Rename coin_change.py to minimum_coin_change.py (#4108)

dynamic_programming/minimum_coin_change.py

@@ -0,0 +1,46 @@
+"""
+You have m types of coins available in infinite quantities
+where the value of each coins is given in the array S=[S0,... Sm-1]
+Can you determine number of ways of making change for n units using
+the given types of coins?
+https://www.hackerrank.com/challenges/coin-change/problem
+"""
+
+
+def dp_count(S, n):
+    """
+    >>> dp_count([1, 2, 3], 4)
+    4
+    >>> dp_count([1, 2, 3], 7)
+    8
+    >>> dp_count([2, 5, 3, 6], 10)
+    5
+    >>> dp_count([10], 99)
+    0
+    >>> dp_count([4, 5, 6], 0)
+    1
+    >>> dp_count([1, 2, 3], -5)
+    0
+    """
+    if n < 0:
+        return 0
+    # table[i] represents the number of ways to get to amount i
+    table = [0] * (n + 1)
+
+    # There is exactly 1 way to get to zero(You pick no coins).
+    table[0] = 1
+
+    # Pick all coins one by one and update table[] values
+    # after the index greater than or equal to the value of the
+    # picked coin
+    for coin_val in S:
+        for j in range(coin_val, n + 1):
+            table[j] += table[j - coin_val]
+
+    return table[n]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()