P3384 【模板】轻重链剖分/树链剖分

R65189455

Luogu/P3384/P3384.cpp

@@ -1,10 +1,63 @@
-#include <bits/stdc++.h>
+#include <iostream>
+#include <vector>
 
-using namespace std;
+using std::cin;
+using std::cout;
+using std::endl;
 
-int n, m, r, p, a[100005], x, y, op, u, v, k;
+const int N = 100005;
-vector<int> g[100005];
+
-int cnt, dep[100005], fa[100005], siz[100005], son[100005], id[100005], top[100005], w[100005];
+int p, a[N];
+std::vector<int> g[N];
+
+// Segment Tree
+void build(int, int, int);
+
+// Heavy Path Decomposition
+int cnt, id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
+void dfs1(int, int);
+void dfs2(int, int);
+void modify_path(int, int, int);
+void modify_tree(int, int);
+long long query_path(int, int);
+long long query_tree(int);
+
+int main() {
+    int n, m, r;
+    cin >> n >> m >> r >> p;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+    for (int i = 1; i < n; i++) {
+        int x, y;
+        cin >> x >> y;
+        g[x].push_back(y);
+        g[y].push_back(x);
+    }
+    dfs1(r, r);
+    dfs2(r, r);
+    build(1, 1, n);
+    while (m--) {
+        int op, x, y, z;
+        cin >> op;
+        if (op == 1) {
+            cin >> x >> y >> z;
+            modify_path(x, y, z);
+        } else if (op == 2) {
+            cin >> x >> y;
+            cout << query_path(x, y) << endl;
+        } else if (op == 3) {
+            cin >> x >> z;
+            modify_tree(x, z);
+        } else {
+            cin >> x;
+            cout << query_tree(x) << endl;
+        }
+    }
+    return 0;
+}
+
+// === Segment Tree ===
 
 struct node {
     int l, r;
@@ -14,11 +67,61 @@ struct node {
         : l(0), r(0), s(0), d(0) {}
     node(int _l, int _r)
         : l(_l), r(_r), s(0), d(0) {}
-} tr[100005 << 2];
+} tr[N << 2];
+
+inline void pushup(int u) {
+    tr[u].s = (tr[u << 1].s + tr[u << 1 | 1].s) % p;
+}
+
+inline void pushdown(int u) {
+    node &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
+    left.s = (left.s + (left.r - left.l + 1) * root.d) % p;
+    left.d = (left.d + root.d) % p;
+    right.s = (right.s + (right.r - right.l + 1) * root.d) % p;
+    right.d = (right.d + root.d) % p;
+    root.d = 0;
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+    if (l == r) {
+        tr[u].s = a[rid[l]] % p;
+        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, int d) {
+    if (l <= tr[u].l && tr[u].r <= r) {
+        tr[u].s = (tr[u].s + (tr[u].r - tr[u].l + 1) * d) % p;
+        tr[u].d = (tr[u].d + d) % p;
+        return;
+    }
+    pushdown(u);
+    int mid = tr[u].l + tr[u].r >> 1;
+    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 % p;
+    pushdown(u);
+    int mid = tr[u].l + tr[u].r >> 1;
+    long long res = 0;
+    if (l <= mid) res = (res + query(u << 1, l, r)) % p;
+    if (r > mid) res = (res + query(u << 1 | 1, l, r)) % p;
+    return res;
+}
+
+// == Heavy Path Decomposition ===
 
 void dfs1(int u, int f) {
-    dep[u] = dep[f] + 1;
     fa[u] = f;
+    dep[u] = dep[f] + 1;
     siz[u] = 1;
     for (int v : g[u]) {
         if (v == f) continue;
@@ -30,7 +133,7 @@ void dfs1(int u, int f) {
 
 void dfs2(int u, int t) {
     id[u] = ++cnt;
-    w[cnt] = a[u];
+    rid[id[u]] = u;
     top[u] = t;
     if (!son[u]) return;
     dfs2(son[u], t);
@@ -41,113 +144,32 @@ void dfs2(int u, int t) {
     }
 }
 
