# ITSA E-tutor Mathematics I Python Version
{%hackmd BJrTq20hE %}
###### tags: `python`
:::warning
:warning:**Warining :**
1. If you have **NOT** read "[Python Basic Notes"](https://hackmd.io/@cheung4843/HycouTvtu) which is designed for the beginners, please read that first.
2. **Do Not merely take a glance at these codes, please try them hands-on.**
3. Some solutions are **NOT** optimal, however, they are relatively easy and Intuitive for the beginners.
:::
:::info
:blue_book: **The Method Of Use :**
1. Here are most solutions to [this problem database](https://e-tutor.itsa.org.tw/e-Tutor/mod/programming/index.php?id=284). Please register an account on e-tutor first, clicking [this](https://portal.itsa.org.tw/user/register).
2. If you have more interest on C++, please click [this](https://hackmd.io/@cheung4843/H1pi30DTr) to see the C++ version.
:::
:::success
:pencil: **Start Programming:**
1. [e-tutor](https://e-tutor.itsa.org.tw/e-Tutor/)
2. [repl.it](https://replit.com/languages/python3)
:::
> [TOC]
---
## [C_MM01-易] 計算梯型面積
```python=
while True:
a, b, c = map(float, input().split())
area = ((a + b) * c) / 2
print("Trapezoid area:" + str(area))
```
## [C_MM02-易] 計算三角形面積
```python=
while True:
a, b = map(float, input().split())
area = (a * b) / 2
print(area)
```
## [C_MM03-易] 兩數總和
```python=
while True:
a, b = map(int, input().split())
print(a + b)
```
## [C_MM04-易] 計算總和、乘積、差、商和餘數
```python=
while True:
a, b = map(int, input().split())
print('{}+{}={}'.format(a, b, a + b))
print('{}*{}={}'.format(a, b, a * b))
print('{}-{}={}'.format(a, b, a - b))
print('{}/{}={}...{}'.format(a, b, a // b, a % b))
```
## [C_MM05-易] 計算正方形面積
```python=
from decimal import Decimal, ROUND_HALF_UP
while True:
a = input()
print((Decimal(a) ** Decimal(2)).quantize(Decimal('0.0'), rounding=ROUND_HALF_UP))
```
## [C_MM06-易] 英哩轉公里
```python=
while True:
mi = int(input())
km = mi * 1.6
print('{0:.1f}'.format(km))
```
## [C_MM07-易] 計算平方值與立方值
```python=
while True:
a = int(input())
print(a, a**2, a**3)
```
## [C_MM08-易] 計算兩數和的平方值
```python=
while True:
a, b = map(int, input().split())
print((a + b) ** 2)
```
## [C_MM09-易] 計算 i 次方的值
```python=
while True:
i = int(input())
if i > 31:
print('Value of more than 31')
else:
print(1 << i)
```
## [C_MM10-易] 攝氏溫度轉華式溫度
```python=
while True:
c = float(input())
f = c * 1.8 + 32
print('{0:.1f}'.format(f))
```
## [C_MM11-易] 購票計算
```python=
while True:
x = int(input())
print('NT10={}'.format(x // 10))
x %= 10
print('NT5={}'.format(x // 5))
x %= 5
print('NT1={}'.format(x))
```
## [C_MM12-易] 相遇時間計算
```python=
from math import ceil
while True:
d = int(input())
t = d * 100 / (100 - 30 * 2.54)
print(ceil(t))
```
## [C_MM13-易] 停車費計算
```python=
while True:
h1, m1 = map(int, input().split())
h2, m2 = map(int, input().split())
s = 0
t = 60 * (h2 - h1) + (m2 - m1)
if t > 240:
s += ((t - 240) // 30) * 60
t = 240
if t > 120:
s += ((t - 120) // 30) * 40
t = 120
s += (t // 30) * 30
print(s)
```
## [C_MM14-易] 計算時間的組合
```python=
while True:
s = int(input())
print('{} days'.format(s // 86400))
print('{} hours'.format(s % 86400 // 3600))
print('{} minutes'.format(s % 3600 // 60))
print('{} seconds'.format(s % 60))
```
## [C_MM15-易] 判斷座標是否在正方形的範圍內
```python=
while True:
x, y = map(int, input().split())
if 0 <= x <= 100 and 0 <= y <= 100:
print('inside')
else:
print('outside')
```
## [C_MM16-易] 判斷座標是否在圓形的範圍內
```python=
while True:
x, y = map(int, input().split())
