Q55 Max sum of M non-overlapping subarrays of size K - GeeksforGeeks (memoization)

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Sat Apr 01 2023 12:58:28 GMT+0000 (Coordinated Universal Time)

Saved by @Ayush_dabas07

// Java program to find Max sum
// of M non-overlapping subarray
// of size K in an Array

import java.io.*;

class GFG
{
// calculating presum of array.
// presum[i] is going to store
// prefix sum of subarray of
// size k beginning with arr[i]
static void calculatePresumArray(int presum[],
								int arr[],
								int n, int k)
{
	for (int i = 0; i < k; i++)
	presum[0] += arr[i];

	// store sum of array index i to i+k
	// in presum array at index i of it.
	for (int i = 1; i <= n - k; i++)
	presum[i] += presum[i - 1] + arr[i + k - 1] -
								arr[i - 1];
}

// calculating maximum sum of
// m non overlapping array
static int maxSumMnonOverlappingSubarray(int presum[],
										int m, int size,
										int k, int start)
{
	// if m is zero then no need
	// any array of any size so
	// return 0.
	if (m == 0)
		return 0;

	// if start is greater then the
	// size of presum array return 0.
	if (start > size - 1)
		return 0;

	int mx = 0;

	// if including subarray of size k
	int includeMax = presum[start] +
			maxSumMnonOverlappingSubarray(presum,
					m - 1, size, k, start + k);

	// if excluding element and searching
	// in all next possible subarrays
	int excludeMax =
			maxSumMnonOverlappingSubarray(presum,
						m, size, k, start + 1);

	// return max
	return Math.max(includeMax, excludeMax);
}

// Driver code
public static void main (String[] args)
{
	int arr[] = { 2, 10, 7, 18, 5, 33, 0 };
	int n = arr.length;
	int m = 3, k = 1;
	int presum[] = new int[n + 1 - k] ;
	calculatePresumArray(presum, arr, n, k);
	
	// resulting presum array
	// will have a size = n+1-k
	System.out.println(maxSumMnonOverlappingSubarray(presum,
										m, n + 1 - k, k, 0));
}
}

// This code is contributed by anuj_67.

https://www.geeksforgeeks.org/max-sum-of-m-non-overlapping-subarrays-of-size-k/

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