Given an array of integers arr[], the task is to count the number of sub-arrays such that the average of elements present in the sub-array is greater than the average of elements that are not present in the sub-array.
Examples:
Input: arr[] = {6, 3, 5}
Output: 3
The sub-arrays are {6}, {5} and {6, 3, 5} because their averages
are greater than {3, 5}, {6, 3} and {} respectively.
Input: arr[] = {2, 1, 4, 1}
Output: 5
Approach: The problem can be solved easily by calculating the prefix sum array of the given array. The ith element of the prefix sum array will contain sum of elements up to i. So, the sum of elements between any two indexes i and j can be found using the prefix sum array. Using a nested loop, find all the possible sub-arrays such that its average sum is greater than average of elements not present in the array.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function to return the count of sub-arrays // such that the average of elements present // in the sub-array is greater than the // average of the elements not present // in the sub-array int countSubarrays( int a[], int n)
{ // Initialize the count variable
int count = 0;
// Initialize prefix sum array
int pre[n + 1] = { 0 };
// Preprocessing prefix sum
for ( int i = 1; i < n + 1; i++) {
pre[i] = pre[i - 1] + a[i - 1];
}
for ( int i = 1; i < n + 1; i++) {
for ( int j = i; j < n + 1; j++) {
// Calculating sum and count
// to calculate averages
int sum1 = pre[j] - pre[i - 1], count1 = j - i + 1;
int sum2 = pre[n] - sum1, count2 = ((n - count1) == 0) ? 1 : (n - count1);
// Calculating averages
int includ = sum1 / count1;
int exclud = sum2 / count2;
// Increment count if including avg
// is greater than excluding avg
if (includ > exclud)
count++;
}
}
return count;
} // Driver code int main()
{ int arr[] = { 6, 3, 5 };
int n = sizeof (arr) / sizeof (arr[0]);
cout << countSubarrays(arr, n);
return 0;
} |
// Java implementation of the approach import java.util.*;
class GFG
{ // Function to return the count of sub-arrays // such that the average of elements present // in the sub-array is greater than the // average of the elements not present // in the sub-array static int countSubarrays( int a[], int n)
{ // Initialize the count variable
int count = 0 ;
// Initialize prefix sum array
int []pre = new int [n + 1 ];
Arrays.fill(pre, 0 );
// Preprocessing prefix sum
for ( int i = 1 ; i < n + 1 ; i++)
{
pre[i] = pre[i - 1 ] + a[i - 1 ];
}
for ( int i = 1 ; i < n + 1 ; i++)
{
for ( int j = i; j < n + 1 ; j++)
{
// Calculating sum and count
// to calculate averages
int sum1 = pre[j] - pre[i - 1 ], count1 = j - i + 1 ;
int sum2 = pre[n] - sum1, count2 =
((n - count1) == 0 ) ? 1 : (n - count1);
// Calculating averages
int includ = sum1 / count1;
int exclud = sum2 / count2;
// Increment count if including avg
// is greater than excluding avg
if (includ > exclud)
count++;
}
}
return count;
} // Driver code public static void main(String args[])
{ int arr[] = { 6 , 3 , 5 };
int n = arr.length;
System.out.println(countSubarrays(arr, n));
} } // This code is contributed by SURENDRA_GANGWAR |
# Python3 implementation of the approach # Function to return the count of sub-arrays # such that the average of elements present # in the sub-array is greater than the # average of the elements not present # in the sub-array def countSubarrays(a, n):
# Initialize the count variable
count = 0
# Initialize prefix sum array
pre = [ 0 for i in range (n + 1 )]
# Preprocessing prefix sum
for i in range ( 1 , n + 1 ):
pre[i] = pre[i - 1 ] + a[i - 1 ]
for i in range ( 1 , n + 1 ):
for j in range (i, n + 1 ):
# Calculating sum and count
# to calculate averages
sum1 = pre[j] - pre[i - 1 ]
count1 = j - i + 1
sum2 = pre[n] - sum1
if n - count1 = = 0 :
count2 = 1
else :
count2 = n - count1
# Calculating averages
includ = sum1 / / count1
