【NOIP提高组】Map

Description

【NOIP提高组】Map_第1张图片

Solution

刚开始看错题了,以为询问的边会一直保留,然后想得超复杂,最后弃掉了。
明白真正题意后才发现这只是一道基础题目,读懂题目后转化模型:现在有N个点,有M条无向边,图中已有若干点能互相到达,且路径至少为两条,也就是这对点在同一个双连通分量中,然后询问新增的点,最后输出所有结果的和。很明显就是用tarjan进行缩点,然后就成了一棵树,在树上求答案。
容易看出缩点后无向图成为一棵树。增加一条边将产生一个环。设环上有 k 个点,第 i 个点的点权为 vi。经过简单的计算可以得到增加的安全点对数为这里写图片描述。在树上倍增计算就可以了!

Code

const mx=100000;
var
    next,data:array[0..8*mx] of longint;
    last,a,dfn,low,dis,zh:array[0..2*mx] of longint;
    f,u,v:array[0..2*mx,0..25] of longint;
    p1,p2:array[0..4*mx] of boolean;
    x,y:array[0..4*mx] of longint;
    n,m,q,i,j,sum,num:longint;
    ans,tot,s:int64;
function min(x,y:longint):longint;
begin
    if xthen exit(x) else exit(y);
end;
procedure ins(x,y:longint);
begin
    inc(sum);
    data[sum]:=y;
    next[sum]:=last[x];
    last[x]:=sum;
end;
procedure tarjan(x:longint);
var i:longint;
begin
    inc(zh[0]);zh[zh[0]]:=x;
    p2[x]:=true;
    inc(sum);
    dfn[x]:=sum;low[x]:=sum;
    i:=last[x];
    while i<>0 do
    begin
        if p1[(i+1) div 2]=false then
            if dfn[data[i]]<>0 then
            begin
                if p2[data[i]] then low[x]:=min(low[x],low[data[i]]);
            end
            else
            begin
                p1[(i+1) div 2]:=true;
                tarjan(data[i]);
                low[x]:=min(low[x],low[data[i]]);
            end;
        i:=next[i];
    end;
    if dfn[x]=low[x] then
    begin
        inc(num);
        while dfn[zh[zh[0]]]<>low[zh[zh[0]]] do
        begin
            dis[zh[zh[0]]]:=num;
            p2[zh[zh[0]]]:=false;
            dec(zh[0]);
        end;
        dis[zh[zh[0]]]:=num;
        p2[zh[zh[0]]]:=false;
        dec(zh[0]);
    end;
end;
procedure dfs(x,fa,deep:longint);
var i,j:longint;
begin
    f[x,0]:=fa;u[x,0]:=a[fa];v[x,0]:=sqr(a[fa]);zh[x]:=deep;
    i:=1;
    while f[f[x,i-1],i-1]<>0 do
    begin
        f[x,i]:=f[f[x,i-1],i-1];
        u[x,i]:=u[f[x,i-1],i-1]+u[x,i-1];
        v[x,i]:=v[f[x,i-1],i-1]+v[x,i-1];
        inc(i);
    end;
    i:=last[x];
    while i<>0 do
    begin
        if p1[(i+1) div 2]=false then
        begin
            p1[(i+1) div 2]:=true;
            dfs(data[i],x,deep+1);
        end;
        i:=next[i];
    end;
end;
procedure rebuild;
var i:longint;
begin
    sum:=0;
    for i:=1 to n do inc(a[dis[i]]);
    fillchar(last,sizeof(last),0);
    fillchar(next,sizeof(next),0);
    fillchar(data,sizeof(data),0);
    for i:=1 to m do
    if dis[x[i]]<>dis[y[i]] then
    begin
        ins(dis[x[i]],dis[y[i]]);ins(dis[y[i]],dis[x[i]]);
    end;
end;
function up(x,deep:longint):longint;
var i:longint;
begin
    while zh[x]>deep do
    begin
        i:=0;
        while (f[x,i+1]<>0)and(zh[f[x,i+1]]>deep) do inc(i);
        ans:=ans+u[x,i];tot:=tot+v[x,i];
        x:=f[x,i];
    end;
    exit(x);
end;
procedure jump(x,y:longint);
var i:longint;
begin
    if x<>y then
    begin
        ans:=ans+a[y];tot:=tot+sqr(a[y]);
    end else exit;
    while x<>y do
    begin
        i:=0;
        while (f[x,i+1]<>0)and(f[y,i+1]<>0)and(f[x,i+1]<>f[y,i+1]) do inc(i);
        ans:=ans+u[x,i]+u[y,i];
        tot:=tot+v[x,i]+v[y,i];
        x:=f[x,i];y:=f[y,i];
    end;
    ans:=ans-a[x];tot:=tot-sqr(a[x]);
end;
begin
    readln(n,m,q);
    for i:=1 to m do
    begin
        readln(x[i],y[i]);
        ins(x[i],y[i]);ins(y[i],x[i]);
    end;
    sum:=0;
    for i:=1 to n do
        if dfn[i]=0 then tarjan(i);
    rebuild;
    fillchar(p1,sizeof(p1),0);
    dfs(1,0,1);
    for i:=1 to q do
    begin
        readln(x[0],y[0]);
        x[0]:=dis[x[0]];y[0]:=dis[y[0]];
        if zh[x[0]]0]] then
        begin
            num:=x[0];x[0]:=y[0];y[0]:=num;
        end;
        ans:=a[x[0]];tot:=sqr(a[x[0]]);
        x[0]:=up(x[0],zh[y[0]]);
        jump(x[0],y[0]);
        s:=s+ans*ans-tot;
    end;
    writeln(s);
end.

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