HDU 5452 Minimum Cut 树链剖分 + LCA

大致题意：N-1条边形成一棵树；接下来M-N+1条边（u，v）表示从u走到v经过的所有边边权+1。这似乎是裸的树链剖分，但是我裸的树链剖分TLE了，M-N+1条边，这个常数还是很大的，我的树链剖分插入复杂度是log(N)*log(N),所以大概的复杂度是M*log(N)*log(N),是在这里超时了，可以想到(1,u)和v到(1,v)经过的边都+1，然后(1，LCA(u,v))经过的边-2，发现处理出来的边都是以1开头，就可以减少插入边的条数了。

Code:

#include <map>#include <set>#include <queue>#include <cmath>#include <cstdio>#include <cstring>#include <cstdlib>#include <iostream>#include <algorithm>using namespace std;const int MAXN = 25000;struct Edge {    int to ;    Edge * next;}E[MAXN*2],*EE;struct Gragh {    Edge * first;}G[MAXN];struct Tree {    int x,y;    int value;    int lazy;}t[MAXN<<2];int pre[MAXN],son[MAXN],siz[MAXN],dep[MAXN],top[MAXN],pos[MAXN],Rank[MAXN];int N,M,K;int num[MAXN];int tree_idx = 0;int tot ;void Init() {    EE = E;    dep[1] = 1;    pre[1] = 0;    tree_idx = 0;    tot = 1;    memset(G,0,sizeof(G));    memset(num,0,sizeof(num));}void addedge(int u,int v) {    EE->to = v ; EE->next = G[u].first ; G[u].first = EE++;    EE->to = u ; EE->next = G[v].first ; G[v].first = EE++;}void dfs1(int u) {    siz[u] = 1;    son[u] = 0;    for(Edge * p = G[u].first ; p ; p = p -> next) {        if(p->to != pre[u]) {            pre[p->to] = u;            dep[p->to] = dep[u] + 1;            dfs1(p->to);            siz[u] += siz[p->to];            if(siz[p->to] > siz[son[u]])                son[u] = p -> to;        }    }}void dfs2(int u,int ancestor) {    top[u] = ancestor;    tree_idx ++;    pos[u] = tree_idx;    if(son[u] != 0) {        dfs2(son[u],ancestor);    }    for(Edge * p = G[u].first ; p ; p = p -> next) {        if(p->to != pre[u] && p->to != son[u]) {            dfs2(p->to,p->to);        }    }} void Push_Up(int rt) {    t[rt].value = min(t[rt<<1].value,t[rt<<1|1].value); }void Push_Down(int rt) {    if(t[rt].lazy) {        t[rt<<1].lazy += t[rt].lazy;        t[rt<<1|1].lazy += t[rt].lazy;        t[rt<<1].value += t[rt].lazy;        t[rt<<1|1].value += t[rt].lazy;        t[rt].lazy = 0;    }}void Build(int x,int y,int rt) {    t[rt].x = x ; t[rt].y = y; t[rt].lazy = 0;     if(x == y) {        t[rt].value = 1;        if(x == 1) t[rt].value = 0x3f3f3f3f;        return ;    }    int mid = (x + y) >> 1;    Build(x,mid,rt<<1);    Build(mid+1,y,rt<<1|1);    Push_Up(rt);}void Update(int rt,int left,int right,int lazy) {    if(t[rt].x >= left && t[rt].y <= right) {        t[rt].lazy += lazy;        t[rt].value += lazy;        return ;    }    int mid = (t[rt].x + t[rt].y) >> 1;    Push_Down(rt);    if(mid >= left) {        Update(rt<<1,left,right,lazy);    }    if(mid < right) {        Update(rt<<1|1,left,right,lazy);    }    Push_Up(rt);}int ans;// void Query(int rt,int left,int right) {//     if(t[rt].x == t[rt].y) {//         ans = min(t[rt].value,ans);//         return ;//     }//     int mid = (t[rt].x + t[rt].y) >> 1;//     Push_Down(rt);//     if(mid >= left) {//         Query(rt<<1,left,right);//     } //     if(mid < right) {//         Query(rt<<1|1,left,right);//     }//     // Push_Up(rt);// }void Change(int x,int y,int lazy) {    //printf("lazy : %d\n",lazy);    while(top[x] != top[y]) {        if(dep[top[x]] < dep[top[y]]) swap(x,y);        Update(1,pos[top[x]],pos[x],lazy);        x = pre[top[x]];    }    if(x == y) return ;//如果是更新路径上的点，去掉这一句;    if(dep[x] > dep[y]) swap(x,y);    Update(1,pos[x]+1,pos[y],lazy);//如果是更新路径上的点，去掉+1}// void Query_Tree(int x,int y) {//     while(top[x] != top[y]) {//         if(dep[top[x]] < dep[top[y]]) swap(x,y);//         Query(1,pos[top[x]],pos[x]);//         x = pre[top[x]];//     }//     if(x == y) return ;//     if(dep[x] > dep[y]) swap(x,y);//     Query(1,pos[x]+1,pos[y]);// }int lca(int x,int y) {    while(top[x] != top[y]) {        if(dep[top[x]] < dep[top[y]]) swap(x,y);        x = pre[top[x]];    }    if(x == y) return x;    if(dep[x] > dep[y]) swap(x,y);    return x;}char op[5];// void print_tree(int rt) {//     //printf("x : %d y : %d lazy : %d\n",t[rt].x,t[rt].y,t[rt].lazy);//     if(t[rt].x == t[rt].y) {//         printf("value : %d lazy : %d\n",t[rt].value,t[rt].lazy);//         return ;//     }//     print_tree(rt<<1);//     print_tree(rt<<1|1);// }int ReadInt() {    char c = getchar();    while(c > '9' || c < '0') c = getchar();    int ret = 0;    while(c <= '9' && c >= '0') {        ret = ret * 10 + c - '0';        c = getchar();    }    return ret;}void input() {    scanf("%d %d",&N,&M);    int u,v;    for(int i = 1 ; i <= N - 1; i++) {        scanf("%d %d",&u,&v);        // u = ReadInt();        // v = ReadInt();        addedge(u,v);    }    dfs1(1);    dfs2(1,1);    Build(1,N,1);    for(int i = 1 ; i <= M - N + 1; i++) {        scanf("%d %d",&u,&v);        num[u] ++;        num[v] ++;        int temp = lca(u,v);        // printf("temp : %d\n",temp);        num[temp] -= 2;        // u = ReadInt();        // v = ReadInt();      }    for(int i = 1 ; i <= N ; i++) {        if(num[i]) {            Change(1,i,num[i]);        }    }    ans = 0x3f3f3f3f;    //print_tree(1);    // Query(1,2,N);    //Query_Tree(2,N);    //print_tree(1);    printf("%d\n",t[1].value);}int main(void) {    //freopen("a.in","r",stdin);    int T,casenum=1;    scanf("%d",&T);    while(T--){        printf("Case #%d: ",casenum++);        Init();        input();        //solve();    }    return 0;}