Recursion Algorithm
In this tutorial we will learn to solve Tower of Hanoi using recursion.
Tower of Hanoi is a very famous game. In this game there are 3 pegs and N number of disks placed one over the other in decreasing size.
The objective of this game is to move the disks one by one from the first peg to the last peg. And there is only ONE condition, we can not place a bigger disk on top of a smaller disk.
To solve this game we will follow 3 simple steps recursively.
We will use a general notation: T(N, Beg, Aux, End) Where, T denotes our procedure N denotes the number of disks Beg is the initial peg Aux is the auxiliary peg End is the final peg
Following are the recursive steps to solve Tower of Hanoi.
1. T(N-1, Beg, End, Aux) 2. T(1, Beg, Aux, End) 3. T(N-1, Aux, Beg, End) Step 1 says: Move top (N-1) disks from Beg to Aux peg. Step 2 says: Move 1 disk from Beg to End peg. Step 3 says: Move top (N-1) disks from Aux to End peg.
/* N = Number of disks Beg, Aux, End are the pegs */ T(N, Beg, Aux, End) Begin if N = 1 then Print: Beg --> End; else Call T(N-1, Beg, End, Aux); Call T(1, Beg, Aux, End); Call T(N-1, Aux, Beg, End); endif End
If there are N disks then we can solve the game in minimum 2N – 1 moves.
Example: N = 3 Minimum moves required = 23 – 1 = 7
#include <stdio.h> void t(int n, char beg, char aux, char end); int main(){ printf("Moves\n"); t(3, 'a', 'b', 'c'); //N = 3 (no. of disks) a, b, c are the three pegs return 0; }//main() ends here void t(int n, char beg, char aux, char end){ if(n == 1){ printf("%c --> %c\n", beg, end); }else{ t(n-1, beg, end, aux); t(1, beg, aux, end); t(n-1, aux, beg, end); } }//t() ends here