Cclauss patch 2

Remainder.py

@@ -0,0 +1,91 @@
+# Chinese Remainder Theorem:
+# GCD ( Greatest Common Divisor ) or HCF ( Highest Common Factor )
+
+# If GCD(a,b) = 1, then for any remainder ra modulo a and any remainder rb modulo b
+# there exists integer n, such that n = ra (mod a) and n = ra(mod b).  If n1 and n2 are
+# two such integers, then n1=n2(mod ab)
+
+# Algorithm :
+
+# 1. Use extended euclid algorithm to find x,y such that a*x + b*y = 1
+# 2. Take n = ra*by + rb*ax
+
+
+# Extended Euclid
+def extended_euclid(a, b):
+    """
+    >>> extended_euclid(10, 6)
+    (-1, 2)
+
+    >>> extended_euclid(7, 5)
+    (-2, 3)
+
+    """
+    if b == 0:
+        return (1, 0)
+    (x, y) = extended_euclid(b, a % b)
+    k = a // b
+    return (y, x - k * y)
+
+
+# Uses ExtendedEuclid to find inverses
+def chinese_remainder_theorem(n1, r1, n2, r2):
+    """
+    >>> chinese_remainder_theorem(5,1,7,3)
+    31
+
+    Explanation : 31 is the smallest number such that
+                (i)  When we divide it by 5, we get remainder 1
+                (ii) When we divide it by 7, we get remainder 3
+
+    >>> chinese_remainder_theorem(6,1,4,3)
+    14
+
+    """
+    (x, y) = extended_euclid(n1, n2)
+    m = n1 * n2
+    n = r2 * x * n1 + r1 * y * n2
+    return (n % m + m) % m
+
+
+# ----------SAME SOLUTION USING InvertModulo instead ExtendedEuclid----------------
+
+# This function find the inverses of a i.e., a^(-1)
+def invert_modulo(a, n):
+    """
+    >>> invert_modulo(2, 5)
+    3
+
+    >>> invert_modulo(8,7)
+    1
+
+    """
+    (b, x) = extended_euclid(a, n)
+    if b < 0:
+        b = (b % n + n) % n
+    return b
+
+
+# Same a above using InvertingModulo
+def chinese_remainder_theorem2(n1, r1, n2, r2):
+    """
+    >>> chinese_remainder_theorem2(5,1,7,3)
+    31
+
+    >>> chinese_remainder_theorem2(6,1,4,3)
+    14
+
+    """
+    x, y = invert_modulo(n1, n2), invert_modulo(n2, n1)
+    m = n1 * n2
+    n = r2 * x * n1 + r1 * y * n2
+    return (n % m + m) % m
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod(name="chinese_remainder_theorem", verbose=True)
+    testmod(name="chinese_remainder_theorem2", verbose=True)
+    testmod(name="invert_modulo", verbose=True)
+    testmod(name="extended_euclid", verbose=True)

web_programming/currency_converter.py

@@ -9,7 +9,7 @@
 
 URL_BASE = "https://www.amdoren.com/api/currency.php"
 TESTING = os.getenv("CI", False)
-API_KEY = os.getenv("AMDOREN_API_KEY")
+API_KEY = os.getenv("AMDOREN_API_KEY", "")
 if not API_KEY and not TESTING:
     raise KeyError("Please put your API key in an environment variable.")