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Find number of unique triangles among given N triangles
  • Last Updated : 10 Apr, 2019

Given three arrays a[], b[] and c[] of N elements representing the three sides of N triangles. The task is to find the number of triangles that are unique out of given triangles. A triangle is non-unique if all of its sides match with all the sides of some other triangle in length.

Examples:

Input: a[] = {1, 2}, b[] = {2, 3}, c[] = {3, 5}
Output: 2
The triangles have sides 1, 2, 3 and 2, 3, 5 respectively.
None of them have same sides. Thus both are unique.

Input: a[] = {7, 5, 8, 2, 2}, b[] = {6, 7, 2, 3, 4}, c[] = {5, 6, 9, 4, 3}
Output: 1
Only triangle with sides 8, 2 and 9 is unique.

Approach: The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.



Below is the implementation of the above approach:

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the number of unique triangles
int UniqueTriangles(int a[], int b[], int c[], int n)
{
    vector<int> sides[n];
  
    // Map to store the frequency of triangles
    // with same sides
    map<vector<int>, int> m;
  
    for (int i = 0; i < n; i++) {
  
        // Push all the sides of the current triangle
        sides[i].push_back(a[i]);
        sides[i].push_back(b[i]);
        sides[i].push_back(c[i]);
  
        // Sort the three sides
        sort(sides[i].begin(), sides[i].end());
  
        // Store the frequency of the sides
        // of the triangle
        m[sides[i]] = m[sides[i]] + 1;
    }
  
    map<vector<int>, int>::iterator i;
  
    // To store the count of unique triangles
    int count = 0;
    for (i = m.begin(); i != m.end(); i++) {
  
        // If current triangle has unique sides
        if (i->second == 1)
            count++;
    }
  
    return count;
}
  
// Driver code
int main()
{
    int a[] = { 7, 5, 8, 2, 2 };
    int b[] = { 6, 7, 2, 3, 4 };
    int c[] = { 5, 6, 9, 4, 3 };
  
    int n = sizeof(a) / sizeof(int);
  
    cout << UniqueTriangles(a, b, c, n);
  
    return 0;
}

Python3




# Python3 implementation of the approach
from collections import defaultdict
  
# Function to return the number
# of unique triangles
def UniqueTriangles(a, b, c, n):
  
    sides = [None for i in range(n)]
  
    # Map to store the frequency of 
    # triangles with same sides
    m = defaultdict(lambda:0)
  
    for i in range(0, n):
  
        # Push all the sides of the current triangle
        sides[i] = (a[i], b[i], c[i]) 
  
        # Sort the three sides
        sides[i] = tuple(sorted(sides[i]))
  
        # Store the frequency of the sides
        # of the triangle
        m[sides[i]] += 1
  
    # To store the count of unique triangles
    count = 0
    for i in m: 
  
        # If current triangle has unique sides
        if m[i] == 1:
            count += 1
  
    return count
  
# Driver code
if __name__ == "__main__":
  
    a = [7, 5, 8, 2, 2
    b = [6, 7, 2, 3, 4
    c = [5, 6, 9, 4, 3
  
    n = len(a)
  
    print(UniqueTriangles(a, b, c, n))
      
# This code is contributed by Rituraj Jain
Output:
1

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