KADANE'S ALGORITHM

 

Maximum Subarray Sum – Kadane’s Algorithm 

Introduction

The maximum subarray sum problem is a classic problem in programming. The goal is to find the maximum possible sum of a contiguous subarray within a given array.

A subarray must contain at least one element and must be continuous.

Problem Statement

Given an array arr[], find the maximum sum of any subarray.

Example

Input:

arr = [2, 3, -8, 7, -1, 2, 3]

Output:

11

Explanation:
Subarray [7, -1, 2, 3] gives the maximum sum = 11

Solution Code

class Solution:
    def maxSubarraySum(self, arr):
        max_sum = arr[0]
        current_sum = arr[0]

        for i in range(1, len(arr)):
            current_sum = max(arr[i], current_sum + arr[i])
            max_sum = max(max_sum, current_sum)

        return max_sum

Approach Used: Kadane’s Algorithm

Idea

At each step, we decide:

  • Either continue the current subarray

  • Or start a new subarray from the current element

How It Works

  1. Initialize:

    • current_sum = arr[0]

    • max_sum = arr[0]

  2. Traverse the array:

    • For each element:

      • Update current_sum:

        • Either take current element alone

        • Or add it to previous sum

      • Update max_sum if needed

  3. Return max_sum

Why This Approach Was Chosen

  • Efficient: Only one pass through the array

  • Handles both positive and negative numbers

  • Avoids checking all subarrays (which is costly)

Alternative Approaches

  • Brute Force (Check all subarrays)
    Time Complexity: O(n²)
     Very slow for large inputs

  • Divide and Conquer
    More complex and less intuitive

Why Kadane’s Algorithm?
Because it provides the best time complexity (O(n)) with simple logic.

Time and Space Complexity

  • Time Complexity: O(n)

  • Space Complexity: O(1)

Important Observation

  • Even if all elements are negative, the algorithm still works

  • It returns the maximum single element in such cases

Conclusion

Kadane’s Algorithm is the most efficient way to solve the maximum subarray sum problem. It simplifies the problem by making local decisions at each step, resulting in a global maximum. This makes it a widely used and important algorithm in problem-solving.

Comments

Post a Comment

Popular posts from this blog

THE DELIVERY MAN

  The Delivery Man – Python List Operations  Introduction Lists in Python are used to store multiple items in a single variable. They are flexible, allowing us to add, remove, update, and manipulate elements easily. In this task, different list operations are performed to simulate a delivery man's workflow. 1. Creating a list and accessing an item items = ["Notebook", "Pencil", "Eraser", "Ruler", "Marker"] print(items[2]) Approach: Indexing Why: Lists use zero-based indexing, so the third item is accessed using index 2. 2. Adding a new item items.append("Glue Stick") print(items) Approach: append() method Why: It adds an item at the end of the list, which is ideal for adding new deliveries. 3. Inserting an item items.insert(2, "Highlighter") print(items) Approach: insert() method Why: Used when we need to add an item at a specific position instead of the end. 4. Removing an item items.remove("Ruler...
Read more

EC2 LAUNCHING

  EC2 Step 1: Launch EC2 Instance Go to: AWS Console --> EC2 --> Launch Instance Configure: Name : my-web-server AMI : Amazon Linux 2 (easy for beginners) Instance Type : t2.micro (free tier) Step 2: Key Pair Create or select a key pair. Step 3: Network Settings  Allow these: SSH (port 22) --> for login  HTTP (port 80) --> for web access Step 4: Launch Instance Click Launch Instance Step 5: Connect to Instance Use: EC2 --> Connect --> EC2 Instance Connect (easiest) OR via terminal: with this command. for this you have to download the pem files while selecting the key pair.  ssh -i your-key.pem ec2-user@<public-ip> Step 6: Install Web Server For Amazon Linux: sudo yum update -y sudo yum install httpd -y Step 7: Start Web Server sudo systemctl start httpd sudo systemctl enable httpd Step 8: Add a Web Page echo "Hello from EC2" | sudo tee /var/www/html/index.html Step 9: Get Public IP Go to EC2 d...
Read more

SORT A LINKED LIST USING MERGE SORT

  Sort a Linked List using Merge Sort Introduction Sorting a linked list efficiently is a common problem in data structures. Unlike arrays, linked lists do not allow direct access to elements, so algorithms like quicksort are not ideal. Merge Sort is the best choice for linked lists because: It does not require random access It works efficiently with node-based structures Problem Statement Given the head of a linked list: Sort the list in ascending order Return the sorted linked list Example Input: 10 -> 30 -> 20 -> 40 -> 60 -> 50 Output: 10 -> 20 -> 30 -> 40 -> 50 -> 60 Solution Code class Solution: def mergeSort(self, head): if not head or not head.next: return head mid = self.getMiddle(head) next_to_mid = mid.next mid.next = None left = self.mergeSort(head) right = self.mergeSort(next_to_mid) return self.merge(left, right) def getMiddle(self,...
Read more