Maximum Number of Points in a Line

Resources:

 wikipedia.org ==>> Collinearity

GFG 

How To Determine If Points Are Collinear In Coordinate Geometry? 

Collinear 

Maximum Number of Points in a Line 

Implementation basis Spoj & Codechef problem:

	///https://www.codechef.com/problems/CB04
	#include <bits/stdc++.h>
	using namespace std;
	#define INF 1<<30
	#define endl '\n'
	#define maxn 1000005
	#define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	typedef long long ll;
	const double PI = acos(-1.0);
	const ll mod = 1e9 + 7;
	inline void normal(ll &a) { a %= mod; (a < 0) && (a += mod); }
	inline ll modMul(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a * b) % mod; }
	inline ll modAdd(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a + b) % mod; }
	inline ll modSub(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); a -= b; normal(a); return a; }
	inline ll modPow(ll b, ll p) { ll r = 1; while (p) { if (p & 1) r = modMul(r, b); b = modMul(b, b); p >>= 1; } return r; }
	inline ll modInverse(ll a) { return modPow(a, mod - 2); }
	inline ll modDiv(ll a, ll b) { return modMul(a, modInverse(b)); }
	///**
	template < typename F, typename S >
	ostream& operator << ( ostream& os, const pair< F, S > & p ) {
	return os << "(" << p.first << ", " << p.second << ")";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const vector< T > &v ) {
	os << "{";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << *it;
	}
	return os << "}";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const set< T > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin()) os << ", ";
	os << *it;
	}
	return os << "]";
	}
	template < typename F, typename S >
	ostream &operator << ( ostream & os, const map< F, S > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << it -> first << " = " << it -> second ;
	}
	return os << "]";
	}
	#define dbg(args...) do {cerr << #args << " : "; faltu(args); } while(0)
	clock_t tStart = clock();
	#define timeStamp dbg("Execution Time: ", (double)(clock() - tStart)/CLOCKS_PER_SEC)
	void faltu () { cerr << endl; }
	template <typename T>
	void faltu( T a[], int n ) {
	for (int i = 0; i < n; ++i) cerr << a[i] << ' ';
	cerr << endl;
	}
	template <typename T, typename ... hello>
	void faltu( T arg, const hello &... rest) { cerr << arg << ' '; faltu(rest...); }
	// Program showing a policy-based data structure.
	#include <ext/pb_ds/assoc_container.hpp> // Common file
	#include <ext/pb_ds/tree_policy.hpp>
	#include <functional> // for less
	#include <iostream>
	using namespace __gnu_pbds;
	using namespace std;
	// GNU link : https://goo.gl/WVDL6g
	typedef tree<int, null_type, less_equal<int>, rb_tree_tag,
	tree_order_statistics_node_update>
	new_data_set;
	// find_by_order(k) – ফাংশনটি kth ordered element এর একটা পয়েন্টার রিটার্ন করে। অর্থাৎ তুমি চাইলেই kth ইন্ডেক্সে কি আছে, সেটা জেনে ফেলতে পারছো!
	// order_of_key(x) – ফাংশনটি x এলিমেন্টটা কোন পজিশনে আছে সেটা বলে দেয়।
	/**___________________________________________________**/
	const int N = 2222;
	typedef struct
	{
	int x, y;
	} point;
	int n;
	vector<double> vec;
	point P[N];
	inline double slope(int x1, int y1, int x2, int y2)
	{
	return (double) (y1 - y2) / (double)(x1 - x2);
	}
	int maxcol()
	{
	if (n == 1) return 1;
	int best = 2, cnt;
	for (int i = 0; i < n - 1; i++) {
	vec.clear();
	for (int j = i + 1; j < n; j++) {
	vec.push_back(slope(P[i].x, P[i].y, P[j].x, P[j].y));
	}
	cnt = 2;
	sort(vec.begin(), vec.end());
	for (int k = 0; k < (int)vec.size() - 1; k++) {
	cnt = (vec[k] == vec[k + 1]) ? cnt + 1 : 2;
	if (cnt > best) best = cnt;
	}
	}
	return best;
	}
	int main()
	{
	FASTIO
	///*
	#ifndef ONLINE_JUDGE
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
	freopen("error.txt", "w", stderr);
	#endif
	//*/
	int t;
	cin >> t;
	while (t--) {
	cin >> n;
	for (int i = 0; i < n; i++) {
	cin >> P[i].x >> P[i].y;
	}
	cout << maxcol()<< endl;
	}
	return 0;
	}

