{"id":58069,"date":"2025-08-16T01:30:16","date_gmt":"2025-08-15T17:30:16","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/58069.html"},"modified":"2025-08-16T01:30:16","modified_gmt":"2025-08-15T17:30:16","slug":"%e6%a0%91%e4%b8%8a%e5%90%af%e5%8f%91%e5%bc%8f%e5%90%88%e5%b9%b6-%e8%8e%ab%e9%98%9f-tree-and-queries","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/58069.html","title":{"rendered":"\u6811\u4e0a\u542f\u53d1\u5f0f\u5408\u5e76\/\u83ab\u961f Tree and Queries"},"content":{"rendered":"

\u9898\u76ee\u94fe\u63a5：Problem – D – Codeforces<\/p>\n

\u9898\u76ee\u5927\u610f：<\/h3>\n

\u4e00\u68f5\u6811\u4e0a (n <= 1e5) \u6bcf\u4e2a\u70b9\u90fd\u6709\u4e00\u4e2a\u989c\u8272 (ci <= 1e5) ，m (m <= 1e5) \u6b21\u8be2\u95ee，\u6bcf\u6b21\u8be2\u95ee\u5305\u542b\u4e00\u4e2a v \u548c\u4e00\u4e2a k ，\u7edf\u8ba1 v \u7684\u5b50\u6811\u4e2d\u8fd9\u6837\u7684\u989c\u8272 x \u7684\u79cd\u7c7b\u6570：\u81f3\u5c11\u6709 k \u4e2a\u70b9\u7684\u989c\u8272\u4e3a x \u3002<\/p>\n

Solution1:<\/h3>\n

\u6811\u4e0a\u542f\u53d1\u5f0f\u5408\u5e76，\u8bb0\u5f55\u6bcf\u4e2a\u989c\u8272\u51fa\u73b0\u7684\u6b21\u6570 col[i]，\u4ee5\u53ca\u4e00\u4e2a\u6570\u7ec4 num[i] \u8868\u793a\u51fa\u73b0\u6b21\u6570\u81f3\u5c11\u4e3a i \u7684\u989c\u8272\u6570<\/span>\u3002（\u6ce8\u610f\u6211\u4eec\u53ef\u4ee5\u5728\u66f4\u65b0 col \u7684\u540c\u65f6 O(1) \u66f4\u65b0 num）<\/p>\n

Code:<\/p>\n

#include<cstdio>
\n#include<cstring>
\n#include<vector>
\nusing namespace std;<\/p>\n

#define N 100005<\/p>\n

int n,m,cnt;
\nint c[N],st[N],siz[N],son[N],dfn[N],col[N],num[N],id[N],ans[N];<\/p>\n

vector< pair<int,int> > q[N];<\/p>\n

struct Edge
\n{
\n int next,to;
\n}ed[N << 1];<\/p>\n

void add(int u,int v)
\n{
\n ed[++ cnt].next = st[u];
\n ed[cnt].to = v;
\n st[u] = cnt;
\n return;
\n}<\/p>\n

void pdfs(int x,int fa)
\n{
\n siz[x] = 1;
\n dfn[x] = ++ cnt;
\n id[cnt] = x;
\n for (int i = st[x]; ~i ;i = ed[i].next)
\n {
\n int rec = ed[i].to;
\n if(rec == fa) continue;
\n pdfs(rec,x);
\n siz[x] += siz[rec];
\n if(!son[x] || siz[rec] > siz[son[x]]) son[x] = rec;
\n }
\n return;
\n}<\/p>\n

void calc(int x) { ++ col[x] , ++ num[col[x]] ; }<\/p>\n

void del(int x) { — num[col[x]] , — col[x] ; }<\/p>\n

void dfs(int x,int fa,int op)
\n{
\n for (int i = st[x]; ~i ;i = ed[i].next)
\n {
\n int rec = ed[i].to;
\n if(rec == fa || rec == son[x]) continue;
\n dfs(rec,x,0);
\n }
\n if(son[x]) dfs(son[x],x,1);
\n calc(c[x]);
\n for (int i = st[x]; ~i ;i = ed[i].next)
\n {
\n int rec = ed[i].to;
\n if(rec == fa || rec == son[x]) continue;
\n for (int j = dfn[rec];j <= dfn[rec] + siz[rec] – 1;++ j)
\n calc(c[id[j]]);
\n }
\n for (auto i : q[x]) ans[i.first] = num[i.second];
\n if(!op)
\n {
\n for (int i = dfn[x];i <= dfn[x] + siz[x] – 1;++ i)
\n del(c[id[i]]);
\n }
\n return;
\n}<\/p>\n

int main()
\n{
\n memset(st,-1,sizeof st);
\n scanf("%d%d",&n,&m),cnt = 0;
\n for (int i = 1;i <= n;++ i) scanf("%d",&c[i]);
\n for (int i = 1,u,v;i < n;++ i)
\n scanf("%d%d",&u,&v),add(u,v),add(v,u);
\n for (int i = 1,v,k;i <= m;++ i)
\n {
\n scanf("%d%d",&v,&k);
\n q[v].push_back({i,k});
\n }
\n cnt = 0;
\n pdfs(1,0);
\n dfs(1,0,1);
\n for (int i = 1;i <= m;++ i) printf("%d\\\\n",ans[i]);
\n return 0;
\n} <\/p>\n

