Tower of Hanoi problem: Move the pile of rings from one peg
to another
• Moving one ring at a time
• No ring can be placed on top of a smaller ring
A
B
C
Hanoi ( 4, 'A', 'B')
A
B
C
Hanoi ( 4, 'A', 'B')
A
B
C
Hanoi ( 4, 'A', 'B') The Recursion
• Move whole pile except bottom ring from A to C
• Move bottom ring from A to B
• Move whole pile sitting on C (missing bottom ring), from C
to B. A
B
C
Hanoi ( 1, 'A', 'B') Base Case
A
B
C
Hanoi ( 1, 'A', 'B')
A
B
C
Hanoi ( 1, 'A', 'C')
A
B
C
Hanoi ( 1, 'A', 'C')
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 2, 'A', 'B')
Hanoi (1, 'A', 'C' )
move ring from 'A' to 'B'
Hanoi(1, 'C', 'B' )
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 3, 'A', 'B')
Hanoi (2, 'A', 'C')
move ring from 'A' to 'B'
Hanoi ( 2, 'C', 'B')
A
B
C
Hanoi ( 4, 'A', 'B')
Hanoi ( n, x, y)
Hanoi (3, 'A', 'C')
Hanoi (n-1, x, z)
move ring from 'A' to 'B'
move ring from x to y
Hanoi ( 3, 'C', 'B')
Hanoi ( n-1, z, y)
A
B
C
Hanoi ( 4, 'A', 'B')
Hanoi ( n, x, y)
Hanoi (3, 'A', 'C')
Hanoi (n-1, x, z)
move ring from 'A' to 'B'
move ring from x to y
Hanoi ( 3, 'C', 'B')
Hanoi ( n-1, z, y)
A
B
C
Hanoi ( 4, 'A', 'B')
Hanoi ( n, x, y)
Hanoi (3, 'A', 'C')
Hanoi (n-1, x, z)
move ring from 'A' to 'B'
move ring from x to y
Hanoi ( 3, 'C', 'B')
Hanoi ( n-1, z, y)
A
B
C
Hanoi ( 4, 'A', 'B')
Hanoi ( n, x, y)
Hanoi (3, 'A', 'C')
Hanoi (n-1, x, z)
move ring from 'A' to 'B'
move ring from x to y
Hanoi ( 3, 'C', 'B')
Hanoi ( n-1, z, y)
A
B
C