Editorial for Cái túi 1


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Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

Code mẫu của flashmt

const fi='';
      fo='';
      maxn=40;
      maxc=1048575;
var n,re,m,mid,max,num:longint;
    v,w:array[1..40] of longint;
    f,g:array[0..maxc] of longint;

procedure rf;
var i:longint;
begin
     read(n,m);
     for i:=1 to n do read(w[i],v[i]);
end;

procedure calc;
var i,j:longint;
begin
     max:=1 shl mid-1;
     for i:=1 to max do
         for j:=0 to mid-1 do
             if (i shr j) and 1=1 then
             begin
                  f[i]:=f[i]+w[j+1];
                  g[i]:=g[i]+v[j+1];
             end;
end;

procedure sort(l,r:longint);
var i,j,x,y,t:longint;
begin
     i:=l; j:=r; x:=f[(i+j) shr 1]; y:=g[(i+j) shr 1];
     repeat
           while (f[i]<x) or ((f[i]=x) and (g[i]>y)) do i:=i+1;
           while (f[j]>x) or ((f[j]=x) and (g[j]<y)) do j:=j-1;
           if i<=j then
           begin
                t:=f[i]; f[i]:=f[j]; f[j]:=t;
                t:=g[i]; g[i]:=g[j]; g[j]:=t;
                i:=i+1; j:=j-1;
           end;
     until i>j;
     if i<r then sort(i,r);
     if l<j then sort(l,j);
end;

procedure edit;
var i:longint;
begin
     num:=0;
     for i:=1 to max do
         if g[i]>g[num] then
         begin
              num:=num+1;
              f[num]:=f[i];
              g[num]:=g[i];
         end;
end;

function bs(t:longint):longint;
var l,r,md,i:longint;
begin
     l:=0; r:=num;
     while l<=r do
     begin
          md:=(l+r) shr 1;
          if f[md]=t then break;
          if f[md]<t then l:=md+1
          else r:=md-1;
     end;
     if f[md]=t then bs:=md
     else
     begin
          for i:=md+1 downto md-1 do
              if (i>=0) and (i<=num) and (f[i]<=t) then
              begin
                   bs:=i; exit;
              end;
     end;
end;

procedure pr;
var i,l,ww,vv,j,x:longint;
begin
     mid:=(n+1) shr 1;
     calc;
     sort(1,max);
     edit;
     l:=mid+1; mid:=n-mid;
     max:=1 shl mid-1;
     re:=0;
     for i:=0 to max do
     begin
          ww:=0; vv:=0;
          for j:=0 to mid-1 do
              if (i shr j) and 1=1 then
              begin
                   ww:=ww+w[l+j];
                   vv:=vv+v[l+j];
              end;
          if ww<=m then
          begin
               x:=bs(m-ww);
               if vv+g[x]>re then re:=vv+g[x];
          end;
     end;
end;


procedure wf;
begin
     writeln(re);
end;

begin
     assign(input,fi); reset(input);
     assign(output,fo); rewrite(output);
     rf;
     pr;
     wf;
     close(input); close(output);
end.

Code mẫu của RR

{$MODE OBJFPC}

uses math;
const
  FINP          =       '';
  FOUT          =       '';
  MAXN          =       40;

var
  f1,f2         :       text;
  n,m           :       longint;
  res           :       int64;
  v,w           :       array[1..MAXN] of longint;

  n1,n2         :       longint;
  sv1,sv2,
  sw1,sw2       :       array[0..1050000] of longint;

procedure inp;
    var
      i:longint;
    begin
      read(f1,n,m);
      for i:=1 to n do
        read(f1,w[i],v[i]);
    end;

procedure swap(var a,b:longint); inline;
    var
      tmp:longint;
    begin
      tmp:=a; a:=b; b:=tmp;
    end;

procedure sort1(l,r:longint); inline;
    var
      i,j,mid:longint;
    begin
      i:=l; j:=r; mid:=sw1[l+random(r-l+1)];
      repeat
        while sw1[i]<mid do inc(i);
        while sw1[j]>mid do dec(j);
        if i<=j then
          begin
            swap(sv1[i],sv1[j]);
            swap(sw1[i],sw1[j]);
            inc(i); dec(j);
          end;
      until i>j;
      if i<r then sort1(i,r);
      if l<j then sort1(l,j);
    end;

procedure sort2(l,r:longint); inline;
    var
      i,j,mid:longint;
    begin
      i:=l; j:=r; mid:=sw2[l+random(r-l+1)];
      repeat
        while sw2[i]<mid do inc(i);
        while sw2[j]>mid do dec(j);
        if i<=j then
          begin
            swap(sv2[i],sv2[j]);
            swap(sw2[i],sw2[j]);
            inc(i); dec(j);
          end;
      until i>j;
      if i<r then sort2(i,r);
      if l<j then sort2(l,j);
    end;

procedure solve;
    var
      i,j,bit,nn,m1:longint;
    begin
      nn:=n shr 1;
      n1:=1 shl nn;
      n2:=1 shl (n-nn);

      for i:=0 to n1-1 do
        for bit:=1 to nn do
          if (i shr (bit-1)) and 1=1 then
            begin
              inc(sv1[i],v[bit]);
              inc(sw1[i],w[bit]);
            end;

      for i:=0 to n2-1 do
        for bit:=1 to n-nn do
          if (i shr (bit-1)) and 1=1 then
            begin
              inc(sv2[i],v[bit+nn]);
              inc(sw2[i],w[bit+nn]);
            end;

      sort1(0,n1-1);
      sort2(0,n2-1);

      j:=0; res:=0; m1:=sv1[j];
      for i:=n2-1 downto 0 do
        begin
          while (j<n1-1) and (sw1[j+1]+sw2[i]<=m) do
            begin
              inc(j);
              m1:=max(m1,sv1[j]);
            end;
          if (sw1[j]+sw2[i]<=m) and (m1+sv2[i]>res) then res:=m1+sv2[i];
        end;
      writeln(f2,res);
    end;

begin
  assign(f1,FINP); reset(f1);
  assign(f2,FOUT); rewrite(f2);
  inp;
  solve;
  close(f1); close(f2);
end.

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