Count the number of possible triangles
Problem Statement - link #
Given an unsorted array arr[] of n positive integers. Find the number of triangles that can be formed with three different array elements as lengths of three sides of triangles.
Your Task: This is a function problem. You only need to complete the function findNumberOfTriangles() that takes arr[] and n as input parameters and returns the count of total possible triangles.
Expected Time Complexity: O(n^2)
Expected Auxiliary Space: O(1)
Examples #
Example 1:
Input:
n = 3
arr[] = {3, 5, 4}
Output:
1
Explanation:
A triangle is possible
with all the elements 5, 3 and 4.
Example 2:
Input:
n = 5
arr[] = {6, 4, 9, 7, 8}
Output:
10
Explanation:
There are 10 triangles
possible with the given elements like
(6,4,9), (6,7,8),...
Constraints #
3 <= n <= 10^31 <= arr[i] = 10^3
Solutions #
class Solution{
public:
//Function to count the number of possible triangles.
int helper(int arr[], int one, int two, int three){
int count = 0;
while(one < two){
if( (arr[one] + arr[two]) > three ){
count += two-one;
two--;
}else one++;
}
return count;
}
int findNumberOfTriangles(int arr[], int n){
// code here
sort(arr, arr+n);
int res = 0;
for(int i=n-1; i>=2; i--)
res += helper(arr, 0, i-1, arr[i]);
return res;
}
};