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graham.py
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'''
github.com/electronwill 2016-11-29
https://en.wikipedia.org/wiki/Graham%27s_number
These functions are only designed and tested to work for integers a >= 0 and b >= 0 .
They are only feasible to execute for a few very small integer values.
'''
def successor(a):
return a + 1
def sum(a, b):
c = a
for _ in range(b):
c = successor(c)
return c
def sum_fast(a,b): return a+b
def product(a, b): #a*b
c = 0
for _ in range(b):
c = sum_fast(a, c)
return c
def product_fast(a,b): return a*b
def exponent(a, b): #a^b
c = 1
for _ in range(b):
c = product_fast(a, c)
return c
def exponent_fast(a,b): return a**b
def tetration(a, b): #a^^b
c = 1
for _ in range(b):
c = exponent_fast(a, c)
return c
def pentation(a, b): #a^^^b
c = 1
for _ in range(b):
c = tetration(a, c)
return c
def hyperoperation(a, b, n):
if n==0: return b+1
if n>2:
result=1
else:
result=[0,a,0][n]
for _ in range(b):
result = hyperoperation(a,result,n-1)
return result
def hyperoperation_fast(a,b,n):
if n==0: return b+1
if n==1: return a+b
if n==2: return a*b
if n==3: return a**b
result=1
for _ in range(b):
result = hyperoperation_fast(a,result,n-1)
return result
def h(a,b,n): return hyperoperation_fast(a,b,n)
def g(): #Graham's number; it is not feasible to execute this code
g = 4
for _ in range(64):
g = h(3,3,g+2)
return g
def test(f):
for a in range(4):
for b in range(4):
print(f(a,b),' ',end='')
print()
print()
def testing():
print('successor sum product exponent tetration pentation')
for a in range(4): print(successor(a),' ',end='')
print()
print()
test(sum)
test(product)
test(exponent)
test(tetration)
for a in range(3):
for b in range(4):
print(pentation(a,b),' ',end='')
print()
for b in range(3):
print(pentation(3,b),' ',end='')
print()
print()
print('hyperoperation')
for n in range(4):
for a in range(4):
for b in range(4):
print(hyperoperation(a,b,n),' ',end='')
print()
print()
print('hyperoperation_fast')
for n in range(5):
for a in range(4):
for b in range(4):
print(h(a,b,n),' ',end='')
print()
print()
for a in range(3):
for b in range(4):
print(h(a,b,5),' ',end='')
print()
for b in range(3):
print(h(3,b,5),' ',end='')
print()
testing()
'''
successor sum product exponent tetration pentation
1 2 3 4
0 1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
0 0 0 0
0 1 2 3
0 2 4 6
0 3 6 9
1 0 0 0
1 1 1 1
1 2 4 8
1 3 9 27
1 0 1 0
1 1 1 1
1 2 4 16
1 3 27 7625597484987
1 0 1 0
1 1 1 1
1 2 4 65536
1 3 7625597484987
hyperoperation
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
0 1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
0 0 0 0
0 1 2 3
0 2 4 6
0 3 6 9
1 0 0 0
1 1 1 1
1 2 4 8
1 3 9 27
hyperoperation_fast
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
0 1 2 3
1 2 3 4
2 3 4 5
3 4 5 6
0 0 0 0
0 1 2 3
0 2 4 6
0 3 6 9
1 0 0 0
1 1 1 1
1 2 4 8
1 3 9 27
1 0 1 0
1 1 1 1
1 2 4 16
1 3 27 7625597484987
1 0 1 0
1 1 1 1
1 2 4 65536
1 3 7625597484987
'''