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 <iostream>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <random>
#include <iomanip>
#include <functional>
#include <cassert>
using namespace std;
typedef long long ll;
const int Inf = 1e9;
int main() {
ios_base::sync_with_stdio(false); cin.tie(0);
#ifdef LOCAL
freopen("input.txt", "r", stdin);
#endif
int n, m;
cin >> n >> m;
vector <int> a(m), b(m), c(m);
for (int i = 0; i < m; ++i) {
cin >> a[i] >> b[i] >> c[i];
--a[i], --b[i];
if (a[i] > b[i]) swap(a[i], b[i]);
}
vector <int> cnt(n);
for (int i = 0; i < m; ++i) {
++cnt[a[i]];
if (b[i] + 1 < n) --cnt[b[i] + 1];
}
vector <vector <int>> who(n);
for (int i = 0; i < m; ++i) {
who[a[i]].push_back(b[i]);
}
for (int i = 1; i < n; ++i) cnt[i] += cnt[i - 1];
vector <int> need(2 * m + 1, Inf);
for (int delta = -m; delta <= m; ++delta) {
vector <int> cur = cnt;
for (int i = 0; i < n; ++i) {
cur[i] += delta;
cur[i] = max(cur[i], 0);
cur[i] = (cur[i] + 1) / 2;
}
int cnt_open = 0;
vector <int> close(n);
multiset <int> have;
int cnt_need = 0;
for (int i = 0; i < n; ++i) {
cur[i] -= cnt_open;
cnt_open -= close[i];
for (auto r : who[i]) have.insert(r);
while (cur[i] > 0) {
if (have.empty()) {
break;
}
++cnt_need;
++cnt_open;
--cur[i];
++close[*have.rbegin()];
have.erase(--have.end());
}
if (cur[i] > 0) {
cnt_need = Inf;
break;
}
}
need[delta + m] = cnt_need;
}
int low = 0, high = m;
while (high - low > 1) {
int mid = (low + high) >> 1;
bool good = false;
for (int cnt_go = 0; cnt_go <= m; ++cnt_go) {
int all_delta = cnt_go - mid;
if (need[all_delta + m] <= cnt_go) {
good = true;
}
}
if (good) high = mid;
else low = mid;
}
cout << high << '\n';
}
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