Pick’s Theorem

Problem link: 1418 - Trees on My Island / (UVA – 10088)

topic: picks theorem

Implementation:

	#include <bits/stdc++.h>
	using namespace std;
	#define INF 1<<30
	#define endl '\n'
	#define maxn 100005
	#define tc printf("Case %d: ", cs)
	#define tcn printf("Case %d:\n", cs);
	#define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	typedef long long ll;
	const double PI = acos(-1.0);
	#define dbg1(x) cerr << #x << " = " << x << endl;
	#define dbg2(x, y) cerr << #x << " = " << x << ", " << #y << " = " << y << endl;
	#define dbg3(x, y, z) cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z << " = " << z << endl;
	#define dbg4(w,x, y, z) cerr << #w << " = " << w << ", " <<#x << " = " << x << ", " << #y << " = " << y << ", " << #z << " = " << z << endl;
	// 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;
	// /**___________________________________________________**/
	const int N = 10005;
	int n;
	struct PT
	{
	ll x, y;
	PT() {}
	PT(ll x, ll y): x(x), y(y) {}
	PT operator - (const PT &a) {
	return {x - a.x, y - a.y};
	}
	} P[N];
	ll cross(PT p, PT q) {
	{return p.x * q.y - p.y * q.x;}
	}
	ll polygonArea()
	{
	ll ret = 0.0;
	for (int i = 0; i < n; i++) {
	ret += cross(P[i], P[(i + 1) % n]);
	}
	return abs(ret);
	}
	ll boundary_point()
	{
	ll ret = n;
	for (int i = 0; i < n; i++) {
	PT v = P[(i + 1) % n] - P[i];
	ret += abs(__gcd(v.x, v.y)) - 1;
	}
	return ret;
	}
	int main()
	{
	FASTIO
	///*
	#ifndef ONLINE_JUDGE
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
	freopen("error.txt", "w", stderr);
	#endif
	//*/
	int T;
	scanf("%d", &T);
	//T = 1;
	for (int cs = 1; cs <= T; cs++) {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
	int x, y;
	scanf("%d %d", &x, &y);
	P[i].x = x;
	P[i].y = y;
	}
	ll S = polygonArea();
	ll B = boundary_point();
	ll I = (S + 2 - B) / 2;
	printf("Case %d: %lld\n", cs, I);
	}
	return 0;
	}

view raw picksTheorem.cpp hosted with ❤ by GitHub

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