-void pushup(int u) {
+void modify_path(int u, int v, int d) {
-    tr[u].s = (tr[u << 1].s + tr[u << 1 | 1].s) % p;
-}
-
-void pushdown(int u) {
-    if (!tr[u].d) return;
-    tr[u << 1].s = (tr[u << 1].s + (tr[u << 1].r - tr[u << 1].l + 1) * tr[u].d) % p;
-    tr[u << 1].d = (tr[u << 1].d + tr[u].d) % p;
-    tr[u << 1 | 1].s = (tr[u << 1 | 1].s + (tr[u << 1 | 1].r - tr[u << 1 | 1].l + 1) * tr[u].d) % p;
-    tr[u << 1 | 1].d = (tr[u << 1 | 1].d + tr[u].d) % p;
-    tr[u].d = 0;
-}
-
-void build(int u, int l, int r) {
-    tr[u] = node(l, r);
-    if (l == r) {
-        tr[u].s = w[r];
-        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, int k) {
-    if (l <= tr[u].l && tr[u].r <= r) {
-        tr[u].s = (tr[u].s + (tr[u].r - tr[u].l + 1) * k) % p;
-        tr[u].d = (tr[u].d + k) % p;
-        return;
-    }
-    int mid = tr[u].l + tr[u].r >> 1;
-    pushdown(u);
-    if (l <= mid) modify(u << 1, l, r, k);
-    if (r > mid) modify(u << 1 | 1, l, r, k);
-    pushup(u);
-}
-
-long long query(int u, int l, int r) {
-    if (l <= tr[u].l && tr[u].r <= r) {
-        return tr[u].s % p;
-    }
-    int mid = tr[u].l + tr[u].r >> 1;
-    long long sum = 0;
-    pushdown(u);
-    if (l <= mid) sum = (sum + query(u << 1, l, r)) % p;
-    if (r > mid) sum = (sum + query(u << 1 | 1, l, r)) % p;
-    return sum;
-}
-
-void modify_path(int u, int v, int k) {
     while (top[u] != top[v]) {
-        if (dep[top[u]] < dep[top[v]]) swap(u, v);
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
-        modify(1, id[top[u]], id[u], k);
+        modify(1, id[top[u]], id[u], d);
         u = fa[top[u]];
     }
-    if (dep[u] < dep[v]) swap(u, v);
+    if (dep[u] < dep[v]) std::swap(u, v);
-    modify(1, id[v], id[u], k);
+    modify(1, id[v], id[u], 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]]) swap(u, v);
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
         sum = (sum + query(1, id[top[u]], id[u])) % p;
         u = fa[top[u]];
     }
-    if (dep[u] < dep[v]) swap(u, v);
+    if (dep[u] < dep[v]) std::swap(u, v);
     sum = (sum + query(1, id[v], id[u])) % p;
     return sum;
 }
 
-void modify_tree(int u, int k) {
+inline void modify_tree(int u, int d) {
-    modify(1, id[u], id[u] + siz[u] - 1, k);
+    modify(1, id[u], id[u] + siz[u] - 1, d);
 }
 
-long long query_tree(int u) {
+inline long long query_tree(int u) {
     return query(1, id[u], id[u] + siz[u] - 1);
 }
-
-int main() {
-    cin >> n >> m >> r >> p;
-    for (int i = 1; i <= n; i++) {
-        cin >> a[i];
-    }
-    for (int i = 1; i < n; i++) {
-        cin >> x >> y;
-        g[x].push_back(y);
-        g[y].push_back(x);
-    }
-    dfs1(r, 0);
-    dfs2(r, r);
-    build(1, 1, n);
-    for (int i = 1; i <= m; i++) {
-        cin >> op >> u;
-        if (op == 1) {
-            cin >> v >> k;
-            modify_path(u, v, k);
-        } else if (op == 2) {
-            cin >> v;
-            cout << query_path(u, v) % p << endl;
-        } else if (op == 3) {
-            cin >> k;
-            modify_tree(u, k);
-        } else {
-            cout << query_tree(u) % p << endl;
-        }
-    }
-    return 0;
-}