漢諾塔問題：將A塔上的5個圓盤移動到C塔上
可以用遞歸的思路來求解該問題，爲了使問題一般化，假設要移動n個圓盤。根據遞歸的思路，可以考慮先把上面n-1個圓盤移動到B塔上，然後將最底下的n號圓盤移動到C塔，再將B塔上n-1個圓盤移動到C塔。
Python實現
#towers of hanoi 漢諾塔問題
def extList(L,length=5):
if len(L) == length:
return L[:]
l = L[:]
l.extend([0]*(length-len(l)))
return l
def disState():
ta = extList(TA,LENGTH)
tb = extList(TB,LENGTH)
tc = extList(TC,LENGTH)
print 'A B C'
for i in range(LENGTH-1,-1,-1):
print '%d %d %d' % (ta[i],tb[i],tc[i])
print '*' * 80
def move(N,frompeg,topeg,auxpeg):
if N == 1:
print 'move disk %d from %s to %s' % (N,frompeg,topeg)
exec 'disk = T%s.pop()' % frompeg
exec 'T%s.append(disk)' % topeg
disState()
return
move(N-1,frompeg,auxpeg,topeg)
print 'move disk %d from %s to %s' % (N,frompeg,topeg)
exec 'disk = T%s.pop()' % frompeg
exec 'T%s.append(disk)' % topeg
disState()
move(N-1,auxpeg,topeg,frompeg)
if __name__ == '__main__':
#定義總共有多少個圓盤，這裏假設有5個圓盤
LENGTH = 5
#假設這5個圓盤一開始放在‘A’號塔上，擺放順序類似於堆棧，頂部存放1號圓盤，底部存放5號圓盤
TA = [i for i in range(LENGTH,0,-1)]
#‘B’號塔，初始化爲空
TB = []
#‘C’號塔，初始化爲空
TC = []
disState()
#將‘A’號塔上的圓盤全部移動到‘C’號塔，‘B’號塔作爲中轉塔
move(LENGTH,'A','C','B')
5個圓盤的輸出結果
>>>
A B C
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
********************************************************************************
move disk 1 from A to C
A B C
0 0 0
2 0 0
3 0 0
4 0 0
5 0 1
********************************************************************************
move disk 2 from A to B
A B C
0 0 0
0 0 0
3 0 0
4 0 0
5 2 1
********************************************************************************
move disk 1 from C to B
A B C
0 0 0
0 0 0
3 0 0
4 1 0
5 2 0
********************************************************************************
move disk 3 from A to C
A B C
0 0 0
0 0 0
0 0 0
4 1 0
5 2 3
********************************************************************************
move disk 1 from B to A
A B C
0 0 0
0 0 0
1 0 0
4 0 0
5 2 3
********************************************************************************
move disk 2 from B to C
A B C
0 0 0
0 0 0
1 0 0
4 0 2
5 0 3
********************************************************************************
move disk 1 from A to C
A B C
0 0 0
0 0 0
0 0 1
4 0 2
5 0 3
********************************************************************************
move disk 4 from A to B
A B C
0 0 0
0 0 0
0 0 1
0 0 2
5 4 3
********************************************************************************
move disk 1 from C to B
A B C
0 0 0
0 0 0
0 0 0
0 1 2
5 4 3
********************************************************************************
move disk 2 from C to A
A B C
0 0 0
0 0 0
0 0 0
2 1 0
5 4 3
********************************************************************************
move disk 1 from B to A
A B C
0 0 0
0 0 0
1 0 0
2 0 0
5 4 3
********************************************************************************
move disk 3 from C to B
A B C
0 0 0
0 0 0
1 0 0
2 3 0
5 4 0
********************************************************************************
move disk 1 from A to C
A B C
0 0 0
0 0 0
0 0 0
2 3 0
5 4 1
********************************************************************************
move disk 2 from A to B
A B C
0 0 0
0 0 0
0 2 0
0 3 0
5 4 1
********************************************************************************
move disk 1 from C to B
A B C
0 0 0
0 1 0
0 2 0
0 3 0
5 4 0
********************************************************************************
move disk 5 from A to C
A B C
0 0 0
0 1 0
0 2 0
0 3 0
0 4 5
********************************************************************************
move disk 1 from B to A
A B C
0 0 0
0 0 0
0 2 0
0 3 0
1 4 5
********************************************************************************
move disk 2 from B to C
A B C
0 0 0
0 0 0
0 0 0
0 3 2
1 4 5
********************************************************************************
move disk 1 from A to C
A B C
0 0 0
0 0 0
0 0 1
0 3 2
0 4 5
********************************************************************************
move disk 3 from B to A
A B C
0 0 0
0 0 0
0 0 1
0 0 2
3 4 5
********************************************************************************
move disk 1 from C to B
A B C
0 0 0
0 0 0
0 0 0
0 1 2
3 4 5
********************************************************************************
move disk 2 from C to A
A B C
0 0 0
0 0 0
0 0 0
2 1 0
3 4 5
********************************************************************************
move disk 1 from B to A
A B C
0 0 0
0 0 0
1 0 0
2 0 0
3 4 5
********************************************************************************
move disk 4 from B to C
A B C
0 0 0
0 0 0
1 0 0
2 0 4
3 0 5
********************************************************************************
move disk 1 from A to C
A B C
0 0 0
0 0 0
0 0 1
2 0 4
3 0 5
********************************************************************************
move disk 2 from A to B
A B C
0 0 0
0 0 0
0 0 1
0 0 4
3 2 5
********************************************************************************
move disk 1 from C to B
A B C
0 0 0
0 0 0
0 0 0
0 1 4
3 2 5
********************************************************************************
move disk 3 from A to C
A B C
0 0 0
0 0 0
0 0 3
0 1 4
0 2 5
********************************************************************************
move disk 1 from B to A
A B C
0 0 0
0 0 0
0 0 3
0 0 4
1 2 5
********************************************************************************
move disk 2 from B to C
A B C
0 0 0
0 0 2
0 0 3
0 0 4
1 0 5
********************************************************************************
move disk 1 from A to C
A B C
0 0 1
0 0 2
0 0 3
0 0 4
0 0 5
********************************************************************************