Submission #1696359

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Source Code Expand

//#define __USE_MINGW_ANSI_STDIO 0
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define int ll
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VL;
typedef vector<VL> VVL;
typedef pair<int, int> PII;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
#define IN(a, b, x) (a<=x&&x<b)
#define MP make_pair
#define PB push_back
#ifdef int
const ll INF = (1LL<<60);
#else
const int INF = (1LL<<30);
#endif
const double PI = 3.14159265359;
const double EPS = 1e-12;
const int MOD = 1000000007;

template <typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};

int x[100010], y[100010], c[100010], d[200010];
vector<PII> g[200010];
bool used[200010];

void dfs(int num) {
  used[num] = true;
  for(auto i: g[num]) {
    if(used[i.first]) continue;
    d[i.first] = i.second - d[num];
    dfs(i.first);
  }
}

int mi1, mi2;
int R, C;
void dfs2(int num) {
  used[num] = true;
  for(auto i: g[num]) {
    if(used[i.first]) continue;
    if(i.first < R) chmin(mi1, d[i.first]);
    else chmin(mi2, d[i.first]);
    dfs2(i.first);
  }
}

signed main(void)
{
  cin >> R >> C;
  int n;
  cin >> n;
  REP(i, n) {
    cin >> y[i] >> x[i] >> c[i];
    x[i]--, y[i]--;
    g[x[i]+R].PB({y[i], c[i]});
    g[y[i]].PB({x[i]+R, c[i]});
  }

  REP(i, R+C) {
    if(!used[i]) {
      dfs(i);
    }
  }

  bool flag = true;
  REP(i, n) {
    if(d[x[i]+R] + d[y[i]] != c[i]) {
      flag = false;
      break;
    }
  }
  if(!flag) {
    cout << "No" << endl;
    return 0;
  }

  // REP(i, R+C) cout << d[i] << " "; cout << endl;

  memset(used, false, sizeof(used));
  REP(i, R+C) {
    if(!used[i]) {
      mi1 = INF, mi2 = INF;
      d[i] = 0;
      dfs2(i);
      // cout << i << " " << mi1 << " " << mi2 << endl;
      if(mi1 + mi2 < 0) {
        cout << "No" << endl;
        return 0;
      }
    }
  }
  cout << "Yes" << endl;

  return 0;
}

Submission Info

Judge Result