Submission #1695725

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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];
vector<PII> a[100010], b[100010];
signed main(void)
{
  int R, C;
  cin >> R >> C;
  int n;
  cin >> n;
  REP(i, n) {
    cin >> y[i] >> x[i] >> c[i];
    a[x[i]].PB({y[i], c[i]});
    b[y[i]].PB({x[i], c[i]});
  }

  int idx = -1;
  REP(i, R+1) sort(ALL(b[i]));
  REP(i, R+1) {
    if(b[i].size()>=2) {
      idx = i;
      break;
    }
  }
  // cout << idx << endl;
  if(idx != -1) {
    // 公差を求める
    int d = -1;
    int num1 = b[idx][0].first, c1 = b[idx][0].second, num2 = b[idx][1].first, c2 = b[idx][1].second;
    if(num1 < num2) {
      if((c2-c1)%(num2-num1)) {cout << "No" << endl; return 0;}
      d = (c2-c1)/(num2-num1);
    } else {
      if((c1-c2)%(num1-num2)) {cout << "No" << endl; return 0;}
      d = (c1-c2)/(num1-num2);
    }
    REP(i, R+1) {
      if(b[i].size()==0) continue;
      FOR(j, 1, b[i].size()) {
        if((b[i][j].first-b[i][j-1].first)*d != b[i][j].second-b[i][j-1].second) {
          cout << "No" << endl;
          return 0;
        }
      }
      if(b[i][0].second - (b[i][0].first-1)*d < 0) {
        cout << "No" << endl;
        return 0;
      }
      if(b[i][b[i].size()-1].second + (C-b[i][b[i].size()-1].first)*d < 0) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  idx = -1;
  REP(i, C+1) sort(ALL(a[i]));
  REP(i, C+1) {
    if(a[i].size()>=2) {
      idx = i;
      break;
    }
  }
  if(idx != -1) {
    // 公差を求める
    int d = -1;
    int num1 = a[idx][0].first, c1 = a[idx][0].second, num2 = a[idx][1].first, c2 = a[idx][1].second;
    if(num1 < num2) {
      if((c2-c1)%(num2-num1)) {cout << "No" << endl; return 0;}
      d = (c2-c1)/(num2-num1);
    } else {
      if((c1-c2)%(num1-num2)) {cout << "No" << endl; return 0;}
      d = (c1-c2)/(num1-num2);
    }
    REP(i, C+1) {
      if(a[i].size()==0) continue;
      FOR(j, 1, a[i].size()) {
        if((a[i][j].first-a[i][j-1].first)*d != a[i][j].second-a[i][j-1].second) {
          cout << "No" << endl;
          return 0;
        }
      }
      if(a[i][0].second - (a[i][0].first-1)*d < 0) {
        cout << "No" << endl;
        return 0;
      }
      if(a[i][a[i].size()-1].second + (R-a[i][a[i].size()-1].first)*d < 0) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  cout << "Yes" << endl;

  return 0;
}

Submission Info

Judge Result