Given an array arr of size N and an integer K, the task is to find the maximum sum subarray of size k among all contiguous sub-array (considering circular subarray also).
Examples:
Input: arr = {18, 4, 3, 4, 5, 6, 7, 8, 2, 10}, k = 3
Output:
max circular sum = 32
start index = 9
end index = 1
Explanation:
Maximum Sum = 10 + 18 + 4 = 32Input: arr = {8, 2, 5, 9}, k = 4
Output:
max circular sum = 24
start index = 0
end index = 3
Approach:
- Iterate the loop till (n + k) times and
- Take (i % n) to handle the case when the array index becomes greater than n.
Below is the implementation of above approach:
C++
// C++ program to find maximum circular// subarray sum of size k#include <bits/stdc++.h>using namespace std;// Function to calculate// maximum sumvoid maxCircularSum(int arr[], int n, int k){ // k must be greater if (n < k) { cout << "Invalid"; return; } int sum = 0, start = 0, end = k - 1; // calculate the sum of first k elements. for (int i = 0; i < k; i++) { sum += arr[i]; } int ans = sum; for (int i = k; i < n + k; i++) { // add current element to sum // and subtract the first element // of the previous window. sum += arr[i % n] - arr[(i - k) % n]; if (sum > ans) { ans = sum; start = (i - k + 1) % n; end = i % n; } } cout << "max circular sum = " << ans << endl; cout << "start index = " << start << "\nend index = " << end << endl;}// Driver Codeint main(){ int arr[] = { 18, 4, 3, 4, 5, 6, 7, 8, 2, 10 }; int n = sizeof(arr) / sizeof(arr[0]); int k = 3; maxCircularSum(arr, n, k); return 0;} |
Java
// Java program to find maximum circular // subarray sum of size kimport java.util.*;class GFG{ // Function to calculate // maximum sum static void maxCircularSum(int[] arr, int n, int k) { // k must be greater if (n < k) { System.out.println("Invalid"); return; } int sum = 0, start = 0, end = k - 1; // calculate the sum of first k elements. for (int i = 0; i < k; i++) sum += arr[i]; int ans = sum; for (int i = k; i < n + k; i++) { // add current element to sum // and subtract the first element // of the previous window. sum += arr[i % n] - arr[(i - k) % n]; if (sum > ans) { ans = sum; start = (i - k + 1) % n; end = i % n; } } System.out.println("max circular sum = " + ans); System.out.println("start index = " + start + "\nend index = " + end); } // Driver Code public static void main(String[] args) { int[] arr = { 18, 4, 3, 4, 5, 6, 7, 8, 2, 10 }; int n = arr.length; int k = 3; maxCircularSum(arr, n, k); }}// This code is contributed by// sanjeev2552 |
Python3
# Python3 program to find maximum circular # subarray sum of size k # Function to calculate # maximum sum def maxCircularSum(arr, n, k) : # k must be greater if (n < k) : print("Invalid"); return; sum = 0; start = 0; end = k - 1; # calculate the sum of first k elements. for i in range(k) : sum += arr[i]; ans = sum; for i in range(k, n + k) : # add current element to sum # and subtract the first element # of the previous window. sum += arr[i % n] - arr[(i - k) % n]; if (sum > ans) : ans = sum; start = (i - k + 1) % n; end = i % n; print("max circular sum = ",ans); print("start index = ", start, "\nend index = ", end); # Driver Code if __name__ == "__main__" : arr = [ 18, 4, 3, 4, 5, 6, 7, 8, 2, 10 ]; n = len(arr); k = 3; maxCircularSum(arr, n, k); # This code is contributed by AnkitRai01 |
C#
// C# program to find maximum circular // subarray sum of size kusing System;class GFG{ // Function to calculate // maximum sum static void maxCircularSum(int[] arr, int n, int k) { // k must be greater if (n < k) { Console.WriteLine("Invalid"); return; } int sum = 0, start = 0, end = k - 1; // calculate the sum of first k elements. for (int i = 0; i < k; i++) sum += arr[i]; int ans = sum; for (int i = k; i < n + k; i++) { // add current element to sum // and subtract the first element // of the previous window. sum += arr[i % n] - arr[(i - k) % n]; if (sum > ans) { ans = sum; start = (i - k + 1) % n; end = i % n; } } Console.WriteLine("max circular sum = " + ans); Console.WriteLine("start index = " + start + "\nend index = " + end); } // Driver Code public static void Main(String[] args) { int[] arr = { 18, 4, 3, 4, 5, 6, 7, 8, 2, 10 }; int n = arr.Length; int k = 3; maxCircularSum(arr, n, k); }}// This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript program to find maximum circular// subarray sum of size k// Function to calculate// maximum sumfunction maxCircularSum(arr, n, k) { // k must be greater if (n < k) { document.write("Invalid"); return; } let sum = 0, start = 0, end = k - 1; // Calculate the sum of first k elements. for(let i = 0; i < k; i++) { sum += arr[i]; } let ans = sum; for(let i = k; i < n + k; i++) { // Add current element to sum // and subtract the first element // of the previous window. sum += arr[i % n] - arr[(i - k) % n]; if (sum > ans) { ans = sum; start = (i - k + 1) % n; end = i % n; } } document.write("max circular sum = " + ans + "<br>"); document.write("start index = " + start + "<br>end index = " + end + "<br>");}// Driver Codelet arr = [ 18, 4, 3, 4, 5, 6, 7, 8, 2, 10 ];let n = arr.lengthlet k = 3;maxCircularSum(arr, n, k);// This code is contributed by _saurabh_jaiswal</script> |
Output:
max circular sum = 32 start index = 9 end index = 1
Time Complexity:
Auxiliary Space: O(1), no extra space is required, so it is a constant.
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