Experiment: The Towers of Hanoi. left middle right

Transcription

1 Experiment: The Towers of Hanoi 1

2 Experiment: The Towers of Hanoi 1

3 Die Türme von Hanoi - So gehts! 2

4 Die Türme von Hanoi - So gehts! 2

5 Die Türme von Hanoi - So gehts! 2

6 Die Türme von Hanoi - So gehts! 2

7 Die Türme von Hanoi - So gehts! 2

8 Die Türme von Hanoi - So gehts! 2

9 Die Türme von Hanoi - So gehts! 2

10 Die Türme von Hanoi - So gehts! 2

11 Die Türme von Hanoi - So gehts! 2

12 Die Türme von Hanoi - So gehts! 2

13 Die Türme von Hanoi - So gehts! 2

14 Die Türme von Hanoi - So gehts! 2

15 Die Türme von Hanoi - So gehts! 2

16 Die Türme von Hanoi - So gehts! 2

17 Die Türme von Hanoi - So gehts! 2

18 Die Türme von Hanoi - So gehts! 2

19 The Towers of Hanoi Recursive Approach 3

20 The Towers of Hanoi Recursive Approach 3 assume we knew how to...

21 The Towers of Hanoi Recursive Approach 3... transfer three discs...

22 The Towers of Hanoi Recursive Approach 3... then it becomes simple!

23 The Towers of Hanoi Recursive Approach 3... and hop!

24 The Towers of Hanoi Recursive Approach 3

25 The Towers of Hanoi Recursive Approach 4 but how can we move three discs?

26 The Towers of Hanoi Recursive Approach 4 assume we knew how to...

27 The Towers of Hanoi Recursive Approach 4... transfer two discs from one pile to another...

28 The Towers of Hanoi Recursive Approach 4

29 The Towers of Hanoi Recursive Approach 4... then it is very simple!

30 The Towers of Hanoi Recursive Approach 5 but how can we transfer two discs?

31 The Towers of Hanoi Recursive Approach 5 We already know, how to...

32 The Towers of Hanoi Recursive Approach 5... move one disc from one pile to the other!

33 The Towers of Hanoi Recursive Approach 5

34 The Towers of Hanoi Recursive Approach 5 All is simple! The rest continues in the same way...

35 The Towers of Hanoi Code 6 Move 4 discs from left to right with auxiliary staple middle: move(4,"left","middle","right")

36 The Towers of Hanoi Code 7 move(n, src, aux, dst) 1 Move the top n 1 discs from src to aux with auxiliary staple dst: move(n 1, src, dst, aux); 2 Move 1 disc from src to dst move(1, src, aux, dst); 3 Move the top n 1 discs from aux to dst with auxiliary staple src: move(n 1, aux, src, dst);

37 The Towers of Hanoi Code 8 void move(int n, const string &src, const string &aux, const string &dst){ if (n == 1) { // base case ( move the disc) std :: cout << src << " > " << dst << std::endl; } else { // recursive case } }

38 The Towers of Hanoi Code 8 void move(int n, const string &src, const string &aux, const string &dst){ if (n == 1) { // base case ( move the disc) std :: cout << src << " > " << dst << std::endl; } else { // recursive case move(n-1, src, dst, aux); } }

39 The Towers of Hanoi Code 8 void move(int n, const string &src, const string &aux, const string &dst){ if (n == 1) { // base case ( move the disc) std :: cout << src << " > " << dst << std::endl; } else { // recursive case move(n-1, src, dst, aux); move(1, src, aux, dst); } }

40 The Towers of Hanoi Code 8 void move(int n, const string &src, const string &aux, const string &dst){ if (n == 1) { // base case ( move the disc) std :: cout << src << " > " << dst << std::endl; } else { // recursive case move(n-1, src, dst, aux); move(1, src, aux, dst); move(n-1, aux, src, dst); } }

41 The Towers of Hanoi Code void move(int n, const string &src, const string &aux, const string &dst){ if (n == 1) { // base case ( move the disc) std :: cout << src << " > " << dst << std::endl; } else { // recursive case move(n 1, src, dst, aux); move(1, src, aux, dst ); move(n 1, aux, src, dst); } } int main() { move(4, " left ", "middle", "right" ); return 0; } 9

42 The Towers of Hanoi Code Alternative void move(int n, const string &src, const string &aux, const string &dst){ // base case if (n == 0) return; } // recursive case move(n 1, src, dst, aux); std :: cout << src << " > " << dst << "\n"; move(n 1, aux, src, dst); int main() { move(4, " left ", "middle", "right" ); return 0; } 10