算法模板——线段树9（区间加+区间求和+区间方和）

如题，实现一个程序，输入N个数，进行如下维护：

1.1 x y 求[x,y]区间的和

2.2 x y 求[x,y]区间的平方和

3.3 x y z 将[x,y]区间全部加上z

4.4 x y 求[x,y]区间内两两数相乘的积之和（其实4是1、2的简单组合）

如下：

  1 var
  2    i,j,k,l,m,n:longint;
  3    t:int64;
  4    a,b,c:array[0..100000] of int64;
  5 type
  6     rec=record
  7               aa,bb:int64;
  8     end;
  9
 10 function max(x,y:longint):longint;
 11          begin
 12               if x>y then max:=x else max:=y;
 13          end;
 14 function min(x,y:longint):longint;
 15          begin
 16               if x<y then min:=x else min:=y;
 17          end;
 18 procedure built(z,x,y:longint);
 19           begin
 20                if x=y then
 21                   begin
 22                        read(a[z]);
 23                        b[z]:=a[z]*a[z];
 24                   end
 25                else
 26                    begin
 27                         built(z*2,x,(x+y) div 2);
 28                         built(z*2+1,(x+y) div 2+1,y);
 29                         a[z]:=a[z*2]+a[z*2+1];
 30                         b[z]:=b[z*2]+b[z*2+1];
 31                    end;
 32                c[z]:=0;
 33           end;
 34 procedure ext(z,x,y:longint);
 35           begin
 36                if c[z]=0 then exit;
 37                b[z]:=b[z]+2*c[z]*a[z]+(y-x+1)*c[z]*c[z];
 38                a[z]:=a[z]+(y-x+1)*c[z];
 39                if x<>y then
 40                   begin
 41                        c[z*2]:=c[z*2]+c[z];
 42                        c[z*2+1]:=c[z*2+1]+c[z];
 43                   end;
 44                c[z]:=0;
 45           end;
 46 function suma(z,x,y,l,r:longint):int64;
 47          begin
 48               if l>r then exit(0);
 49               ext(z,x,y);
 50               if (x=l) and (y=r) then exit(a[z]);
 51               exit(suma(z*2,x,(x+y) div 2,l,min(r,(x+y) div 2))+suma(z*2+1,(x+y) div 2+1,y,max((x+y) div 2+1,l),r));
 52          end;
 53 function sumb(z,x,y,l,r:longint):int64;
 54          begin
 55               if l>r then exit(0);
 56               ext(z,x,y);
 57               if (x=l) and (y=r) then exit(b[z]);
 58               exit(sumb(z*2,x,(x+y) div 2,l,min(r,(x+y) div 2))+sumb(z*2+1,(x+y) div 2+1,y,max((x+y) div 2+1,l),r));
 59          end;
 60 function add(z,x,y,l,r:longint;t:int64):rec;
 61          var tt,tt1,tt2:rec;
 62          begin
 63               tt.aa:=0;tt.bb:=0;
 64               if l>r then exit(tt);
 65               if (x=l) and (y=r) then
 66                  begin
 67                       tt.aa:=t*(r-l+1);
 68                       tt.bb:=2*t*(a[z]+c[z]*(r-l+1))+t*t*(r-l+1);
 69                       c[z]:=c[z]+t;
 70                       exit(tt);
 71                  end;
 72               ext(z,x,y);
 73               tt1:=add(z*2,x,(x+y) div 2,l,min(r,(x+y) div 2),t);
 74               tt2:=add(z*2+1,(x+y) div 2+1,y,max((x+y) div 2+1,l),r,t);
 75               tt.aa:=tt1.aa+tt2.aa;
 76               tt.bb:=tt1.bb+tt2.bb;
 77               a[z]:=a[z]+tt.aa;
 78               b[z]:=b[z]+tt.bb;
 79               exit(tt);
 80          end;
 81 begin
 82      readln(n);
 83      built(1,1,n);
 84      while true do
 85          begin
 86               read(j,k,l);
 87               case j of
 88                    1:begin
 89                           writeln(suma(1,1,n,k,l));
 90                    end;
 91                    2:begin
 92                           writeln(sumb(1,1,n,k,l));
 93                    end;
 94                    3:begin
 95                           read(t);
 96                           add(1,1,n,k,l,t);
 97                    end;
 98                    4:begin
 99                           t:=suma(1,1,n,k,l);
100                           writeln((t*t-sumb(1,1,n,k,l)) div 2);
101                    end;
102               end;
103               readln;
104          end;
105 end.
106