[[問題文>練習問題#r471e69d]]
解答例1
#coding:utf-8
import math, fractions
t = []
for i in range(int(math.sqrt(10000)), 1, -1):
t.append(i**2)
dic = {}
for r in range(2, 10000 + 1):
u = [str(r)]
if r in t:
dic.update(dict.fromkeys(u, [int(math.sqrt(r)), 1]))
else:
x = 1
for w in t:
if r % w == 0:
r /= w
x *= (int(math.sqrt(w)))
if x > 1:
dic.update(dict.fromkeys(u, [int(x), r]))
else:
dic.update(dict.fromkeys(u, [1, r]))
for a in range(1, 101):
for b in range(2, 101):
c = a * b
z = dic[str(c)]
if z[0] == 1:
print "√" + str(a) + "/" + "√" + str(b) + " -> " + "√" + str(z[1]) + "/" + str(b)
elif z[1] == 1:
print "√" + str(a) + "/" + "√" + str(b) + " -> " + str(fractions.Fraction(z[0], b))
else:
if fractions.Fraction(z[0], b) == 1:
print "√" + str(a) + "/" + "√" + str(b) + " -> " + "√" + str(z[1])
else:
print "√" + str(a) + "/" + "√" + str(b) + " -> " + "(" + str((fractions.Fraction(z[0], b))) + ")" + "*" + "√" + str(z[1])
解答例2
# -*- coding: utf-8 -*-
from fractions import gcd
from collections import defaultdict
N = 100
# √nの有理化
# 答え: x√y
def f1(n):
p = n
d = 2
dic = defaultdict(int)
while d * d <= p:
while p % d == 0:
dic[d] += 1
p /= d
d += 1
if p > 1:
dic[p] += 1
y = n
for k, v in dic.items():
while v >= 2:
y /= (k * k)
v -= 2
x = int( (n/y) ** .5 )
return x, y
dictionary = {}
cache = {}
def f2(n):
if not n in dictionary:
dictionary[n] = f1(n)
return dictionary[n]
if not n in cache:
cache[n] = f1(n)
return cache[n]
for a in xrange(1, N+1):
for b in xrange(2, N+1):
# √a xa√ya
# --- = ----------
# √b xb√yb
xa, ya = f2(a)
xb, yb = f2(b)
if yb > 1:
ya *= yb
xb *= yb
# yb = 1 #になる
xxa, yya = f2(ya)
xa *= xxa
ya = yya
g = gcd(xa, xb)
xa /= g
xb /= g
left = '√{0}/√{1} -> '.format(a, b)
# 分母が1
if xb == 1:
if ya == 1:
print(left + '{0}'.format(xa))
elif xa == 1:
print(left + '√{0}'.format(ya))
else:
print(left + '{0}√{1}'.format(xa, ya))
# 分母がある
else:
if ya == 1:
print(left + '{0}/{1}'.format(xa, xb))
elif xa == 1:
print(left + '√{0}/{1}'.format(ya, xb))
else:
print(left + '{0}√{1}/{2}'.format(xa, ya, xb))
