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 pair<int, int> pii;
const int MAXN = 2e5;
const int MAXM = 1e5;
int n, m;
int overall[MAXN];
int arr[MAXN];
int req_red[MAXN];
int r_end[MAXN];
vector<int> ranges[MAXN]; // right endpoint, index
int num_req(int target) {
for (int i = 0; i < n; i++) req_red[i] = max(0, arr[i]-target);
fill(r_end, r_end+n, 0);
priority_queue<int> pq;
int sub = 0;
int num = 0;
for (int i: ranges[0]) pq.push(i);
for (int i = 0; i < n; i++) {
if (sub < req_red[i]) {
int r = pq.top();
r_end[r]++;
sub++;
i--;
num++;
continue;
}
for (int v: ranges[i+1]) pq.push(v);
sub -= r_end[i];
}
return num;
}
int solve() {
int mn = -1;
int mx = 0;
for (int i = 0; i < n; i++) mx = max(mx, arr[i]);
mx++;
while (mx > mn+2) {
int cur = (mn+mx)/2;
int v1 = num_req(cur);
int v2 = num_req(cur+1);
if (v1 >= v2+2) mn = cur;
else mx = v2;
}
return 2*(mn+1)+num_req(mn+1);
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> n >> m;
n--;
for (int i = 0; i < m; i++) {
int a, b, c; cin >> a >> b >> c;
a--; b--;
if (a > b) swap(a, b);
ranges[a].push_back(b-1);
overall[a]++;
overall[b]--;
}
for (int i = 0; i < n; i++) {
overall[i+1] += overall[i];
}
for (int i = 0; i < n; i++) {
arr[i] = (overall[i]+(overall[i]&1))/2;
}
int ans = solve();
for (int i = 0; i < n; i++) arr[i] = overall[i]/2;
ans = min(ans, solve()+1);
cout << ans << "\n";
}
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