Java: Find subarray which has the largest sum in a given circular array of integers

Java Array: Exercise-67 with Solution

Write a Java program to find the subarray with the largest sum in a given circular array of integers.

Example:
Input :
nums1 = { 2, 1, -5, 4, -3, 1, -3, 4, -1 }
nums2 = { 1, -2, 3, 0, 7, 8, 1, 2, -3 }
Output:
The sum of subarray with the largest sum is 6
The sum of subarray with the largest sum is 21

Sample Solution:

Java Code:

// Import the necessary Java class.
import java.util.Arrays;

// Define a class named 'solution'.
class solution {
    // Method to find the maximum sum of a subarray within a circular array.
    public static int max_Subarray_Sum_Circular(int[] nums) {
        int n = nums.length;
        int result = nums[0];  // Initialize 'result' with the first element.
        int sum = nums[0];     // Initialize 'sum' with the first element.

        // Iterate through the array starting from the second element.
        for (int i = 1; i < n; i++) {
            // Calculate the maximum of 'sum + nums[i]' and 'nums[i]' (Kadane's algorithm).
            sum = Math.max(sum + nums[i], nums[i]);
            // Update 'result' with the maximum value.
            result = Math.max(result, sum);
        }

        // Create arrays to store right sum and right max.
        int[] right_Sum = new int[n];
        int[] right_Max = new int[n];

        // Initialize the last elements of right sum and right max arrays.
        right_Sum[n - 1] = nums[n - 1];
        right_Max[n - 1] = nums[n - 1];

        // Iterate through the array in reverse order.
        for (int i = n - 2; i >= 0; i--) {
            // Calculate right sum and right max values.
            right_Sum[i] = right_Sum[i + 1] + nums[i];
            right_Max[i] = Math.max(right_Sum[i], right_Max[i + 1]);
        }

        int left_Sum = 0;  // Initialize the left sum.

        // Iterate through the array with a circular view, except the last two elements.
        for (int i = 0; i < n - 2; i++) {
            left_Sum += nums[i];
            // Update 'result' with the maximum of 'left_Sum + right_Max[i + 2]' and the current 'result'.
            result = Math.max(result, left_Sum + right_Max[i + 2]);
        }

        return result;
    }
	
    // Main method to demonstrate finding the maximum sum of a subarray in a circular array.
    public static void main(String[] args) {
        // Initialize two circular arrays.
        int[] nums1 = { 2, 1, -5, 4, -3, 1, -3, 4, -1 };
        int[] nums2 = { 1, -2, 3, 0, 7, 8, 1, 2, -3 };

        // Print the original circular arrays.
        System.out.println("\nOriginal circular array 1: " + Arrays.toString(nums1));
        System.out.println("The sum of subarray with the largest sum is " + max_Subarray_Sum_Circular(nums1));
        System.out.println("\nOriginal circular array 2: " + Arrays.toString(nums2));
        System.out.println("The sum of subarray with the largest sum is " + max_Subarray_Sum_Circular(nums2));
    }
}

Sample Output:

Original circular array: [2, 1, -5, 4, -3, 1, -3, 4, -1]
The sum of subarray with the largest sum is 6

Original circular array: [1, -2, 3, 0, 7, 8, 1, 2, -3]
The sum of subarray with the largest sum is 21

Flowchart:

Java Code Editor:

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