Maximum size of sub-array that satisfies the given condition in C++ program

In this problem, we are given an array arr[] of n integers. Our task is to create a program to find the maximum size of sub-array that satisfies the given condition.

Problem Description − We need to find the length of largest subarray that satisfies any one of the below condition,

• arr[k] > arr[k+1], if k is odd and arr[k] < arr[k+1], if k is even. For all elements of the subarray.

• arr[k] < arr[k+1], if k is odd and arr[k] > arr[k+1], if k is even. For all elements of the subarray.

Here, k is the index of the element of the subarray in arr[].

Let’s take an example to understand the problem,

Input

arr[] = {7, 3, 1, 5, 4, 2, 9}

Output

4

Explanation

The subarray {3, 1, 5, 4} satisfies the condition 1.
k = 1(odd), arr[k] > arr[k+1], 3 > 1
k = 2(even), arr[k] < arr[k+1], 1 < 5
k = 3(odd), arr[k] > arr[k+1], 5 > 4

Solution Approach

We can see from the example that for any of the conditions to be true. The subarray should have alternate greater-smaller elements i.e. if 1st > 2nd, then 2nd > 3rd, and so on.

Now, for ease of calculation, we will create a relation array indicating this relationship. The following is how we will be tailoring the relation array,

If arr[i] == arr[i + 1],relArr[i] = ‘E’
If arr[i] > arr[i + 1],relArr[i] = ‘G’
If arr[i] < arr[i + 1],relArr[i] = ‘S’

Using this array we can easily find the max subarray size. Subarray to be considered will have alternate ‘G’ and ‘S’.

Example

Program to illustrate the working of our solution,

#include<iostream>
using namespace std;
char findRel(int a, int b) {
   if(a > b)
      return 'G';
   else if(a < b)
      return 'S';
   return 'E';
}
int calcMaxSubArray(int arr[], int n) {
   int maxLen = 1;
   int len = 1;
   char c = findRel(arr[0], arr[1]);
   for(int i = 1; i <= n−1; i++){
      if(c == 'S' && findRel(arr[i], arr[i + 1]) == 'G')
         len++;
      else if(c == 'G' && findRel(arr[i], arr[i + 1]) == 'S')
         len++;
      else {
         if(maxLen < (len + 1))
            maxLen = (len + 1);
         len = 1;
      }
      c = findRel(arr[i], arr[i+1]);
   }
   return maxLen;
}
int main() {
   int arr[] = {7, 3, 1, 5, 4, 2, 9};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout<<"The maximum size of sub−array that satisfies the given
   condition is "<<calcMaxSubArray(arr, n);
}

Output

The maximum size of sub-array that satisfies the given condition is 4