Submission #7123556

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Source Code Expand

#include<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define all(c) (c).begin(),(c).end()
#define pb push_back
#define dbg(...) do{cerr<<__LINE__<<": ";dbgprint(#__VA_ARGS__, __VA_ARGS__);}while(0);

using namespace std;

namespace std{template<class S,class T>struct hash<pair<S,T>>{size_t operator()(const pair<S,T>&p)const{return ((size_t)1e9+7)*hash<S>()(p.first)+hash<T>()(p.second);}};template<class T>struct hash<vector<T>>{size_t operator()(const vector<T> &v)const{size_t h=0;for(auto i : v)h=h*((size_t)1e9+7)+hash<T>()(i)+1;return h;}};}
template<class T>ostream& operator<<(ostream &os, const vector<T> &v){os<<"[ ";rep(i,v.size())os<<v[i]<<(i==v.size()-1?" ]":", ");return os;}template<class T>ostream& operator<<(ostream &os,const set<T> &v){os<<"{ "; for(const auto &i:v)os<<i<<", ";return os<<"}";}
template<class T,class U>ostream& operator<<(ostream &os,const map<T,U> &v){os<<"{";for(const auto &i:v)os<<" "<<i.first<<": "<<i.second<<",";return os<<"}";}template<class T,class U>ostream& operator<<(ostream &os,const pair<T,U> &p){return os<<"("<<p.first<<", "<<p.second<<")";}
void dbgprint(const string &fmt){cerr<<endl;}template<class H,class... T>void dbgprint(const string &fmt,const H &h,const T&... r){cerr<<fmt.substr(0,fmt.find(","))<<"= "<<h<<" ";dbgprint(fmt.substr(fmt.find(",")+1),r...);}
typedef long long ll;typedef vector<int> vi;typedef pair<int,int> pi;const int inf = (int)1e9;const double INF = 1e12, EPS = 1e-9;

struct uf{
	vi p;
	vector<ll> h;
	vector<set<int>> s;
	uf(int n){
		p.resize(n);
		h.resize(n);
		s.resize(n);
		rep(i, n){
			p[i] = i;
			s[i].insert(i);
		}
	}
	int root(int x){
		return x == p[x] ? x : (p[x] = root(p[x]));
	}
	bool merge(int a, int b, ll b_minus_a){
		int A = a, B = b;
		a = root(a); b = root(b);
		if(a == b){
			return h[B] - h[A] == b_minus_a;
		}
		if(s[a].size() < s[b].size()){
			swap(a, b);
			b_minus_a *= -1;
		}
		p[b] = a;
		
		ll d = h[A] - h[B] + b_minus_a;
		for(int i : s[b]){
			s[a].insert(i);
			h[i] += d;
		}
		return 1;
	}
};
bool check(vector<vector<pi>> &es){
	int n = es.size();
	uf *u_ = new uf(n);
	uf &u = *u_;
	
	rep(i, n) if(es[i].size() > 1){
		rep(j, es[i].size() - 1){
			pi a = es[i][j], b = es[i][j + 1];
			if(!u.merge(a.first, b.first, b.second - a.second)) return 0;
		}
	}
	map<int,ll> mnR;
	for(auto v : es) for(pi p : v){
		int pos = p.first, val = p.second, r = u.root(pos);
		ll mn = mnR.count(r) ? mnR[r] : 1e18;
		mnR[r] = mn = min(mn, val - u.h[pos]);
	}
	//dbg(mnR);
	for(auto v : es) for(pi p : v){
		int pos = p.first, val = p.second, r = u.root(pos);
		//dbg(r, mnR[r], u.h[pos], val);
		if(mnR[r] + u.h[pos] < 0) return 0;
	}
	delete u_;
	return 1;
}
int main(){
	cin.tie(0); cin.sync_with_stdio(0);
	
	int h, w, n; cin >> h >> w >> n;
	vector<vector<pi>> tate(w), yoko(h);
	rep(i, n){
		int y, x, a; cin >> y >> x >> a; y--; x--;
		yoko[y].emplace_back(x, a);
		tate[x].emplace_back(y, a);
	}
	cout << (check(tate) && check(yoko) ? "Yes" : "No") << endl;
	
	return 0;
}

Submission Info

Judge Result