exclud = sum2 / / count2
# Increment count if including avg
# is greater than excluding avg
if (includ > exclud):
count + = 1
return count
# Driver code arr = [ 6 , 3 , 5 ]
n = len (arr)
print (countSubarrays(arr, n))
# This code is contributed by mohit kumar |
// C# implementation of the approach using System;
class GFG
{ // Function to return the count of sub-arrays // such that the average of elements present // in the sub-array is greater than the // average of the elements not present // in the sub-array static int countSubarrays( int []a, int n)
{ // Initialize the count variable
int count = 0;
// Initialize prefix sum array
int []pre = new int [n + 1];
Array.Fill(pre, 0);
// Preprocessing prefix sum
for ( int i = 1; i < n + 1; i++)
{
pre[i] = pre[i - 1] + a[i - 1];
}
for ( int i = 1; i < n + 1; i++)
{
for ( int j = i; j < n + 1; j++)
{
// Calculating sum and count
// to calculate averages
int sum1 = pre[j] - pre[i - 1], count1 = j - i + 1;
int sum2 = pre[n] - sum1, count2 =
((n - count1) == 0) ? 1 : (n - count1);
// Calculating averages
int includ = sum1 / count1;
int exclud = sum2 / count2;
// Increment count if including avg
// is greater than excluding avg
if (includ > exclud)
count++;
}
}
return count;
} // Driver code public static void Main()
{ int []arr = { 6, 3, 5 };
int n = arr.Length;
Console.WriteLine(countSubarrays(arr, n));
} } // This code is contributed by Akanksha Rai |
<?php // PHP implementation of the approach // Function to return the count of sub-arrays // such that the average of elements present // in the sub-array is greater than the // average of the elements not present // in the sub-array function countSubarrays( $a , $n )
{ // Initialize the count variable
$count = 0;
// Initialize prefix sum array
$pre = array_fill (0, $n + 1, 0);
// Preprocessing prefix sum
for ( $i = 1; $i < $n + 1; $i ++)
{
$pre [ $i ] = $pre [ $i - 1] + $a [ $i - 1];
}
for ( $i = 1; $i < $n + 1; $i ++)
{
for ( $j = $i ; $j < $n + 1; $j ++)
{
// Calculating sum and count
// to calculate averages
$sum1 = $pre [ $j ] - $pre [ $i - 1] ;
$count1 = $j - $i + 1;
$sum2 = $pre [ $n ] - $sum1 ;
$count2 = (( $n - $count1 ) == 0) ?
1 : ( $n - $count1 );
// Calculating averages
$includ = floor ( $sum1 / $count1 );
$exclud = floor ( $sum2 / $count2 );
// Increment count if including avg
// is greater than excluding avg
if ( $includ > $exclud )
$count ++;
}
}
return $count ;
} // Driver code $arr = array ( 6, 3, 5 );
$n = count ( $arr ) ;
echo countSubarrays( $arr , $n );
// This code is contributed by Ryuga ?> |
<script> // JavaScript implementation of the approach // Function to return the count of sub-arrays // such that the average of elements present // in the sub-array is greater than the // average of the elements not present // in the sub-array function countSubarrays(a, n)
{ // Initialize the count variable
let count = 0;
// Initialize prefix sum array
let pre = new Uint8Array(n + 1);
// Preprocessing prefix sum
for (let i = 1; i < n + 1; i++) {
pre[i] = pre[i - 1] + a[i - 1];
}
for (let i = 1; i < n + 1; i++) {
for (let j = i; j < n + 1; j++) {
// Calculating sum and count
// to calculate averages
let sum1 = pre[j] - pre[i - 1], count1 = j - i + 1;
let sum2 = pre[n] - sum1, count2 = ((n - count1) == 0) ? 1 : (n - count1);
// Calculating averages
let includ = Math.floor(sum1 / count1);
let exclud = Math.floor(sum2 / count2);
// Increment count if including avg
// is greater than excluding avg
if (includ > exclud)
count++;
}
}
return count;
} // Driver code let arr = [ 6, 3, 5 ];
let n = arr.length;
document.write(countSubarrays(arr, n));
// This code is contributed by Surbhi Tyagi. </script> |
3
Time Complexity: O(N^2) where N is the length of the array, as are using nested loops to traverse N*N times.
Auxiliary Space: O(N), as we are using pre array of size N while is extra space.