From 90c68ba9facc17d2a5d17331d352120fa6d42756 Mon Sep 17 00:00:00 2001
From: Ren Baoshuo <i@baoshuo.ren>
Date: Mon, 29 Nov 2021 20:13:52 +0800
Subject: [PATCH] =?UTF-8?q?#2125.=20=E3=80=8CHAOI2015=E3=80=8D=E6=A0=91?=
 =?UTF-8?q?=E4=B8=8A=E6=93=8D=E4=BD=9C?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

https://loj.ac/s/1312868
---
 LibreOJ/2125/2125.cpp        | 169 +++++++++++++++++++++++++++++++++++
 LibreOJ/2125/data/data1.in   |   3 +
 LibreOJ/2125/data/data1.out  |   3 +
 LibreOJ/2125/data/data10.in  |   3 +
 LibreOJ/2125/data/data10.out |   3 +
 LibreOJ/2125/data/data2.in   |   3 +
 LibreOJ/2125/data/data2.out  |   3 +
 LibreOJ/2125/data/data3.in   |   3 +
 LibreOJ/2125/data/data3.out  |   3 +
 LibreOJ/2125/data/data4.in   |   3 +
 LibreOJ/2125/data/data4.out  |   3 +
 LibreOJ/2125/data/data5.in   |   3 +
 LibreOJ/2125/data/data5.out  |   3 +
 LibreOJ/2125/data/data6.in   |   3 +
 LibreOJ/2125/data/data6.out  |   3 +
 LibreOJ/2125/data/data7.in   |   3 +
 LibreOJ/2125/data/data7.out  |   3 +
 LibreOJ/2125/data/data8.in   |   3 +
 LibreOJ/2125/data/data8.out  |   3 +
 LibreOJ/2125/data/data9.in   |   3 +
 LibreOJ/2125/data/data9.out  |   3 +
 21 files changed, 229 insertions(+)
 create mode 100644 LibreOJ/2125/2125.cpp
 create mode 100644 LibreOJ/2125/data/data1.in
 create mode 100644 LibreOJ/2125/data/data1.out
 create mode 100644 LibreOJ/2125/data/data10.in
 create mode 100644 LibreOJ/2125/data/data10.out
 create mode 100644 LibreOJ/2125/data/data2.in
 create mode 100644 LibreOJ/2125/data/data2.out
 create mode 100644 LibreOJ/2125/data/data3.in
 create mode 100644 LibreOJ/2125/data/data3.out
 create mode 100644 LibreOJ/2125/data/data4.in
 create mode 100644 LibreOJ/2125/data/data4.out
 create mode 100644 LibreOJ/2125/data/data5.in
 create mode 100644 LibreOJ/2125/data/data5.out
 create mode 100644 LibreOJ/2125/data/data6.in
 create mode 100644 LibreOJ/2125/data/data6.out
 create mode 100644 LibreOJ/2125/data/data7.in
 create mode 100644 LibreOJ/2125/data/data7.out
 create mode 100644 LibreOJ/2125/data/data8.in
 create mode 100644 LibreOJ/2125/data/data8.out
 create mode 100644 LibreOJ/2125/data/data9.in
 create mode 100644 LibreOJ/2125/data/data9.out

diff --git a/LibreOJ/2125/2125.cpp b/LibreOJ/2125/2125.cpp
new file mode 100644
index 00000000..1db47bf3
--- /dev/null
+++ b/LibreOJ/2125/2125.cpp
@@ -0,0 +1,169 @@
+#include <bits/stdc++.h>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 100005;
+
+// Basic
+int n, m, u, v, op, a[N];
+std::vector<int> g[N];
+
+// Heavy Path Decomposition
+int cnt, w[N], id[N], fa[N], dep[N], son[N], siz[N], top[N];
+void dfs1(int, int);
+void dfs2(int, int);
+void modify_path(int, int, long long);
+void modify_tree(int, long long);
+long long query_path(int, int);
+
+// Segment Tree
+void pushup(int);
+void pushdown(int);
+void build(int, int, int);
+void modify(int, int, int, long long);
+long long query(int, int, int);
+
+int main() {
+    cin >> n >> m;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+    for (int i = 1; i < n; i++) {
+        cin >> u >> v;
+        g[u].push_back(v);
+        g[v].push_back(u);
+    }
+    dfs1(1, 0);
+    dfs2(1, 1);
+    build(1, 1, n);
+    while (m--) {
+        cin >> op >> u;
+        if (op == 1) {
+            cin >> v;
+            modify_path(u, u, v);
+        } else if (op == 2) {
+            cin >> v;
+            modify_tree(u, v);
+        } else {
+            cout << query_path(1, u) << endl;
+        }
+    }
+    return 0;
+}
+
+// === Heavy Path Decomposition ===
+
+void dfs1(int u, int f) {
+    fa[u] = f;
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+    for (int v : g[u]) {
