Given an array arr[] of size N (1 ? N ? 105), the task is to find the number of ways to select triplet i, j, and k such that i < j < k and the product arr[i] * arr[j] * arr[k] is positive.
Note: Each triplet can consist of at most one negative element.
Examples:
Input: arr[] = {2, 5, -9, -3, 6}
Output: 1
Explanation: The total number ways to obtain a triplet i, j and k to satisfy given conditions is 1 {0, 1, 4}.Input : arr[] = {2, 5, 6, -2, 5}
Output : 4
Explanation: The total number ways to obtain a triplet i, j and k to satisfy given conditions are 4 {0, 1, 2}, {0, 1, 4}, {1, 2, 4} and {0, 2, 4}.
Approach: All possible combinations of a triplet are as follows:
- # negative elements or 2 negative elements and 1 positive element. Both these combinations cannot be considered as the maximum allowed negative elements in a triplet is 1.
- 2 negative (-ve) elements and 1 positive (+ve) element. Since the product of the triplet will be negative, the triplet cannot be considered.
- 3 positive elements.
Follow the steps below to solve the problem:
- Traverse the array and count frequency of positive array elements, say freq.
- Count of ways to select a valid triplet from freq number of array elements using the formula PnC = NC3= (N * (N – 1) * (N – 2)) / 6. Add the count obtained to the answer.
- Print the count obtained.
Below is the implementation of the above approach:
// C++ Program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to calculate // possible number of triplets long long int possibleTriplets( int arr[], int N)
{ int freq = 0;
// counting frequency of positive numbers
// in array
for ( int i = 0; i < N; i++) {
// If current array
// element is positive
if (arr[i] > 0) {
// Increment frequency
freq++;
}
}
// Select a triplet from freq
// elements such that i < j < k.
return (freq * 1LL * (freq - 1)
* (freq - 2))
/ 6;
} // Driver Code int main()
{ int arr[] = { 2, 5, -9, -3, 6 };
int N = sizeof (arr) / sizeof (arr[0]);
cout << possibleTriplets(arr, N);
return 0;
} |
// Java Program to implement // the above approach import java.util.*;
class GFG
{ // Function to calculate // possible number of triplets static int possibleTriplets( int arr[], int N)
{ int freq = 0 ;
// counting frequency of positive numbers
// in array
for ( int i = 0 ; i < N; i++)
{
// If current array
// element is positive
if (arr[i] > 0 )
{
// Increment frequency
freq++;
}
}
// Select a triplet from freq
// elements such that i < j < k.
return ( int ) ((freq * 1L * (freq - 1 )
* (freq - 2 ))
/ 6 );
} // Driver Code public static void main(String[] args)
{ int arr[] = { 2 , 5 , - 9 , - 3 , 6 };
int N = arr.length;
System.out.print(possibleTriplets(arr, N));
} } // This code is contributed by 29AjayKumar |
# Python3 Program to implement # the above approach # Function to calculate # possible number of triplets def possibleTriplets(arr, N):
freq = 0
# counting frequency of positive numbers
# in array
for i in range (N):
# If current array
# element is positive
if (arr[i] > 0 ):
# Increment frequency
freq + = 1
# Select a triplet from freq
# elements such that i < j < k.
return (freq * (freq - 1 ) * (freq - 2 )) / / 6
# Driver Code if __name__ = = '__main__' :
arr = [ 2 , 5 , - 9 , - 3 , 6 ]
N = len (arr)
print (possibleTriplets(arr, N))
# This code is contributed by mohit kumar 29
|
// C# Program to implement // the above approach using System;
public class GFG
{ // Function to calculate // possible number of triplets static int possibleTriplets( int []arr, int N)
{ int freq = 0;
// counting frequency of positive numbers
// in array
for ( int i = 0; i < N; i++)
{
// If current array
// element is positive
if (arr[i] > 0)
{
// Increment frequency
freq++;
}
}
// Select a triplet from freq
// elements such that i < j < k.
return ( int ) ((freq * 1L * (freq - 1)
* (freq - 2)) / 6);
} // Driver Code public static void Main(String[] args)
{ int []arr = { 2, 5, -9, -3, 6 };
int N = arr.Length;
Console.Write(possibleTriplets(arr, N));
} } // This code is contributed by 29AjayKumar |
<script> // Javascript Program to implement // the above approach // Function to calculate // possible number of triplets function possibleTriplets(arr, N)
{ var freq = 0;
// counting frequency of positive numbers
// in array
for ( var i = 0; i < N; i++) {
// If current array
// element is positive
if (arr[i] > 0) {
// Increment frequency
freq++;
}
}
// Select a triplet from freq
// elements such that i < j < k.
return (freq * 1 * (freq - 1)
* (freq - 2))
/ 6;
} // Driver Code var arr = [ 2, 5, -9, -3, 6 ];
var N = arr.length;
document.write( possibleTriplets(arr, N)); </script> |
1
Time Complexity : O(N)
Auxiliary Space : O(1)