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;
#define ar array
#define ll long long
const int MAX_N = 1e5 + 1;
const ll MOD = 1e9 + 7;
const ll INF = 1e9;
struct segtree {
struct tdata {
ll mn, addval;
tdata(): mn(), addval() {}
tdata(ll val): mn(val), addval() {}
tdata(tdata l, tdata r): mn(min(l.mn, r.mn)), addval() {}
};
int ln(int node) {return 2 * node;}
int rn(int node) {return 2 * node + 1;}
int n; vector<tdata> st;
segtree(int n): n(n), st(4 * n) {}
void apply(int node, int start, int end, ll val) {
st[node].mn += val;
st[node].addval += val;
}
void combine(int node) {
st[node].mn = min(st[ln(node)].mn, st[rn(node)].mn);
}
void propagate(int node, int start, int end) {
if (start == end || st[node].addval == 0) return;
int mid = (start + end) / 2;
apply(ln(node), start, mid, st[node].addval);
apply(rn(node), mid + 1, end, st[node].addval);
st[node].addval = 0;
}
void update(int node, int start, int end, int l, int r, ll val) {
propagate(node, start, end);
if (r < start || end < l) return;
if (l <= start && end <= r) {
apply(node, start, end, val);
return;
}
int mid = (start + end) / 2;
update(ln(node), start, mid, l, r, val);
update(rn(node), mid + 1, end, l, r, val);
combine(node);
}
tdata query(int node, int start, int end, int l, int r) {
propagate(node, start, end);
if (r < start || end < l) return tdata();
if (l <= start && end <= r) return st[node];
int mid = (start + end) / 2;
return tdata(query(ln(node), start, mid, l, r), query(rn(node), mid + 1, end, l, r));
}
void update(int l, int r, ll val) {update(1, 0, n - 1, l, r, val);}
tdata query(int l, int r) {return query(1, 0, n - 1, l, r);}
};
void solve() {
int n, d; cin >> n >> d;
vector<ar<int,3>> arr(n + 1); // {b, x, a}
vector<int> pos(n + 1);
for (int i = 0; i < n; i++) {
int x, a, b; cin >> x >> a >> b;
arr[i] = {b, x, a};
pos[i] = x;
}
arr[n] = {d, d, 0};
pos[n] = d;
sort(arr.rbegin(), arr.rend());
sort(pos.begin(), pos.end());
segtree st(n + 1);
for (int i = 0; i <= n; i++) {
st.update(i, i, -pos[i]);
}
ll ans = INF, b_pre = 0;
for (auto [b, x, a] : arr) {
st.update(0, n, b - b_pre);
int idx = lower_bound(pos.begin(), pos.end(), x) - pos.begin();
if (idx < n) st.update(idx + 1, n, a);
ll left = st.query(0, n).mn;
if (left >= 0) ans = min(ans, b - left);
b_pre = b;
}
cout << ans << "\n";
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
int tc = 1;
// cin >> tc;
for (int t = 1; t <= tc; t++) {
// cout << "Case #" << t << ": ";
solve();
}
}
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