+        if (v == f) continue;
+        dfs1(v, u);
+        siz[u] += siz[v];
+        if (siz[son[u]] < siz[v]) son[u] = v;
+    }
+}
+
+void dfs2(int u, int t) {
+    id[u] = ++cnt;
+    w[cnt] = a[u];
+    top[u] = t;
+    if (!son[u]) return;
+    dfs2(son[u], t);
+    for (int v : g[u]) {
+        if (v == fa[u]) continue;
+        if (v == son[u]) continue;
+        dfs2(v, v);
+    }
+}
+
+void modify_path(int u, int v, long long d) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        modify(1, id[top[u]], id[u], d);
+        u = fa[top[u]];
+    }
+    if (dep[u] < dep[v]) std::swap(u, v);
+    modify(1, id[v], id[u], d);
+}
+
+inline void modify_tree(int u, long long d) {
+    modify(1, id[u], id[u] + siz[u] - 1, d);
+}
+
+long long query_path(int u, int v) {
+    long long sum = 0;
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        sum += query(1, id[top[u]], id[u]);
+        u = fa[top[u]];
+    }
+    if (dep[u] < dep[v]) std::swap(u, v);
+    sum += query(1, id[v], id[u]);
+    return sum;
+}
+
+// === Segment Tree ===
+
+struct node {
+    int l, r;
+    long long s, d;
+
+    node()
+        : l(0), r(0), s(0), d(0) {}
+    node(int _l, int _r)
+        : l(_l), r(_r), s(0), d(0) {}
+} tr[N << 2];
+
+inline void pushup(int u) {
+    tr[u].s = tr[u << 1].s + tr[u << 1 | 1].s;
+}
+
+inline void pushdown(int u) {
+    auto &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
+    left.s += (left.r - left.l + 1) * root.d;
+    left.d += root.d;
+    right.s += (right.r - right.l + 1) * root.d;
+    right.d += root.d;
+    root.d = 0;
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+    if (l == r) {
+        tr[u].s = w[l];
+        return;
+    }
+    int mid = l + r >> 1;
+    build(u << 1, l, mid);
+    build(u << 1 | 1, mid + 1, r);
+    pushup(u);
+}
+
+void modify(int u, int l, int r, long long d) {
+    if (l <= tr[u].l && tr[u].r <= r) {
+        tr[u].d += d;
+        tr[u].s += (tr[u].r - tr[u].l + 1) * d;
+        return;
+    }
+    int mid = tr[u].l + tr[u].r >> 1;
+    pushdown(u);
+    if (l <= mid) modify(u << 1, l, r, d);
+    if (r > mid) modify(u << 1 | 1, l, r, d);
+    pushup(u);
+}
+
+long long query(int u, int l, int r) {
+    if (l <= tr[u].l && tr[u].r <= r) {
+        return tr[u].s;
+    }
+    int mid = tr[u].l + tr[u].r >> 1;
+    long long sum = 0;
+    pushdown(u);
+    if (l <= mid) sum += query(u << 1, l, r);
+    if (r > mid) sum += query(u << 1 | 1, l, r);
+    return sum;
+}
diff --git a/LibreOJ/2125/data/data1.in b/LibreOJ/2125/data/data1.in
new file mode 100644
index 00000000..2215e55e
--- /dev/null
+++ b/LibreOJ/2125/data/data1.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b1f8d334e5025a91c79065887ec461c65189ff058b92ca0f7e128caebbf6a4d4
+size 28160
diff --git a/LibreOJ/2125/data/data1.out b/LibreOJ/2125/data/data1.out
new file mode 100644
index 00000000..897faee3
--- /dev/null
+++ b/LibreOJ/2125/data/data1.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7d62e728efd4080d3e83d261cdd2203a98f5232cc6629709268b2dce8b558b8c
+size 1967
diff --git a/LibreOJ/2125/data/data10.in b/LibreOJ/2125/data/data10.in
new file mode 100644
index 00000000..56f103aa
--- /dev/null
+++ b/LibreOJ/2125/data/data10.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:00d640b63aa4ab769b220f96275ccf0c04e08cc1d777a12bee558acaa774b01b
+size 3247756
diff --git a/LibreOJ/2125/data/data10.out b/LibreOJ/2125/data/data10.out
new file mode 100644
index 00000000..420bdec7
--- /dev/null
+++ b/LibreOJ/2125/data/data10.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:01c569d94e69f3b3fe941cb739039ee1f1836a05e9ab782164e266e59527a37d
+size 340197
