Language: C++

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debugm(m) {printf("L%d %s \n",__LINE__,#m);for(auto v:m){for(auto e:v){cout<<e<<" ";}cout<<endl;}}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,w,h) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[x][y]<<" ";}cout<<endl;}}
#define debugaar(m,w,h) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0;cnt<(l);++cnt)
#define iterate(cnt,b,e) for(auto cnt=(b);cnt!=(e);++cnt)
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2>
ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }

mt19937 mt(8901016);
inline int rand_int(int l, int h) {
    return uniform_int_distribution<>(l, h)(mt);
}

#ifdef __MAI
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
#ifdef __VSCC
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
#ifdef __MAI
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
#ifdef __VSCC
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0;
            T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) {
            input_integer<int>(var);
            return *this;
        }
        inline MaiScanner& operator>>(long long& var) {
            input_integer<long long>(var);
            return *this;
        }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
        }
        template<typename IT> void in(IT begin, IT end) {
            for (auto it = begin; it != end; ++it) *this >> *it;
        }
    };
}
MaiScanner scanner;




template<typename T = ll>
class bitree {
public:
    int size;
    vector<T> data;
    bitree(int size) :size(size + 1), data(size + 1, 0) {}

    // -------------------------------------------------------
    // 和に関するBIT
    // 1..rの範囲の値の和を求める．
    T sum(int r) {
        T s = 0;
        while (r) {
            s += data[r];
            r -= r&-r; //  r&-r と書くことで最下のビットを得る
        }
        return s;
    }
    // idxの要素の値をval増やす
    void add(int idx, T val) {
        while (idx <= size) {
            data[idx] += val;
            idx += idx&-idx;
        }
    }
};


template<typename INTEGER>
INTEGER b_search(INTEGER l, INTEGER h, auto func) {
    ++h;
    // --l;
    INTEGER c;
    while (l + 1 < h) {
        c = (l + h) / 2;
        if (func(c)) {
            h = c;
        }
        else {
            l = c;
        }
    }
    return h;
    // return l;
}


ll m, n;
ll cc;

vector<pair<int, int>> sche;

ll table[100010];

int main() {
    scanner >> n >> cc;

    sche.reserve(n);

    repeat(i, n) {
        int a, b, c;
        scanner >> a >> b >> c;
        --c;
        ll x = 1 << c;
        table[a] ^= x;
        table[b] ^= x; 
    }
    
    ll x = 0;
    vector<int> start(cc);
    repeat(t, 100005) {
        ll x1 = x ^ table[t];
        repeat(c, cc) {
            ll u = (x  & (1<<c));
            ll v = (x1 & (1<<c));
            if (!u && v)
                start[c] = t;
            if (u && !v)
                sche.push_back(t*2 + 2, start[c]*2 + 1);
        }
    }

    sort(ALL(sche));

    const int rangend = 2e5+10;

    for (int kei = 1; kei <= 40; ++kei) {
        bitree<int> bit(rangend);

        int ans = 0;
        int cnt;
        for (auto s : sche) {
            if (0 < (cnt = bit.sum(s.second - 1))) {
                int x = b_search(1, s.second - 1, [&](int x) {return cnt == bit.sum(x); });
                if (x < s.second) {
                    bit.add(x, -1);
                    bit.add(s.first, 1);
                    ++ans;
                    continue;
                }
            }
            if (bit.sum(rangend) < kei)
                bit.add(s.first, 1),
                ++ans;
        }
        if (ans == n) {
            cout << kei << endl;
            return 0;
        }
    }
    abort();


    return 0;
}



Compiler output:
a.cc: In member function '{anonymous}::MaiScanner& {anonymous}::MaiScanner::operator>>(std::string&)':
a.cc:71:9: warning: no return statement in function returning non-void [-Wreturn-type]
   71 |         }
      |         ^
a.cc: At global scope:
a.cc:111:40: warning: use of 'auto' in parameter declaration only available with '-std=c++20' or '-fconcepts'
  111 | INTEGER b_search(INTEGER l, INTEGER h, auto func) {
      |                                        ^~~~
a.cc: In function 'int main()':
a.cc:160:31: error: no matching function for call to 'std::vector<std::pair<int, int> >::push_back(int, __gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type)'
  160 |                 sche.push_back(t*2 + 2, start[c]*2 + 1);
      |                 ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/c++/14/vector:66,
                 from /usr/include/c++/14/functional:64,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53,
                 from a.cc:3:
/usr/include/c++/14/bits/stl_vector.h:1283:7: note: candidate: 'void std::vector<_Tp, _Alloc>::push_back(const value_type&) [with _Tp = std::pair<int, int>; _Alloc = std::allocator<std::pair<int, int> >; value_type = std::pair<int, int>]'
 1283 |       push_back(const value_type& __x)
      |       ^~~~~~~~~
/usr/include/c++/14/bits/stl_vector.h:1283:7: note:   candidate expects 1 argument, 2 provided
/usr/include/c++/14/bits/stl_vector.h:1300:7: note: candidate: 'void std::vector<_Tp, _Alloc>::push_back(value_type&&) [with _Tp = std::pair<int, int>; _Alloc = std::allocator<std::pair<int, int> >; value_type = std::pair<int, int>]'
 1300 |       push_back(value_type&& __x)
      |       ^~~~~~~~~
/usr/include/c++/14/bits/stl_vector.h:1300:7: note:   candidate expects 1 argument, 2 provided