From 48169fb6f09cd1554fe139a47c0fe8b98f880fea Mon Sep 17 00:00:00 2001
From: Segcolt <9hmbzr275@mozmail.com>
Date: Wed, 12 Feb 2025 18:15:05 -0300
Subject: [PATCH] Add another problem

---
 CSES Problem Set/Path Queries.cpp | 212 ++++++++++++++++++++++++++++++
 1 file changed, 212 insertions(+)
 create mode 100644 CSES Problem Set/Path Queries.cpp

diff --git a/CSES Problem Set/Path Queries.cpp b/CSES Problem Set/Path Queries.cpp
new file mode 100644
index 0000000..0bd2529
--- /dev/null
+++ b/CSES Problem Set/Path Queries.cpp	
@@ -0,0 +1,212 @@
+/* Problem URL: https://cses.fi/problemset/task/1138/ */
+
+#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;
+}
+
+vvi graph;
+vi sizes;
+vi parent;
+vi head;
+vl v;
+vi pos;
+vl seg;
+int t = 0;
+
+void dfs(int i, int p)
+{
+    parent[i] = p;
+
+    sizes[i] = 1;
+    for (auto &u : graph[i]) {
+        if (u == p)  {
+            continue;
+        }
+
+        dfs(u, i);
+        if (sizes[graph[i][0]] < sizes[u]) {
+            swap(graph[i][0], u);
+        }
+
+        sizes[i] += sizes[u];
+    }
+}
+
+void f(int i, int p, vl &values)
+{
+    pos[i] = t;
+    v[t] = values[i];
+    t++;
+
+    for (auto u : graph[i]) {
+        if (u == p) {
+            continue;
+        }
+
+        if (u == graph[i][0]) {
+            head[u] = head[i];
+        } else {
+            head[u] = u;
+        }
+
+        f(u, i, values);
+    }
+}
+
+ll seg_query(int i, int l, int r, int la, int ra)
+{
+    if (l > ra || r < la) {
+        return 0;
+    }
+
+    if (l >= la && r <= ra) {
+        return seg[i];
+    }
+
+    int mid = (l + r) / 2;
+    return seg_query(i * 2, l, mid, la, ra) + seg_query(i * 2 + 1, mid + 1, r, la, ra);
+}
+
+ll query(int a, int b)
+{
+    if (pos[a] > pos[b]) {
+        swap(a, b);
+    }
+
+    if (head[a] == head[b]) {
+        return seg_query(1, 0, v.size() - 1, pos[a], pos[b]);
+    }
+
+    return seg_query(1, 0, v.size() - 1, pos[head[b]], pos[b]) + query(parent[head[b]], a);
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, q;
+    cin >> n >> q;
+
+    vl values(n);
+    cin >> values;
+
+    graph.resize(n);
+    sizes.resize(n);
+    parent.resize(n);
+    head.resize(n);
+    v.resize(n);
+    pos.resize(n);
+
+    rep(i, n - 1) {
+        int a, b;
+        cin >> a >> b;
+        a--, b--;
+
+        graph[a].push_back(b);
+        graph[b].push_back(a);
+    }
+
+    dfs(0, -1);
+    f(0, -1, values);
+
+    while (__builtin_popcountll(v.size()) != 1) {
+        v.push_back(0);
+    }
+
+    size_t sz = v.size();
+    seg.resize(sz * 2);
+
+    for (size_t i = sz; i < sz * 2; i++) {
+        seg[i] = v[i - sz];
+    }
+    for (size_t i = sz - 1; i > 0; i--) {
+        seg[i] = seg[i * 2] + seg[i * 2 + 1];
+    }
+
+    while (q--) {
+        int op;
+        cin >> op;
+
+        if (op == 1) {
+            ll a, v;
+            cin >> a >> v;
+            a--;
+
+            seg[sz + pos[a]] = v;
+            for (size_t i = (sz + pos[a]) / 2; i > 0; i /= 2) {
+                seg[i] = seg[i * 2] + seg[i * 2 + 1];
+            }
+            continue;
+        }
+
+        int num;
+        cin >> num;
+        cout << query(0, num - 1) << '\n';
+    }
+}