view raw CB04.cpp hosted with ❤ by GitHub

	///https://www.spoj.com/problems/CHASE/
	#include <bits/stdc++.h>
	using namespace std;
	#define INF 1<<30
	#define endl '\n'
	#define maxn 1000005
	#define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	typedef long long ll;
	const double PI = acos(-1.0);
	const ll mod = 1e9 + 7;
	inline void normal(ll &a) { a %= mod; (a < 0) && (a += mod); }
	inline ll modMul(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a * b) % mod; }
	inline ll modAdd(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a + b) % mod; }
	inline ll modSub(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); a -= b; normal(a); return a; }
	inline ll modPow(ll b, ll p) { ll r = 1; while (p) { if (p & 1) r = modMul(r, b); b = modMul(b, b); p >>= 1; } return r; }
	inline ll modInverse(ll a) { return modPow(a, mod - 2); }
	inline ll modDiv(ll a, ll b) { return modMul(a, modInverse(b)); }
	///**
	template < typename F, typename S >
	ostream& operator << ( ostream& os, const pair< F, S > & p ) {
	return os << "(" << p.first << ", " << p.second << ")";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const vector< T > &v ) {
	os << "{";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << *it;
	}
	return os << "}";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const set< T > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin()) os << ", ";
	os << *it;
	}
	return os << "]";
	}
	template < typename F, typename S >
	ostream &operator << ( ostream & os, const map< F, S > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << it -> first << " = " << it -> second ;
	}
	return os << "]";
	}
	#define dbg(args...) do {cerr << #args << " : "; faltu(args); } while(0)
	clock_t tStart = clock();
	#define timeStamp dbg("Execution Time: ", (double)(clock() - tStart)/CLOCKS_PER_SEC)
	void faltu () { cerr << endl; }
	template <typename T>
	void faltu( T a[], int n ) {
	for (int i = 0; i < n; ++i) cerr << a[i] << ' ';
	cerr << endl;
	}
	template <typename T, typename ... hello>
	void faltu( T arg, const hello &... rest) { cerr << arg << ' '; faltu(rest...); }
	// Program showing a policy-based data structure.
	#include <ext/pb_ds/assoc_container.hpp> // Common file
	#include <ext/pb_ds/tree_policy.hpp>
	#include <functional> // for less
	#include <iostream>
	using namespace __gnu_pbds;
	using namespace std;
	// GNU link : https://goo.gl/WVDL6g
	typedef tree<int, null_type, less_equal<int>, rb_tree_tag,
	tree_order_statistics_node_update>
	new_data_set;
	// find_by_order(k) – ফাংশনটি kth ordered element এর একটা পয়েন্টার রিটার্ন করে। অর্থাৎ তুমি চাইলেই kth ইন্ডেক্সে কি আছে, সেটা জেনে ফেলতে পারছো!
	// order_of_key(x) – ফাংশনটি x এলিমেন্টটা কোন পজিশনে আছে সেটা বলে দেয়।
	/**___________________________________________________**/
	const int N = 2222;
	typedef struct
	{
	int x, y;
	} point;
	int n;
	vector<double> vec;
	point P[N];
	inline double slope(int x1, int y1, int x2, int y2)
	{
	return (double) (y1 - y2) / (double)(x1 - x2);
	}
	int maxcol()
	{
	if (n == 1) return 1;
	int best = 2, cnt;
	for (int i = 0; i < n - 1; i++) {
	vec.clear();
	for (int j = i + 1; j < n; j++) {
	vec.push_back(slope(P[i].x, P[i].y, P[j].x, P[j].y));
	}
	cnt = 2;
	sort(vec.begin(), vec.end());
	for (int k = 0; k < (int)vec.size() - 1; k++) {
	cnt = (vec[k] == vec[k + 1]) ? cnt + 1 : 2;
	if (cnt > best) best = cnt;
	}
	}
	return best;
	}
	int main()
	{
	FASTIO
	///*
	#ifndef ONLINE_JUDGE
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
	freopen("error.txt", "w", stderr);
	#endif
	//*/
	int t;
	cin >> t;
	while (t--) {
	cin >> n;
	for (int i = 0; i < n; i++) {
	cin >> P[i].x >> P[i].y;
	}
	cout << maxcol() - 1 << endl;
	}
	return 0;
	}

view raw CHASE.cpp hosted with ❤ by GitHub

 

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