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C++ Program for Number of local extrema in an array

Assume we have an n-element array A. A local minimum is an element of this array A[i] that is strictly smaller than both of its neighbours. It will also be the local maximum if it is strictly larger than its neighbours. Because A[0] and A[n-1] have just one neighbor, they are not maximum or minimum. The number of local extrema in the provided array must be determined.

So, if A = [1, 5, 2, 5], the output will be 2, since 5 at A[1] is a local maximum and 2 at A[2] is a local minimum.

Approach: To calculate the number of extrema, we must first determine if an element is maxima or minima, that is, whether it is more than or less than both of its neighbors. Cycle over the array, checking each element's likelihood of becoming an extrema.

It is worth noting that a[0] and a[n-1] each have precisely one neighbor and are neither minima nor maxima.

Example:

Filename: Extreme.cpp

// Program to find the local extreme value
#include <bits/stdc++.h>
using namespace std;

// function for finding the loacl maximum value
int extrema(int arr[], int num)
{
	int c = 0;

	// ierate a loop upto num-1 times
	for (int i = 1; i < num - 1; i++)
	{

		// Only one criterion will be true at any one time: arr[i] must be bigger than or less than its neighbors.
		// If arr[i] is bigger than both of its neighbors, add 1 to x.
		c += (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]);
 //If a[i] is less than both of its // neighbors, then add 1 to x.
		c += (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]);
	}

	return c;
}

// Main
int main()
{
	int arr[] = { 2, 5, 1, 6 };
	int num = sizeof(arr) / sizeof(arr[0]);
	cout << extrema(arr, num);
	return 0;
}

Output:

Complexity Analysis:

Time complexity: O(n), where n is the length of the input array. It is due to the fact that a for loop executes from 1 to n.

Space Complexity: O(1) since no additional space was utilized.

Next TopicC++ Program to concatenate two strings using Operator Overloading

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