Count the number of non-increasing subarrays in C++

Given an array arr[] containing positive integers. The goal is to find the number of subarrays of length at least 1 which are non−increasing. If arr[]= {1,3,2}, then subarrays will be {1}, {2}, {3}, {3,2}. Count is 4.

For Example

Input

arr[] = {5,4,5}

Output

Count of number of non-increasing subarrays are: 7

Explanation

The subarrays will be −
{5}, {4}, {5}, {5,4}

Input

arr[] = {10,9,8,7}

Output

Count of number of non−increasing subarrays are − 10

Explanation

The subarrays will be −
{10}, {9}, {8}, {7}, {10,9}, {9,8}, {8,7}, {10,9,8}, {9,8,7}, {10,9,8,7}

Approach used in the below program is as follows −

In this approach, we will use the fact that if elements between indexes i and j in arr[] are not non−increasing then elements between indexes i to j+1, i to j+2….i to j+n−1 can never be non increasing so keep incrementing the length of this subarray till elements are non-increasing. If any lesser element is found arr[j]<arr[j−1] then add len*(len+1)/2 ( subarrays of current non−increasing subarray containing len elements ) to count such subarrays and reset the length of the subarray to 1.

• Take an integer array arr[].

• Function subarrays(int arr[], int size) takes the array and its size and returns the count of the number of non-increasing subarrays.

• Take the initial count as 0 and length of smallest subarray as temp=1.

• Traverse arr[] using for loop, if arr[i + 1] <= arr[i] then increment temp as subarray is non−increasing.

• Otherwise add (temp + 1) * temp) / 2 to count for number of subrrays of subarray of length temp which is non−increasing.

• Set temp=1 for new subarray.

• At the end of all loops, if length temp>1 again add (temp + 1) * temp) / 2 to count for last subarray.

• Return count as result.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int subarrays(int arr[], int size){
   int count = 0;
   int temp = 1;
   for(int i = 0; i < size − 1; ++i){
      if (arr[i + 1] <= arr[i]){
         temp++;
      } else {
         count += (((temp + 1) * temp) / 2);
         temp = 1;
      }
   }
   if(temp > 1){
      count += (((temp + 1) * temp) / 2);
   }
   return count;
}
int main(){
   int arr[] = {2, 6, 1, 8, 3};
   int size = sizeof(arr) / sizeof(arr[0]);
   cout<<"Count of number of non−increasing subarrays are: "<<subarrays(arr, size);
   return 0;
}

Output

If we run the above code it will generate the following output −

Count the number of non-increasing subarrays are: 7