CH Round #52 - Thinking Bear #1 (NOIP模拟赛)

A.拆地毯

题目：http://www.contesthunter.org/contest/CH%20Round%20%2352%20-%20Thinking%20Bear%20%231%20(NOIP模拟赛)/拆地毯

题解：按最大生成树顺序加k条边即可

代码：

 const maxn=+;
 var c:array[..maxn] of int64;
     fa,a,b:array[..maxn] of longint;
     i,j,n,m,k:longint;
     ans:int64;
 function find(x:longint):longint;
  begin
  if fa[x]<>x then fa[x]:=find(fa[x]);
  exit(fa[x]);
  end;

 procedure sort(l,r:longint);
  var i,j:longint;x,y:int64;
  begin
  i:=l;j:=r;x:=c[(i+j)>>];
  repeat
   while c[i]>x do inc(i);
   while c[j]<x do dec(j);
   if i<=j then
    begin
    y:=a[i];a[i]:=a[j];a[j]:=y;
    y:=b[i];b[i]:=b[j];b[j]:=y;
    y:=c[i];c[i]:=c[j];c[j]:=y;
    inc(i);dec(j);
    end;
  until i>j;
  if i<r then sort(i,r);
  if j>l then sort(l,j);
  end;
 procedure init;
  begin
    readln(n,m,k);
    for i:= to m do readln(a[i],b[i],c[i]);
  end;
 procedure main;
  begin
   sort(,m);
   for i:= to n do fa[i]:=i;
   j:=;
   ans:=;
   for i:= to k do
    begin
      while (find(a[j])=find(b[j])) do inc(j);
      fa[find(a[j])]:=find(b[j]);
      inc(ans,c[j]);
    end;
   writeln(ans);
  end;

 begin
   init;
   main;
 end.     

B.还教室

题目：http://www.contesthunter.org/contest/CH%20Round%20%2352%20-%20Thinking%20Bear%20%231%20(NOIP模拟赛)/还教室

题解：前两个操作都是线段树基础操作，第三个操作需要一点变形

首先我们要知道：方差s=sigma（xi-x0）^2  (i=1..n) /n =sigma（xi^2）-x0^2        x0表示平均数

这手推一下就知道了，我们只需要指导一段区间内的平方和即可，线段树也是可以维护的

（ms贴吧里有人说 只要是具有加和性？就能用线段树来维护？

我理解的是 加上1个值x1 又加了1个值x2，不管第一次加的值，直接把需要加的值更改为x1+x2在维护的时候可以正确就是对的。。。）

代码：

 const maxn=+;
 type node=record
      l,r,mid,lch,rch:longint;
      sum,pf,tag:int64;
      end;
 var t:array[..*maxn] of node;
     a:array[..maxn] of longint;
     i,j,n,m,ch,x,y:longint;
     xx,yy,z:int64;
 procedure pushup(k:longint);
  begin
  with t[k] do
    begin
      sum:=t[lch].sum+t[rch].sum;
      pf:=t[lch].pf+t[rch].pf;
    end;
  end;
 procedure update(k:longint;val:int64);
  begin
  with t[k] do
    begin
      inc(tag,val);
      inc(pf,*val*sum+(r-l+)*val*val);
      inc(sum,(r-l+)*val);
    end;
  end;
 procedure pushdown(k:longint);
  begin
  with t[k] do
    begin
      if tag= then exit;
      update(lch,tag);update(rch,tag);
      tag:=;
    end;
  end;

 procedure build(k,x,y:longint);
  begin
  with t[k] do
   begin
     l:=x;r:=y;mid:=(l+r)>>;lch:=k<<;rch:=k<<+;tag:=;
     if l=r then begin sum:=a[l];pf:=a[l]*a[l];exit;end;
     build(lch,l,mid);build(rch,mid+,r);
     pushup(k);
   end;
  end;
 procedure change(k,x,y,z:longint);
  begin
  with t[k] do
   begin
     if (l=x) and (r=y) then begin update(k,z);exit;end;
     pushdown(k);
     if y<=mid then change(lch,x,y,z)
     else if x>mid then change(rch,x,y,z)
     else
        begin
          change(lch,x,mid,z);change(rch,mid+,y,z);
        end;
     pushup(k);
   end;
  end;
 function getsum(k,x,y:longint):int64;
  begin
  with t[k] do
    begin
      if (l=x) and (r=y) then exit(sum);
      pushdown(k);
      if y<=mid then exit(getsum(lch,x,y))
      else if x>mid then exit(getsum(rch,x,y))
      else exit(getsum(lch,x,mid)+getsum(rch,mid+,y));
    end;
  end;
 function getsqr(k,x,y:longint):int64;
  begin
  with t[k] do
    begin
      if (l=x) and (r=y) then exit(pf);
      pushdown(k);
      if y<=mid then exit(getsqr(lch,x,y))
      else if x>mid then exit(getsqr(rch,x,y))
      else exit(getsqr(lch,x,mid)+getsqr(rch,mid+,y));
    end;
  end;

