane's Algorithm.

🚀 Key Takeaways:

• Kadane’s Algorithm runs in O(n) time and is ideal for large datasets.

• It introduces dynamic programming concepts in a simple, intuitive way.

• This problem is a favorite in coding interviews—a must-practice!

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📌 Stay tuned for more DSA tutorials by Shradha Ma’am as we cover more dynamic programming problems, array-based algorithms, and essential interview questions.

💬 Have a question? Drop it in the comments!
🧠 Keep practicing, keep improving. Happy coding!