From 3c58d9001110a6a9477353f0756843d7e8cb1783 Mon Sep 17 00:00:00 2001
From: Segcolt <9hmbzr275@mozmail.com>
Date: Thu, 26 Sep 2024 16:34:42 -0300
Subject: [PATCH] Do a problem about merging on a segment tree

Hope I can do it for real when it comes
---
 .../A. Segment with the Maximum Sum.cpp       | 124 ++++++++++++++++++
 1 file changed, 124 insertions(+)
 create mode 100644 ITMO Academy: pilot course - Segment Tree, part 1 - Step 2/A. Segment with the Maximum Sum.cpp

diff --git a/ITMO Academy: pilot course - Segment Tree, part 1 - Step 2/A. Segment with the Maximum Sum.cpp b/ITMO Academy: pilot course - Segment Tree, part 1 - Step 2/A. Segment with the Maximum Sum.cpp
new file mode 100644
index 0000000..c3ed4bf
--- /dev/null
+++ b/ITMO Academy: pilot course - Segment Tree, part 1 - Step 2/A. Segment with the Maximum Sum.cpp	
@@ -0,0 +1,124 @@
+/* Problem URL: https://codeforces.com/edu/course/2/lesson/4/2/practice/contest/273278/problem/A */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+struct node {
+    ll ans;
+    ll sum;
+    ll pref;
+    ll suf;
+
+    node(ll ans, ll sum, ll pref, ll suf): ans(ans), sum(sum), pref(pref), suf(suf) {}
+    node() = default;
+};
+
+V<node> segtree;
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, m;
+    cin >> n >> m;
+    vl ar(n);
+    cin >> ar;
+
+    while (__builtin_popcount(n) != 1) {
+        ar.push_back(-1);
+        n++;
+    }
+
+    segtree.resize(n * 2);
+
+    for (size_t i = n; i < n * 2; i++) {
+        segtree[i] = node(max(ar[i - n], 0LL), ar[i - n], max(ar[i - n], 0LL), max(ar[i - n], 0LL));
+    }
+    for (size_t i = n - 1; i > 0; i--) {
+        segtree[i].ans = max(segtree[i * 2].suf + segtree[i * 2 + 1].pref, max(segtree[i * 2].ans, segtree[i * 2 + 1].ans));
+        segtree[i].sum = segtree[i * 2].sum + segtree[i * 2 + 1].sum;
+        segtree[i].pref = max(segtree[i * 2].pref, segtree[i * 2].sum + segtree[i * 2 + 1].pref);
+        segtree[i].suf = max(segtree[i * 2 + 1].suf, segtree[i * 2 + 1].sum + segtree[i * 2].suf);
+    }
+
+    cout << segtree[1].ans << '\n';
+    while (m--) {
+        ll i, v;
+        cin >> i >> v;
+        segtree[n + i] = node(max(v, 0LL), v, max(v, 0LL), max(v, 0LL));
+        for (size_t j = (n + i) / 2; j > 0; j /= 2) {
+            segtree[j].ans = max(segtree[j * 2].suf + segtree[j * 2 + 1].pref, max(segtree[j * 2].ans, segtree[j * 2 + 1].ans));
+            segtree[j].sum = segtree[j * 2].sum + segtree[j * 2 + 1].sum;
+            segtree[j].pref = max(segtree[j * 2].pref, segtree[j * 2].sum + segtree[j * 2 + 1].pref);
+            segtree[j].suf = max(segtree[j * 2 + 1].suf, segtree[j * 2 + 1].sum + segtree[j * 2].suf);
+        }
+        cout << segtree[1].ans << '\n';
+    }
+}