if x ** 2 <= 10000 and y ** 2 <= 10000:
print('inside')
else:
print('outside')
```
## [C_MM17-易] 求最大公因數
```python=
from math import gcd
while True:
x, y = map(int, input().split())
print(gcd(x, y))
```
## [C_MM18-易] 十進制轉二進制
```python=
byte = [1] * 8
while True:
x = int(input())
isPos = x > 0
if not isPos:
x = ~x
for i in range(7, -1, -1):
byte[i] = x % 2
x //= 2
if not isPos:
for i in range(0, 8):
byte[i] ^= 1
for bit in byte:
print(bit, end='')
print()
```
## [C_MM19-易] 電話費計算
```python=
while True:
m = int(input())
s = m * 0.9
if m >= 1500:
s *= 0.79
elif m > 800:
s *= 0.9
print('{0:.1f}'.format(s))
```
## [C_MM20-易] 十進位轉十六進位
```python=
while True:
x = int(input())
print(format(x, 'X'))
```
## [C_MM21-易] 算階乘
```python=
from math import factorial
while True:
x = int(input())
print(factorial(x))
```
## [C_MM24-易] 計算薪水
```python=
while True:
h, p = map(int, input().split())
if h <= 60:
s = h * p
elif 60 < h < 121:
s = (60 * p) + (h - 60) * p * 1.33
elif h >= 121:
s = (60 * p * 2.33) + (h - 120) * p * 1.66
print('{0:.1f}'.format(s))
```
## [C_MM25-易] 計算正整數被3整除之數值之總和
```python=
while True:
N = int(input())
s = 0
for i in range(0, N + 1, 3):
s += i
print(s)
```
## [C_MM26-易] 輸出 1x1、2x2、...、NxN之結果
```python=
while True:
N = int(input())
for i in range(1, N + 1):
print('{}*{}={}'.format(i, i, i * i))
```
## [C_MM27-易] 計算兩整數間所有整數的總和
```python=
while True:
a, b = map(int, input().split())
print(((a + b) * (abs(a - b) + 1)) // 2)
```
## [C_MM28-易] 計算1到N之間屬於5和7的倍數
```python=
while True:
N = int(input())
if N >= 35:
print(35, end='')
for i in range(70, N + 1, 35):
print(' {}'.format(i), end='')
print()
```
## [C_MM29-易] 最大質數問題
此處採用$Bruteforce$。
```python=
def is_prime(x):
if x > 1:
for j in range(2, int(x ** (1 / 2)) + 1):
if x % j == 0:
return False
return True
else:
return False
while True:
N = int(input())
for i in range(N - 1, 2, -1):
if is_prime(i):
print(i)
break
```
## [C_MM30-易] 質數判別
此處採用$Eratosthenes$，後台測資小於$2^{10}$，如果把表開到$2^{31}$，會TLE。
```python=
MAX = 2 ** 10
prime = [True] * MAX
for i in range(2, int(MAX ** 0.5) + 1):
if prime[i]:
for j in range(i * i, MAX, i):
prime[j] = False
while True:
N = int(input())
if prime[N]:
print('YES')
else:
print('NO')
```
## [C_MM31-易] 計算1~N內能被2跟3整除，但不能被12整除的整數總和
```python=
while True:
N = int(input())
print(sum([i for i in range(0, N + 1, 6) if i % 6 == 0 and i % 12 != 0]))
```
## [C_MM32-易] Armstrong數
```python=
while True:
N = int(input())
if (N // 100) ** 3 + (N % 100 // 10) ** 3 + (N % 10) ** 3 == N:
print('Yes')
else:
print('No')
```
## [C_MM33-易] 找1~N的完美數
測資小於$2^{13}$，事實上，直接建好表會更快；這裡只是示範如何建表。
```python=
table = []
for i in range(6, 2 ** 13, 2):
s = 0
for j in range(1, i):
if i % j == 0:
s += j
if s == i:
table.append(i)
while True:
N = int(input())
print(' '.join([str(x) for x in table if x <= N]))
```
## [C_MM34-易] 因數問題
```python=
while True:
N = int(input())
ans = []
for i in range(1, N + 1):
if N % i == 0:
ans.append(str(i))
print(' '.join(ans))
```
## [C_MM35-易] 平、閏年判定
```python=
while True:
N = int(input())
if N % 400 == 0 or (N % 4 == 0 and N % 100 != 0):
print('Bissextile Year')
else:
print('Common Year')
```
## [C_MM36-易] 季節判定
```python=
while True:
N = int(input())
if N in [3, 4, 5]:
print('Spring')
elif N in [6, 7, 8]:
print('Summer')
elif N in [9, 10, 11]:
print('Autumn')
elif N in [12, 1, 2]:
print('Winter')
```
## [C_MM37-易] 判斷座標位於何處
```python=
while True:
x, y = map(int, input().split())
