Section 4.5

OnlineJudges/lydsy/1036.cpp

@@ -0,0 +1,135 @@
+#include <cstdio>
+#include <cctype>
+#define L(x) ((x) << 1)
+#define R(x) ((x) << 1 | 1)
+#define avg(x, y) (((x) + (y)) >> 1)
+inline int max(int a, int b) { return a > b ? a : b; }
+inline int min(int a, int b) { return a < b ? a : b; }
+template <typename T> inline void swap(T &a, T &b)
+{
+    T t = a;
+    a = b;
+    b = t;
+}
+inline void read(int &x)
+{
+    int ch = x = 0, sign = 1;
+    while (!isdigit(ch = getchar())) if (ch == '-') sign = -1;
+    for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
+    x *= sign;
+}
+const int N = int(3e4 + 5), inf = 0x3f3f3f3f;
+int adj[N], nxt[N << 1], to[N << 1], ecnt;
+int sum[N << 2], mx[N << 2];
+int n, sz[N], son[N], dep[N], fa[N], top[N], idx[N], pos[N], val[N];
+inline void addEdge(int f, int t)
+{
+    ecnt++;
+    nxt[ecnt] = adj[f];
+    adj[f] = ecnt;
+    to[ecnt] = t;
+}
+void build(int k, int l, int r)
+{
+    if (l == r - 1) return void(sum[k] = mx[k] = val[idx[l]]);
+    int m = avg(l, r);
+    build(L(k), l, m);
+    build(R(k), m, r);
+    sum[k] = sum[L(k)] + sum[R(k)];
+    mx[k] = max(mx[L(k)], mx[R(k)]);
+}
+void modify(int k, int l, int r, int p, int v)
+{
+    if (l == r - 1) return void(sum[k] = mx[k] = v);
+    int m = avg(l, r);
+    (p < m) ? modify(L(k), l, m, p, v) : modify(R(k), m, r, p, v);
+    sum[k] = sum[L(k)] + sum[R(k)];
+    mx[k] = max(mx[L(k)], mx[R(k)]);
+}
+int qsum(int k, int l, int r, int x, int y)
+{
+    if (x <= l && r <= y) return sum[k];
+    int m = avg(l, r), res = 0;
+    if (x < m) res += qsum(L(k), l, m, x, y);
+    if (y > m) res += qsum(R(k), m, r, x, y);
+    return res;
+}
+int qmax(int k, int l, int r, int x, int y)
+{
+    if (x <= l && r <= y) return mx[k];
+    int m = avg(l, r), res = -inf;
+    if (x < m) res = max(res, qmax(L(k), l, m, x, y));
+    if (y > m) res = max(res, qmax(R(k), m, r, x, y));
+    return res;
+}
+int psum(int u, int v)
+{
+    int res = 0;
+    while (top[u] != top[v])
+    {
+        if (dep[top[u]] < dep[top[v]]) swap(u, v);
+        res += qsum(1, 0, n, pos[top[u]], pos[u] + 1);
+        u = fa[top[u]];
+    }
+    if (dep[u] > dep[v]) swap(u, v);
+    return res + qsum(1, 0, n, pos[u], pos[v] + 1);
+}
+int pmax(int u, int v)
+{
+    int res = -inf;
+    while (top[u] != top[v])
+    {
+        if (dep[top[u]] < dep[top[v]]) swap(u, v);
+        res = max(res, qmax(1, 0, n, pos[top[u]], pos[u] + 1));
+        u = fa[top[u]];
+    }
+    if (dep[u] > dep[v]) swap(u, v);
+    return max(res, qmax(1, 0, n, pos[u], pos[v] + 1));
+}
+void init()
+{
+    static int que[N];
+    int len = 0, u, v;
+    que[len++] = 1;
+    for (int i = 0; i < len; i++)
+    {
+        sz[u = que[i]] = 1;
+        for (int e = adj[u]; e; e = nxt[e])
+            if ((v = to[e]) != fa[u])
+                fa[v] = u, dep[v] = dep[u] + 1, que[len++] = v;
+    }
+    for (int i = len - 1; i; i--)
+    {
+        u = que[i], v = fa[u];
+        sz[v] += sz[u];
+        if (sz[u] > sz[son[v]]) son[v] = u;
+    }
+    for (int i = 0, tot = 0; i < len; i++)
+        if (top[u = que[i]] == 0)
+            for (v = u; v; v = son[v])
+                idx[pos[v] = tot++] = v, top[v] = u;
+}
+int main()
+{
+    read(n);
+    for (int i = 1, x, y; i < n; i++)
+    {
+        read(x), read(y);
+        addEdge(x, y), addEdge(y, x);
+    }
+    for (int i = 1; i <= n; i++) read(val[i]);
+    init();
+    build(1, 0, n);
+    int m, u, v;
+    read(m);
+    static char op[10];
+    while (m--)
+    {
+        scanf("%s", op);
+        read(u), read(v);
+        if (op[1] == 'H') modify(1, 0, n, pos[u], v);
+        if (op[1] == 'M') printf("%d\n", pmax(u, v));
+        if (op[1] == 'S') printf("%d\n", psum(u, v));
+    }
+    return 0;
+}

