Kadane’s Algorithm: Find the maximum subarray sum in an array.

This article will talk about Kadane’s algorithm, which is a straightforward and effective method for finding the highest sum of a subarray within an array. Kadane’s algorithm falls under dynamic programming, breaking down the problem into smaller parts and solving them step by step.

What is the Kadanes algorithm?

Kadane’s algorithm works by maintaining two variables: a running sum and a maximum sum. The running sum starts at 0, and the maximum sum is initialized to the smallest possible value. As we iterate through the array, we add the current element to the running sum. If the running sum is negative, we reset it to 0. If the running sum is greater than the maximum sum, we update the maximum sum. At the end of the loop, the maximum sum will contain the maximum subarray sum.

Example 1:

Input: arr = [-2,1,-3,4,-1,2,1,-5,4] 

Output: 6 

Explanation: [4,-1,2,1] has the largest sum = 6. 

Examples 2: 

Input: arr = [1] 

Output: 1 

Explanation: An array has only one element, which is a positive sum of 1.

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Pseudocode

Time and space complexity

The time complexity of Kadane’s algorithm is O(n), where n is the length of the array. This is because the algorithm iterates through the array once, and each iteration takes constant time. The space complexity of Kadane’s algorithm is O(1), as it only uses two variables to store the running sum and the maximum sum.

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Practical Applications in Problem-Solving

Kadane’s algorithm can be used to solve a variety of problems, including:

• Finding the maximum subarray sum in an array
• Finding the maximum product subarray in an array
• Finding the maximum contiguous increasing subsequence in an array
• Finding the maximum contiguous decreasing subsequence in an array

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Kadanes algorithm in Java for beginners

Implementing Kadane’s Algorithm in Java:

public class Kadane {

    public static int kadane(int[] array) {
        int runningSum = 0;
        int maxSum = Integer.MIN_VALUE;
        for (int i = 0; i < array.length; i++) {
            runningSum = Math.max(runningSum + array[i], array[i]);
            maxSum = Math.max(maxSum, runningSum);
        }
        return maxSum;
    }

    public static void main(String[] args) {
        int[] array = {-2, -3, 4, -1, -2, 1, 5, -3};
        System.out.println(kadane(array));
    }
}

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Powerful Tool in Competitive Programming

Kadane’s algorithm is a popular algorithm in competitive programming, as it is a simple and efficient way to solve a variety of problems. The algorithm is also relatively easy to implement, which makes it a good choice for beginners.

Impress Interviewers with Kadane’s Algorithm

Kadane’s algorithm is a common interview question for software engineers, as it is a good way to assess a candidate’s knowledge of dynamic programming. The algorithm is also relatively easy to explain, which makes it a good choice for whiteboard interviews.

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Conclusion

The Kadanes algorithm is a simple and efficient algorithm for finding the maximum subarray sum in an array. The algorithm is easy to understand and implement, and it is a popular choice for competitive programming and interview questions.

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If you want to solve the problem, visit leetcode.