if x == 0 and y == 0:
print('Origin')
elif x != 0 and y == 0:
print('x-axis')
elif x == 0 and y != 0:
print('y-axis')
elif x > 0 and y > 0:
print('1st Quadrant')
elif x < 0 < y:
print('2nd Quadrant')
elif x < 0 and y < 0:
print('3rd Quadrant')
elif x > 0 > y:
print('4th Quadrant')
```
## [C_MM38-易] 判斷3整數是否能構成三角形之三邊長
```python=
while True:
x, y, z = map(int, input().split())
if x + y > z and x + z > y and y + z > x:
print('fit')
else:
print('unfit')
```
## [C_MM39-易] 判斷是何種三角形
```python=
while True:
a, b, c = map(int, input().split())
a2, b2, c2 = a * a, b * b, c * c
if a + b > c and a + c > b and b + c > a:
if a2 + b2 == c2 or a2 + c2 == b2 or b2 + c2 == a2:
print('Right Triangle')
elif a2 + b2 < c2 or a2 + c2 < b2 or b2 + c2 < a2:
print('Obtuse Triangle')
elif a2 + b2 > c2 and a2 + c2 > b2 and b2 + c2 > a2:
print('Acute Triangle')
else:
print('Not Triangle')
```
## [C_MM40-易] 1~N之間的總和
```python=
while True:
N = int(input())
s = 1
print(1, end='')
for i in range(2, N + 1):
s += i
print(' + {}'.format(i), end='')
print(' = {}'.format(s))
```
## [C_MM42-中] 求(-1)^(n+1)x[1/(2n-1)]的和
```python=
s = [0] * 16
s[1] = 1.0
for i in range(2, 16):
s[i] = s[i - 1] + ((-1) ** (i + 1)) / (2 * i - 1)
while True:
n = int(input())
print('{0:.3f}'.format(s[n]))
```
## [C_MM44-易] The Numbers
```python=
while True:
N, M = input().split()
cnt = 0
for i in range(0, 6):
if M[i] == N[0] and M[i + 1] == N[1]:
cnt += 1
print(cnt)
```
## [C_MM45-中] 分禮物
```python=
class Participant:
def __init__(self, name, gift_name):
self.name = name
self.gift_name = gift_name
class Permutation:
step = 0
n = 0
cnt = 0
def __init__(self, n):
self.n = n
self.list_name = []
self.arrangement = [''] * n
self.book = [False] * n
self.result = ''
def dfs(self, step):
if step == n:
for k in range(n):
if self.list_name[k].gift_name == self.arrangement[k]:
return
for k in range(0, n):
if k != 0:
self.result += ','
self.result += '{} {}'.format(self.list_name[k].name, self.arrangement[k])
self.result += '\n'
self.cnt += 1
for j in range(n):
if self.book[j]:
continue
self.arrangement[step] = self.list_name[j].gift_name
self.book[j] = True
self.dfs(step + 1)
self.book[j] = False
def answer(self):
print(self.cnt)
print(self.result, end='')
n = int(input())
p = Permutation(n)
for i in range(0, n):
name, gift_name = input().split()
p.list_name.append(Participant(name, gift_name))
p.dfs(0)
p.answer()
```
## [C_MM46-易] 複數運算
```python=
n = int(input())
for i in range(0, n):
opr, a, b, c, d = input().split()
A = complex(int(a), int(b))
B = complex(int(c), int(d))
if opr == '+':
C = A + B
elif opr == '-':
C = A - B
elif opr == '*':
C = A * B
print(int(C.real), int(C.imag))
```
## [C_MM48-易] F91
```python=
def f91(z):
if z >= 101:
return z - 10
else:
return 91
k = int(input())
n = list(map(int, input().split()))
for x in n:
print(f91(x))
```
## [C_MM49-易] 連續1的倍數
```python=
def f(x):
num = '1'
while int(num) % x != 0:
num += '1'
else:
return len(num)
k = int(input())
n = list(map(int, input().split()))
for i in range(k):
print(f(n[i]))
```
## [C_MM50-易] 分贓
```python=
while True:
k = int(input())
things = list(map(int, input().split()))
total = sum(things)
half = total // 2
bag = [0] * (half + 1)
for w in things:
for j in range(half, w - 1, -1):
bag[j] = max(bag[j - w] + w, bag[j])
print(abs(total - 2 * bag[half]))
```
---
> [time=Sun, Jun 6, 2021 7:00 PM]
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