練習問題/解答例/有理化するプログラム/Python
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開始行:
[[問題文>練習問題#r471e69d]]
解答例1
import math, fractions
N = 100
squares = []
for i in range(int(math.sqrt(N**2)), 1, -1):
squares.append(i**2)
simplifier = {}
for n in range(2, N**2 + 1):
if n in squares:
simplifier[n] = (int(math.sqrt(n)), 1)
else:
x = 1
y = n
for s in squares:
if y % s == 0:
y //= s
x *= int(math.sqrt(s))
simplifier[n] = (x, y)
for a in range(1, N+1):
for b in range(2, N+1):
c = a * b
integer, sqrt = simplifier[c]
frac = fractions.Fraction(integer, b)
numer, denom = frac.as_integer_ratio()
if sqrt == 1:
res = f"{frac}"
elif frac == 1:
res = f"√{sqrt}"
elif numer == 1:
res = f"√{sqrt}/{denom}"
elif denom == 1:
res = f"{numer}√{sqrt}"
else:
res = f"{numer}√{sqrt}/{denom}"
print(f"√{a}/√{b} -> {res}")
解答例2
from math 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
x, y = 1, 1
for p, e in dic.items():
x *= p ** (e // 2)
y *= p ** (e % 2)
return x, y
cache = {}
def f2(n):
if not n in cache:
cache[n] = f1(n)
return cache[n]
for a in range(1, N+1):
for b in range(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
# 分母が1
if xb == 1:
if ya == 1:
right = f'{xa}'
elif xa == 1:
right = f'√{ya}'
else:
right = f'{xa}√{ya}'
# 分母がある
else:
if ya == 1:
right = f'{xa}/{xb}'
elif xa == 1:
right = f'√{ya}/{xb}'
else:
right = f'{xa}√{ya}/{xb}'
print(f'√{a}/√{b} -> {right}')
終了行:
[[問題文>練習問題#r471e69d]]
解答例1
import math, fractions
N = 100
squares = []
for i in range(int(math.sqrt(N**2)), 1, -1):
squares.append(i**2)
simplifier = {}
for n in range(2, N**2 + 1):
if n in squares:
simplifier[n] = (int(math.sqrt(n)), 1)
else:
x = 1
y = n
for s in squares:
if y % s == 0:
y //= s
x *= int(math.sqrt(s))
simplifier[n] = (x, y)
for a in range(1, N+1):
for b in range(2, N+1):
c = a * b
integer, sqrt = simplifier[c]
frac = fractions.Fraction(integer, b)
numer, denom = frac.as_integer_ratio()
if sqrt == 1:
res = f"{frac}"
elif frac == 1:
res = f"√{sqrt}"
elif numer == 1:
res = f"√{sqrt}/{denom}"
elif denom == 1:
res = f"{numer}√{sqrt}"
else:
res = f"{numer}√{sqrt}/{denom}"
print(f"√{a}/√{b} -> {res}")
解答例2
from math 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
x, y = 1, 1
for p, e in dic.items():
x *= p ** (e // 2)
y *= p ** (e % 2)
return x, y
cache = {}
def f2(n):
if not n in cache:
cache[n] = f1(n)
return cache[n]
for a in range(1, N+1):
for b in range(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
# 分母が1
if xb == 1:
if ya == 1:
right = f'{xa}'
elif xa == 1:
right = f'√{ya}'
else:
right = f'{xa}√{ya}'
# 分母がある
else:
if ya == 1:
right = f'{xa}/{xb}'
elif xa == 1:
right = f'√{ya}/{xb}'
else:
right = f'{xa}√{ya}/{xb}'
print(f'√{a}/√{b} -> {right}')
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