 1624438320

# Kadane’s Algorithm Explained with Examples

Given an array, the algorithm to find the maximum subarray sum is called Kadane’s Algorithm.

2

The array can be of any dimension. For simplicity, let’s start with a 1D array.

### Let’s take a 0-indexed array:

arr: [5, 7, -3, 2, 9, 6, 16, 22, 21, 29, -14, 10, 12]

We can start the subarray at any point. Let’s say we start at index 2 i.e., arr = -3.

Now, at index 3, the sum will be -3 + 2 = -1.

If we started the subarray at index 3 instead, the sum at index 3 is 2, which is greater than the previous sum.

So we have two choices: either start at the current index or add the current element to the previous sum.

And since we want the maximum subarray sum, we add the current element to the maximum of 0 and previous sum (zero here denotes that we’re starting anew from the current element).

### This Problem Falls Under the Dynamic Programming Paradigm

Let’s take an array dp[] where each dp[i] denotes maximum subarray sum ending at index i (including i).

#algorithms #mathematics #math #learning #indexes

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## Kadane’s Algorithm: Gateway to Dynamic Programming

In the process of learning algorithms, there are many case-specific solutions we need to learn. Not all can teach us broadly applicable lessons, though they’re still good to know. A few of these problems, however, are especially good for broadening our thinking and can give us tools that we can use in a broad spectrum of cases.
The Maximum Subarray problem was one of these eye-opening problems for me. The solution, using Kadane’s Algorithm, is a great introduction to dynamic programming and I think taking a little extra time on this problem is worthwhile. After studying this problem I knew how to look for much more efficient solutions rather than always writing iterative solutions with inefficient nested loops. It’ll show you how to take a solution with exponential time complexity and take it to linear time complexity. 1624438320

## Kadane’s Algorithm Explained with Examples

Given an array, the algorithm to find the maximum subarray sum is called Kadane’s Algorithm.

2

The array can be of any dimension. For simplicity, let’s start with a 1D array.

### Let’s take a 0-indexed array:

arr: [5, 7, -3, 2, 9, 6, 16, 22, 21, 29, -14, 10, 12]

We can start the subarray at any point. Let’s say we start at index 2 i.e., arr = -3.

Now, at index 3, the sum will be -3 + 2 = -1.

If we started the subarray at index 3 instead, the sum at index 3 is 2, which is greater than the previous sum.

So we have two choices: either start at the current index or add the current element to the previous sum.

And since we want the maximum subarray sum, we add the current element to the maximum of 0 and previous sum (zero here denotes that we’re starting anew from the current element).

### This Problem Falls Under the Dynamic Programming Paradigm

Let’s take an array dp[] where each dp[i] denotes maximum subarray sum ending at index i (including i).

#algorithms #mathematics #math #learning #indexes 1626459600

## Introduction

Genetic Algorithm (GA) can sometimes be a bit difficult to understand !! :(

In this article, I’ll help you understand GA with a simple example. So don’t worry. Hang tight. All will be clear soon !! :)

Below are the steps to be followed to solve any optimization problem with the help of GA.

• Step 1- Choose an encoding technique, a selection operator, and a crossover operator
• Step 2- Choose a population size
• Step 3- Randomly choose the initial population
• Step 4- Select parental chromosomes
• Step 5- Perform Crossover (random crossover points)
• Step 6- Evaluation of offsprings
• Step 7- Repeat the process

Now we’ll see an example of a simple optimization problem and try to solve it with the help of the steps mentioned above.

#evolutionary-algorithms #data-science #genetic-algorithm #example 1625696040

## Kadane's Algorithm | Largest Sum Contiguous Subarray | DSA-One Course #13 | Anuj Bhaiya

Hey guys, In this video, we’ll be solving Largest Sum Contiguous Subarray Problem using Kadane’s Algorithm.

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