1.4.4 Mother's Milk

Mother's Milk

Farmer John has three milking buckets of capacity A, B, and C liters. Each of the numbers A, B, and C is an integer from 1 through 20, inclusive. Initially, buckets A and B are empty while bucket C is full of milk. Sometimes, FJ pours milk from one bucket to another until the second bucket is filled or the first bucket is empty. Once begun, a pour must be completed, of course. Being thrifty, no milk may be tossed out.

Write a program to help FJ determine what amounts of milk he can leave in bucket C when he begins with three buckets as above, pours milk among the buckets for a while, and then notes that bucket A is empty.

PROGRAM NAME: milk3

INPUT FORMAT

A single line with the three integers A, B, and C.

SAMPLE INPUT (file milk3.in)

8 9 10

OUTPUT FORMAT

A single line with a sorted list of all the possible amounts of milk that can be in bucket C when bucket A is empty.

SAMPLE OUTPUT (file milk3.out)

1 2 8 9 10

SAMPLE INPUT (file milk3.in)

2 5 10

SAMPLE OUTPUT (file milk3.out)

5 6 7 8 9 10

{
ID:makeeca1
PROG: milk3
LANG: PASCAL
}
program milk3;
var a,b,c,x,y,z,i:longint;
    can:array[0..20]of boolean;
    f:array[0..20,0..20]of boolean;
function max(xx,yy:longint):longint;
begin if xx>yy then exit(xx)else exit(yy);end;
function min(xx,yy:longint):longint;
begin if xx>yy then exit(yy)else exit(xx);end;
procedure dfs(x,y,z:longint);
begin
  if f[x,y]then exit;
  f[x,y]:=true;
  if (x=0) then can[z]:=true;
  if (x>0)and(y<b) then dfs(max(0,x+y-b),min(b,x+y),z);
  if (x>0)and(z<c) then dfs(max(0,x+z-c),y,min(c,x+z));
  if (y>0)and(x<a) then dfs(min(a,y+x),max(0,y+x-a),z);
  if (y>0)and(z<c) then dfs(x,max(0,y+z-c),min(c,y+z));
  if (z>0)and(x<a) then dfs(min(a,z+x),y,max(0,z+x-a));
  if (z>0)and(y<b) then dfs(x,min(b,z+y),max(0,z+y-b));
end;

begin
  assign(input,'milk3.in');reset(input);
  assign(output,'milk3.out');rewrite(output);
  readln(a,b,c);
  fillchar(can,sizeof(can),0);
  fillchar(f,sizeof(f),0);
  dfs(0,0,c);
  for i:=0 to c-1 do if can[i]then write(i,' ');
  writeln(c);
  close(input);close(output);
end.