 procedure init;
  begin
    readln(n,m);
    for i:= to n do read(a[i]);readln;
    build(,,n);
  end;
 procedure solvechange;
  begin
    readln(x,y,z);
    change(,x,y,z);
  end;
 function gcd(x,y:int64):int64;
  begin
    if y= then exit(x) else exit(gcd(y,x mod y));
  end;
 procedure solveaverage;
  begin
    readln(x,y);
    xx:=getsum(,x,y);yy:=y-x+;
    z:=gcd(xx,yy);
    if xx= then writeln('0/1')
    else writeln(xx div z,'/',yy div z);
  end;
 procedure solvefangcha;
  begin
    readln(x,y);
    yy:=y-x+;
    xx:=yy*getsqr(,x,y)-sqr(getsum(,x,y));
    yy:=yy*yy;
    z:=gcd(xx,yy);
    if xx= then writeln('0/1')
    else writeln(xx div z,'/',yy div z);
  end;

 procedure main;
  begin
    for i:= to m do
     begin
       read(ch);
       case ch of
       :solvechange;
       :solveaverage;
       :solvefangcha;
       end;
     end;
  end;

 begin
   init;
   main;
 end.               

C.皇后游戏

题目：http://www.contesthunter.org/contest/CH%20Round%20%2352%20-%20Thinking%20Bear%20%231%20(NOIP模拟赛)/皇后游戏

题解：不会捉。。。按a排序，骗了30分。。。

代码：

1.我的

 const maxn=+;
 var a,b,c:array[..maxn] of int64;
     ans,sum:int64;
     i,j,n,cs:longint;
     function max(x,y:int64):int64;
      begin
      if x>y then exit(x) else exit(y);
      end;

 procedure sort(l,r:longint);
  var i,j:longint;x,y:int64;
  begin
  i:=l;j:=r;x:=c[(i+j)>>];
  repeat
   while c[i]<x do inc(i);
   while c[j]>x do dec(j);
   if i<=j then
    begin
    y:=a[i];a[i]:=a[j];a[j]:=y;
    y:=b[i];b[i]:=b[j];b[j]:=y;
    y:=c[i];c[i]:=c[j];c[j]:=y;
    inc(i);dec(j);
    end;
  until i>j;
  if i<r then sort(i,r);
  if j>l then sort(l,j);
  end;
 procedure init;
  begin
    readln(n);
    for i:= to n do readln(a[i],b[i]);
    for i:= to n do c[i]:=a[i];
  end;
 procedure main;
  begin
    sort(,n);sum:=;ans:=;
    for i:= to n do
     begin
      sum:=sum+a[i];
      ans:=max(ans,sum)+b[i];
     end;
    writeln(ans);
  end;

 begin
   readln(cs);
   while cs> do
    begin
     dec(cs);
     init;
     main;
    end;
 end.  

2.标程 也是排序，不过好高大上啊。。。

 //#include <cmath>
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <string>
 #include <cstdlib>
 #include <vector>
 #include <set>
 #include <algorithm>
 #define mp make_pair
 #define fi first
 #define se second

 using namespace std;

 typedef long long int64;
 typedef pair<int,int> PII;
 const int MAXN=;

 int n;
 PII a[MAXN];
 int64 dp[MAXN];

 inline bool cmp(const PII &x,const PII &y)
 {
     return min(x.fi,y.se)<min(x.se,y.fi);
 }

 int main()
 {
     int testCase;
     for (scanf("%d",&testCase);testCase;testCase--)
     {
         scanf("%d",&n);
         for (int i=;i<=n;i++) scanf("%d%d",&a[i].fi,&a[i].se);
         sort(a+,a+n+,cmp);
         int64 s=;
         for (int i=;i<=n;i++)
         {
             s+=a[i].fi;
             dp[i]=max(s,dp[i-])+a[i].se;
         }
         cout<<dp[n]<<endl;
     }
     return ;
 }