diff --git a/LibreOJ/2125/data/data2.in b/LibreOJ/2125/data/data2.in
new file mode 100644
index 00000000..52449ef8
--- /dev/null
+++ b/LibreOJ/2125/data/data2.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4303e6b8346264655fd9325e14b45685c466f65d73d865f8dc15f843e26dc2a2
+size 28046
diff --git a/LibreOJ/2125/data/data2.out b/LibreOJ/2125/data/data2.out
new file mode 100644
index 00000000..3f983143
--- /dev/null
+++ b/LibreOJ/2125/data/data2.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:c191c22ea4849ca5893f9241788f67fe30d91c7956173a7de65c3c853eadd9fd
+size 2083
diff --git a/LibreOJ/2125/data/data3.in b/LibreOJ/2125/data/data3.in
new file mode 100644
index 00000000..77c1fdba
--- /dev/null
+++ b/LibreOJ/2125/data/data3.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d2cc1c1732b37891a44a1758ba95ce8b4a13691434aae27b2e5663155f7bdd79
+size 28096
diff --git a/LibreOJ/2125/data/data3.out b/LibreOJ/2125/data/data3.out
new file mode 100644
index 00000000..348b16ba
--- /dev/null
+++ b/LibreOJ/2125/data/data3.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bac854429ac9397f0deddaaea9196c4cdf5d8f3c2e7b8dc6e1e738dc5eab00e0
+size 1980
diff --git a/LibreOJ/2125/data/data4.in b/LibreOJ/2125/data/data4.in
new file mode 100644
index 00000000..96402aa4
--- /dev/null
+++ b/LibreOJ/2125/data/data4.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4fc0d9a3add4fe374b2435d237a7e46914cdaf26bb0a58ba0f3a74339a9e3183
+size 3408894
diff --git a/LibreOJ/2125/data/data4.out b/LibreOJ/2125/data/data4.out
new file mode 100644
index 00000000..c96c4ce8
--- /dev/null
+++ b/LibreOJ/2125/data/data4.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:baf18353566e9235be3f8d910016f2e7ccd414a299df5d5900b4dc6edf5a5f87
+size 204927
diff --git a/LibreOJ/2125/data/data5.in b/LibreOJ/2125/data/data5.in
new file mode 100644
index 00000000..1cd73c54
--- /dev/null
+++ b/LibreOJ/2125/data/data5.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:85288fcb128d2c14baa9e0cb5d601b183feb9b52b9c9d6ccb36cdfd9b94dee1a
+size 3406236
diff --git a/LibreOJ/2125/data/data5.out b/LibreOJ/2125/data/data5.out
new file mode 100644
index 00000000..3f751f1a
--- /dev/null
+++ b/LibreOJ/2125/data/data5.out
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:745baf2dc5aa0e0392fbbf29e6294e467d4cb613c109f1119fb28f743869f7d8
+size 212342
diff --git a/LibreOJ/2125/data/data6.in b/LibreOJ/2125/data/data6.in
new file mode 100644
index 00000000..27982600
--- /dev/null
+++ b/LibreOJ/2125/data/data6.in
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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+size 3291370
diff --git a/LibreOJ/2125/data/data6.out b/LibreOJ/2125/data/data6.out
new file mode 100644
index 00000000..932e90ce
--- /dev/null
+++ b/LibreOJ/2125/data/data6.out
@@ -0,0 +1,3 @@
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diff --git a/LibreOJ/2125/data/data7.in b/LibreOJ/2125/data/data7.in
new file mode 100644
index 00000000..ae06b055
--- /dev/null
+++ b/LibreOJ/2125/data/data7.in
@@ -0,0 +1,3 @@
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new file mode 100644
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--- /dev/null
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diff --git a/LibreOJ/2125/data/data8.in b/LibreOJ/2125/data/data8.in
new file mode 100644
index 00000000..7114c6fd
--- /dev/null
+++ b/LibreOJ/2125/data/data8.in
@@ -0,0 +1,3 @@
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new file mode 100644
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diff --git a/LibreOJ/2125/data/data9.in b/LibreOJ/2125/data/data9.in
new file mode 100644
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