Merge pull request #87 from rehassachdeva/modular_multiplicative_inverse

Implement modular multiplicative inverse

pydsa/__init__.py

@@ -14,3 +14,4 @@
 from .radix_sort import radix_sort
 from .binary_tree import BTNode
 from .gnome_sort import gnome_sort
+from .mod_inverse import mod_inverse

pydsa/mod_inverse.py

@@ -0,0 +1,30 @@
+"""
+Modular Multiplicative Inverse
+
+Complexity: O(m)
+
+Reference Used:
+http://www.geeksforgeeks.org/multiplicative-inverse-under-modulo-m/
+"""
+
+
+def mod_inverse(a, m):
+    """
+    Modular Multiplicative Inverse of two integers 'a' and 'm' is a positive
+    integer 'x' less than m such that (ax) % m is 1.
+
+    Finds modular inverse of 'a' modulo 'm' by checking for all integers from
+    1 to 'm' and returns -1 if it doesn't exist.
+
+    >>> from pydsa import mod_inverse
+    >>> mod_inverse(3, 11)
+    4
+    >>> mod_inverse(2, 12)
+    -1
+    """
+    a = a % m
+    for x in range(1, m):
+        if (a*x) % m == 1:
+            return x
+
+    return -1       # modular inverse of 'a' modulo 'm' doesn't exist.

pydsa/tests/test_mod_inverse.py

@@ -0,0 +1,6 @@
+from pydsa.mod_inverse import mod_inverse
+
+
+def test_mod_inverse():
+    assert mod_inverse(3, 13) == 9
+    assert mod_inverse(30, 120000) == -1