树的统计
题目描述
思路
树链剖分模板
代码
#include <cstdio>
#include <cstring>
#define lc k<<1
#define rc k<<1|1
#define max(a, b) ((a) > (b) ? a : b)
#define FOR(a, b) for(int i=a;i<=b;++i)
const int MAX = 3e4 + 5;
int n, ot, oa[20], inf = 0x3f3f3f3f;
char it[10];
int head[MAX], ver[MAX << 1], nt[MAX << 1], ht;
int wt[MAX], zt;
char str[10];
int fa[MAX], son[MAX], size[MAX], dep[MAX];
int dfn[MAX], dt, tr[MAX], top[MAX];
int mx[MAX << 2], sum[MAX << 2];
int ans_mx, ans_sum;
char showStr[100];
inline int read() {
int s = 0, f = 1;
char ch = getchar();
while (ch < '0' || ch > '9') {
if (ch == '-') f = -1;
ch = getchar();
}
while (ch >= '0' && ch <= '9') s = s * 10 + ch - '0', ch = getchar();
return s * f;
}
inline void write(int x) {
ot = 0;
if (x == 0) { putchar('0'); return; }
if (x < 0) putchar('-'), x = -x;
while (x) oa[++ot] = x % 10 + '0', x /= 10;
while (ot) putchar(oa[ot--]);
}
void add(int x, int y) {
nt[++ht] = head[x], head[x] = ht, ver[ht] = y;
}
void dfs1(int x, int u) {
fa[x] = u;
dep[x] = dep[u] + 1;
size[x] = 1;
for (int i = head[x], j; i; i = nt[i]) {
j = ver[i];
if (j == u) continue;
dfs1(j, x);
size[x] += size[j];
if (size[j] > size[son[x]]) son[x] = j;
}
}
void dfs2(int x, int u) {
dfn[x] = ++dt;
tr[dt] = x;
top[x] = u;
if (son[x]) {
dfs2(son[x], u);
}
for (int i = head[x], j; i; i = nt[i]) {
j = ver[i];
if (!dfn[j]) dfs2(j, j);
}
}
void build(int k, int l, int r) {
if (l == r) {
sum[k] = mx[k] = wt[tr[l]];
return;
}
int mid = l + r >> 1;
build(lc, l, mid);
build(rc, mid + 1, r);
sum[k] = sum[lc] + sum[rc];
mx[k] = max(mx[lc], mx[rc]);
}
void change(int k, int l, int r, int x, int y) {
if (l == r && x == l) {
sum[k] = mx[k] = y;
return;
}
int mid = l + r >> 1;
if (x <= mid) change(lc, l, mid, x, y);
else change(rc, mid + 1, r, x, y);
mx[k] = max(mx[lc], mx[rc]);
sum[k] = sum[lc] + sum[rc];
}
void query(int k, int l, int r, int x, int y) {
// printf("query: %d %d %d %d %d\n", k, l, r, x, y);
if (x <= l && r <= y) {
ans_mx = max(ans_mx, mx[k]);
ans_sum += sum[k];
return;
}
int mid = l + r >> 1;
if (x <= mid) query(lc, l, mid, x, y);
if (y > mid) query(rc, mid + 1, r, x, y);
}
void swap(int &x, int &y) {
int t = x;
x = y;
y = t;
}
void ask(int x, int y) {
int fx = top[x], fy = top[y];
while (fx != fy) {
if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
query(1, 1, n, dfn[fx], dfn[x]);
x = fa[fx], fx = top[x];
}
if (dep[x] > dep[y]) swap(x, y);
query(1, 1, n, dfn[x], dfn[y]);
}
void showArray(int arr[]) {
printf("%s", showStr);
for (int i = 1; i <= n; ++i) printf("%2d ", arr[i]);
puts("");
}
void show() {
printf("n: %d\n", n);
for (int i = 1; i <= n; ++i) {
printf("%d:", i);
for (int j = head[i]; j; j = nt[j]) {
printf("%d ", ver[j]);
}
puts("");
}
printf("zt: %d\n", zt);
strcpy(showStr, "weight:"),showArray(wt);
strcpy(showStr, "dep :"),showArray(dep);
strcpy(showStr, "fa :"),showArray(fa);
strcpy(showStr, "size :"),showArray(size);
strcpy(showStr, "son :"),showArray(son);
strcpy(showStr, "dfn :"),showArray(dfn);
strcpy(showStr, "top :"),showArray(top);
strcpy(showStr, "tr :"),showArray(tr);
}
int main() {
n = read();
for (int i = 1, a, b; i < n; ++i) {
a = read(), b = read();
add(a, b), add(b, a);
}
for (int i = 1; i <= n; ++i) wt[i] = read();
zt = read();
dfs1(1, 0);
dfs2(1, 1);
// show();
build(1, 1, n);
for (int i = 1, x, y; i <= zt; ++i) {
scanf("%s", str);
x = read(), y = read();
ans_sum = 0, ans_mx = -inf;
if (strcmp(str, "QMAX") == 0) {
ask(x, y);
write(ans_mx);
puts("");
}
else if (strcmp(str, "QSUM") == 0) {
ask(x, y);
write(ans_sum);
puts("");
}
else change(1, 1, n, dfn[x], y);
}
return 0;
}