Submission #1650257

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Source Code Expand

// 基本テンプレート

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
using namespace std;

#define rep(i,a,n) for(int (i)=(a); (i)<(n); (i)++)
#define repq(i,a,n) for(int (i)=(a); (i)<=(n); (i)++)
#define repr(i,a,n) for(int (i)=(a); (i)>=(n); (i)--)
#define int long long int

template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}

typedef pair<int, int> pii;
typedef long long ll;

int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
constexpr ll INF = 1001001001001001LL;
constexpr ll MOD = 1000000007LL;

vector<pii> G[200010];
bool visited[200010];
int rec[200010];

void dfs(int p, int par=-1) {
    for(auto e : G[p]) {
        int to = e.first, cost = e.second;
        if(par == to || visited[to]) continue;
        visited[to] = true;
        rec[to] = cost - rec[p];
        dfs(to, p);
    }
}

signed main() {
    int R, C; cin >> R >> C;
    int N; cin >> N;

    rep(i,0,N) {
        int r, c, a; cin >> r >> c >> a;
        r--; c--;
        int u = r, v = R+c;
        G[u].push_back(pii(v, a));
        G[v].push_back(pii(u, a));
    }

    bool ng = false;
    rep(i,0,R+C) dfs(i);
    rep(i,0,R+C) rep(j,0,G[i].size()) {
        int u = i, v = G[i][j].first;
        if(rec[u] + rec[v] != G[i][j].second) ng = true;
    }

    int x = INF, y = INF;
    rep(i,0,R) chmin(x, rec[i]);
    rep(i,0,C) chmin(y, rec[R+i]);
    if(x + y < 0) ng = true;

    cout << (ng ? "No" : "Yes") << endl;
    return 0;
}

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