This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
LL two(vector<vector<LL> > z, LL n){
LL maxcross = 0;
LL numcross[n][n];
vector<LL> ends(n, 0);
vector<LL> backs[n];
for(int j = 0; j < z.size(); j++){
int c = z[j][0];
int d = z[j][1];
ends[c]++;
ends[d]++;
backs[d].push_back(c);
}
for(int a = 0; a < n; a++){
LL f = 0;
for(int b = a+1; b < n; b++){
f += ends[b];
for(int r : backs[b]){
if(r >= a+1){
f -= 2;
}
}
numcross[a][b] = f;
maxcross = max(maxcross, numcross[a][b]);
}
}
vector<pair<LL,LL> > pairs;
for(int a = 0; a < n; a++){
LL f = 0;
for(int b = a+1; b < n; b++){
if(numcross[a][b] == maxcross){
pairs.push_back({a,b});
}
}
}
LL realbound = (maxcross + 1) / 2;
if(maxcross % 2 == 1) return realbound;
for(auto p1 : pairs){
for(auto p2 : pairs){
int a = p1.first;
int c = p1.second;
int b = p2.first;
int d = p2.first;
if(a >= b || b >= c || c >= d) continue;
if(numcross[a][b] % 2 == 1){
return realbound + 1;
}
}
}
return realbound;
}
int main(){
cin.sync_with_stdio(0); cin.tie(0);
LL n, m;
cin >> n >> m;
// stations 1 to n
vector<vector<LL> > z;
for(int i = 0; i < m; i++){
LL a, b, c;
cin >> a >> b >> c;
a--; b--;
if(a > b) swap(a,b);
for(int j = 0; j < c; j++){
z.push_back(vector<LL>({a,b}));
}
}
LL bound = two(z, n);
cout << bound << '\n';
}
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