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Find the Subarray of given length with Least Average

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Dynamic Programming, Longest Bitonic SubSequence

Given an array and an input integer X, write a program to find the subarray of length X with least/minimum average

Prints the starting and ending indexes of the subarray which has the least average.

Example

INPUT :
arr[] = {3, 5, 1, 7, 6}
X = 2

OUTPUT :
subarray is between index 1 and 2

In the above example we can see that the sum of 5 and  1 is the least.

Time Complexity : O(n)

In this method we use the idea of sliding window of size X.

Algorithm

1. Initialize index =0, which is the starting index of the subarray with least average

2. Find the sum of first X elements and store it in sum variable

3. Initialize least_sum to the above sum variable

4. Traverse the array from (X+1)th index till end of the array
    a. For every element arr[i], calculate sum = sum + arr[i] -arr[i-X]
    b. If sum < least_sum, then make index = (i-X+1) and least_sum =sum.

5. Print the index and the index + X -1 as the starting and ending of the subarray with least average.

C++ Program

#include <bits/stdc++.h>
using namespace std;
int lavgSubarray(int arr[],int X,int n)
{
	int index, sum =0;  //index is for keeping track of starting of least avg subarrray
						//sum is to calculate the sum of all subarays
	for (int i = 0; i < X; ++i)
	{
		sum = sum + arr[i];
	}
	int least_sum = sum;

	for (int i = X; i < n; ++i) //moving the window of size X.
	{
		sum = sum + arr[i] - arr[i-X];
		if(sum<least_sum)
		{
			least_sum = sum;
			index = (i-X+1);
		}
	}
	cout<<"subarray in between indexes "<<index<<", "<<index+X-1<<" has least average";
}
int main()
{
	int arr[] = {3, 5, 1, 7, 6};
	int X= 2;					//subarray length
	int n = sizeof(arr)/sizeof(arr[0]);
	lavgSubarray(arr,X,n);
}
Try It


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