int rand7() //random number from 1 - 7{ int r = 0; do { int a = rand(5) - 1; //uniformly at random from 0 to 4 int b = rand(5) - 1; //uniformly at random from 0 to 4 r = 5*b + a; //uniformly at random from 0 to 24 } while (r >= 21); // in this event, we have to roll again //postcondition of loop: we have a number uniformly at random between 0 and 20 return r % 7 + 1; //there are 3 numbers in [0, 20] for each possible return value //so each has equal probability. }
确保每一步都是distribution uniformly.