省选准备/assets/day4/bzoj1036.cpp

@@ -0,0 +1,135 @@
+#include <cstdio>
+#include <cctype>
+#define L(x) ((x) << 1)
+#define R(x) ((x) << 1 | 1)
+#define avg(x, y) (((x) + (y)) >> 1)
+inline int max(int a, int b) { return a > b ? a : b; }
+inline int min(int a, int b) { return a < b ? a : b; }
+template <typename T> inline void swap(T &a, T &b)
+{
+    T t = a;
+    a = b;
+    b = t;
+}
+inline void read(int &x)
+{
+    int ch = x = 0, sign = 1;
+    while (!isdigit(ch = getchar())) if (ch == '-') sign = -1;
+    for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
+    x *= sign;
+}
+const int N = int(3e4 + 5), inf = 0x3f3f3f3f;
+int adj[N], nxt[N << 1], to[N << 1], ecnt;
+int sum[N << 2], mx[N << 2];
+int n, sz[N], son[N], dep[N], fa[N], top[N], idx[N], pos[N], val[N];
+inline void addEdge(int f, int t)
+{
+    ecnt++;
+    nxt[ecnt] = adj[f];
+    adj[f] = ecnt;
+    to[ecnt] = t;
+}
+void build(int k, int l, int r)
+{
+    if (l == r - 1) return void(sum[k] = mx[k] = val[idx[l]]);
+    int m = avg(l, r);
+    build(L(k), l, m);
+    build(R(k), m, r);
+    sum[k] = sum[L(k)] + sum[R(k)];
+    mx[k] = max(mx[L(k)], mx[R(k)]);
+}
+void modify(int k, int l, int r, int p, int v)
+{
+    if (l == r - 1) return void(sum[k] = mx[k] = v);
+    int m = avg(l, r);
+    (p < m) ? modify(L(k), l, m, p, v) : modify(R(k), m, r, p, v);
+    sum[k] = sum[L(k)] + sum[R(k)];
+    mx[k] = max(mx[L(k)], mx[R(k)]);
+}
+int qsum(int k, int l, int r, int x, int y)
+{
+    if (x <= l && r <= y) return sum[k];
+    int m = avg(l, r), res = 0;
+    if (x < m) res += qsum(L(k), l, m, x, y);
+    if (y > m) res += qsum(R(k), m, r, x, y);
+    return res;
+}
+int qmax(int k, int l, int r, int x, int y)
+{
+    if (x <= l && r <= y) return mx[k];
+    int m = avg(l, r), res = -inf;
+    if (x < m) res = max(res, qmax(L(k), l, m, x, y));
+    if (y > m) res = max(res, qmax(R(k), m, r, x, y));
+    return res;
+}
+int psum(int u, int v)
+{
+    int res = 0;
+    while (top[u] != top[v])
+    {
+        if (dep[top[u]] < dep[top[v]]) swap(u, v);
+        res += qsum(1, 0, n, pos[top[u]], pos[u] + 1);
+        u = fa[top[u]];
+    }
+    if (dep[u] > dep[v]) swap(u, v);
+    return res + qsum(1, 0, n, pos[u], pos[v] + 1);
+}
+int pmax(int u, int v)
+{
+    int res = -inf;
+    while (top[u] != top[v])
+    {
+        if (dep[top[u]] < dep[top[v]]) swap(u, v);
+        res = max(res, qmax(1, 0, n, pos[top[u]], pos[u] + 1));
+        u = fa[top[u]];
+    }
+    if (dep[u] > dep[v]) swap(u, v);
+    return max(res, qmax(1, 0, n, pos[u], pos[v] + 1));
+}
+void init()
+{
+    static int que[N];
+    int len = 0, u, v;
+    que[len++] = 1;
+    for (int i = 0; i < len; i++)
+    {
+        sz[u = que[i]] = 1;
+        for (int e = adj[u]; e; e = nxt[e])
+            if ((v = to[e]) != fa[u])
+                fa[v] = u, dep[v] = dep[u] + 1, que[len++] = v;
+    }
+    for (int i = len - 1; i; i--)
+    {
+        u = que[i], v = fa[u];
+        sz[v] += sz[u];
+        if (sz[u] > sz[son[v]]) son[v] = u;
+    }
+    for (int i = 0, tot = 0; i < len; i++)
+        if (top[u = que[i]] == 0)
+            for (v = u; v; v = son[v])
+                idx[pos[v] = tot++] = v, top[v] = u;
+}
+int main()
+{
+    read(n);
+    for (int i = 1, x, y; i < n; i++)
+    {
+        read(x), read(y);
+        addEdge(x, y), addEdge(y, x);
+    }
+    for (int i = 1; i <= n; i++) read(val[i]);
+    init();
+    build(1, 0, n);
+    int m, u, v;
+    read(m);
+    static char op[10];
+    while (m--)
+    {
+        scanf("%s", op);
+        read(u), read(v);
+        if (op[1] == 'H') modify(1, 0, n, pos[u], v);
+        if (op[1] == 'M') printf("%d\n", pmax(u, v));
+        if (op[1] == 'S') printf("%d\n", psum(u, v));
+    }
+    return 0;
+}

省选准备/省选基础算法.tex

@@ -393,4 +393,9 @@ Manacher 模板题
 	这种情况下$add$标记将不会被下传，子节点的影响在修改时便已计算，递归时要累加祖先节点上的标记。
 	\codeinput[标记永久化例程：2.0s]{assets/day4/3468_persistentTag.cpp}
 	经过测试，发现标记永久化的写法快一些，可能是因为没有那么多的pushdown导致的。
+\subsection{树链剖分}
+	轻重链剖分，把重链连续的铺在一棵线段树上，然后就解决了！是不是很容易？233333333333333333333333
+\paragraph{练习题}
+\subparagraph{\href{http://www.lydsy.com/JudgeOnline/problem.php?id=1036}{BZOJ1036} - [ZJOI2008]树的统计Count} 模板题
+\codeinput[ZJOI2008 树的统计Count]{assets/day4/bzoj1036.cpp}
 \end{document}