Solution2:<\/h3>\n

\u5229\u7528 "\u5b50\u6811\u5185\u8282\u70b9\u7684 dfn \u662f\u4e00\u6bb5\u8fde\u7eed\u533a\u95f4" ，\u53ef\u4ee5\u5c06\u7edf\u8ba1\u5b50\u6811\u5185\u7684\u7b54\u6848\u8f6c\u5316\u6210\u7edf\u8ba1\u533a\u95f4\u5185\u7684\u7b54\u6848<\/span>，\u79bb\u7ebf\u83ab\u961f\u5904\u7406\u3002<\/p>\n

Code:<\/p>\n

#include<cstdio>
\n#include<cstring>
\n#include<cmath>
\n#include<algorithm>
\nusing namespace std;<\/p>\n

#define N 100005<\/p>\n

int n,m,cnt,B;
\nint c[N],st[N],dfn[N],siz[N],col[N],num[N],id[N],ans[N],bel[N];<\/p>\n

struct Query
\n{
\n int l,r,bar,id;
\n}q[N];<\/p>\n

struct Edge
\n{
\n int next,to;
\n}ed[N << 1];<\/p>\n

int cmp(Query x,Query y)
\n{
\n if(bel[x.l] == bel[y.l]) return x.r < y.r ;
\n return bel[x.l] < bel[y.l] ;
\n}<\/p>\n

void added(int u,int v)
\n{
\n ed[++ cnt].next = st[u];
\n ed[cnt].to = v;
\n st[u] = cnt;
\n return;
\n}<\/p>\n

void dfs(int x,int fa)
\n{
\n dfn[x] = ++ cnt;
\n id[cnt] = x;
\n siz[x] = 1;
\n for (int i = st[x]; ~i ;i = ed[i].next)
\n {
\n int rec = ed[i].to;
\n if(rec == fa) continue;
\n dfs(rec,x);
\n siz[x] += siz[rec];
\n }
\n return;
\n}<\/p>\n

void add(int x) { ++ col[c[id[x]]] , ++ num[col[c[id[x]]]] ; }<\/p>\n

void sub(int x) { — num[col[c[id[x]]]] , — col[c[id[x]]] ; }<\/p>\n

int main()
\n{
\n memset(st,-1,sizeof st);
\n scanf("%d%d",&n,&m),cnt = 0,B = (int)sqrt(n);
\n for (int i = 1;i <= n;++ i) scanf("%d",&c[i]),bel[i] = (i – 1) \/ B + 1;
\n for (int i = 1,u,v;i < n;++ i)
\n scanf("%d%d",&u,&v),added(u,v),added(v,u);
\n cnt = 0;
\n dfs(1,0);
\n for (int i = 1,v,k;i <= m;++ i)
\n {
\n scanf("%d%d",&v,&k);
\n q[i].l = dfn[v];
\n q[i].r = dfn[v] + siz[v] – 1;
\n q[i].bar = k;
\n q[i].id = i;
\n }
\n sort(q + 1,q + m + 1,cmp);
\n int l,r;
\n l = 1,r = 0;
\n for (int i = 1;i <= m;++ i)
\n {
\n while (l > q[i].l) add(– l);
\n while (l < q[i].l) sub(l ++);
\n while (r < q[i].r) add(++ r);
\n while (r > q[i].r) sub(r –);
\n ans[q[i].id] = num[q[i].bar];
\n }
\n for (int i = 1;i <= m;++ i) printf("%d\\\\n",ans[i]);
\n return 0;
\n} <\/p>\n","protected":false},"excerpt":{"rendered":"

\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb81\u6b21\u3002\u4e00\u68f5\u6811\u4e0a (n <= 1e5) \u6bcf\u4e2a\u70b9\u90fd\u6709\u4e00\u4e2a\u989c\u8272 (ci <= 1e5) \uff0cm (m <= 1e5) \u6b21\u8be2\u95ee\uff0c\u6bcf\u6b21\u8be2\u95ee\u5305\u542b\u4e00\u4e2a v \u548c\u4e00\u4e2a k \uff0c\u7edf\u8ba1\u3002\u6811\u4e0a\u542f\u53d1\u5f0f\u5408\u5e76\uff0c\u8bb0\u5f55\u6bcf\u4e2a\u989c\u8272\u51fa\u73b0\u7684\u6b21\u6570 col[i]\uff0c\u4ee5\u53ca\u4e00\u4e2a\u6570\u7ec4\u3002\uff08\u6ce8\u610f\u6211\u4eec\u53ef\u4ee5\u5728\u66f4\u65b0 col \u7684\u540c\u65f6 O(1) \u66f4\u65b0 num\uff09\u5229\u7528 "\u5b50\u6811\u5185\u8282\u70b9\u7684 dfn \u662f\u4e00\u6bb5\u8fde\u7eed\u533a\u95f4" \uff0c\u53ef\u4ee5\u3002\u5c06\u7edf\u8ba1\u5b50\u6811\u5185\u7684\u7b54\u6848\u8f6c\u5316\u6210\u7edf\u8ba1\u533a\u95f4\u5185\u7684\u7b54\u6848\u3002<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[6104,427,6103],"topic":[],"class_list":["post-58069","post","type-post","status-publish","format-standard","hentry","category-server","tag-6104","tag-427","tag-6103"],"yoast_head":"\n\u6811\u4e0a\u542f\u53d1\u5f0f\u5408\u5e76\/\u83ab\u961f Tree and Queries - 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