 xenon_shivam

subash23

EASY

Math, STL

# PROBLEM:

Given N points find how many straight line we can make such that non of them will neither parallel to X-axis nor parallel to Y-axis.

# QUICK EXPLANATION:

As if n points are given so number of straight lines we can form is \binom {n}{2}.
Now we have to remove those lines which are parallel to X- axis or Y-axis.

# EXPLANATION:

Now removing the lines which are parallel to X- axis or Y-axis, we just have to count the number of points having X-coordinates same and number of points having Y-coordinates same (of course independently as all points are unique). Now just subtract the lines which can be formed using these X-coordinates and Y-coordinates by applying the same formula \binom {x}{2} and \binom {y}{2}

Note: Overlapping Straight lines are counted differently as they are formed using different set of (x,y) co-ordinates, since, we have asked about straight lines and not about the straight lines equation.

# SOLUTIONS:

Setter's Solution

#include<bits/stdc++.h>
using namespace std;
#define ll long long int

int main(){
ll t;t=1;
cin>>t;
while(t–){
ll n;
cin>>n;
map<ll,ll>mpx,mpy;
for(int i=0;i<n;i++){
ll x,y;
cin>>x>>y;
mpx[x]++;
mpy[y]++;
}
ll ans=(n*(n-1))/2;
for(auto i:mpx)
ans-=(i.second*(i.second-1))/2;

``````    for(auto i:mpy)
ans-=(i.second*(i.second-1))/2;

cout<<ans<<"\n";
}
``````

return 0;
}