# Maximum circular subarray sum of size K

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 = 32

Input: arr = {8, 2, 5, 9}, k = 4
Output:
max circular sum = 24
start index = 0
end index = 3

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `using` `namespace` `std; ` ` `  `// Function to calculate ` `// maximum sum ` `void` `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 Code ` `int` `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 k ` ` `  `import` `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 k ` `using` `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 `

Output:

```max circular sum = 32
start index = 9
end index = 1
```

Time Complexity:

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