recursion-and-dp: add coin change problem

README.md

@@ -66,6 +66,7 @@ I have also created a directory to save my implementations of some [Data Structu
 | - | Ways To Climb Stairs | [Python](./problems/recursion-and-dp/ways_to_climb_stairs.py) | - | - |
 | 79 | [Word Search](https://leetcode.com/problems/word-search/) | [Python](./problems/recursion-and-dp/word_search.py) | Medium | LeetCode |
 | - | Winning Hand | [Python](./problems/recursion-and-dp/winning_hand.py) | - | - |
+| - | [The Coin Change Problem](https://www.hackerrank.com/challenges/coin-change/problem) | [Python](./problems/recursion-and-dp/coin_change_problem.py) | Medium | HackerRank |
 
 ## Sorting and Searching
 

problems/recursion-and-dp/coin_change_problem.py

@@ -0,0 +1,107 @@
+
+"""
+HackerRank - The Coin Change Problem
+https://www.hackerrank.com/challenges/coin-change/problem
+"""
+
+
+#!/bin/python3
+
+"""
+n = 3
+coins = [8,1,2,3]
+
+[1,1,1]
+[1,2]
+[3]
+
+
+           3
+        /  | \  \
+    -5 (X) 2  1  0
+           | \
+           1  0
+           |
+           0
+
+We can start with the amount 3 and try to use
+each of the coins recursively.
+If we reach zero, we have found one way to solve it.
+We return 1 from the leaf nodes and sum them in the end.
+
+- Start from the amount n
+- For each coin, try to take that amount
+(we do not go back to coins we have already used, otherwise we would make different
+combinations)
+- If we reach zero, return 1, if less than zero, return 0
+
+Time Complexity: O(coins ^ amount)
+Space Complexity: O(amount)
+
+However, we can use memoization/dynamic programming to speed this up.
+
+- For every amount we have found, we memoize the nways to find a solution
+on that amount.
+
+Time Complexity: O(coins * amount)
+Space Complexity: O(amount)
+
+
+
+"""
+
+import math
+import os
+import random
+import re
+import sys
+
+#
+# Complete the 'getWays' function below.
+#
+# The function is expected to return a LONG_INTEGER.
+# The function accepts following parameters:
+#  1. INTEGER n
+#  2. LONG_INTEGER_ARRAY c
+#
+
+def getWays(amount, coins):
+    memo = dict()
+
+    def getWaysRec(amount, coins, pos):
+        if amount < 0:
+            return 0
+
+        if amount == 0:
+            return 1
+
+        if (amount, pos) in memo:
+            return memo[(amount, pos)]
+
+        n_ways = 0
+        for coin_pos in range(pos, len(coins)):
+            n_ways += getWaysRec(amount-coins[coin_pos], coins, coin_pos)
+
+        memo[(amount, pos)] = n_ways
+        return n_ways
+
+    return getWaysRec(amount, coins, 0)
+
+if __name__ == '__main__':
+    fptr = open(os.environ['OUTPUT_PATH'], 'w')
+
+    first_multiple_input = input().rstrip().split()
+
+    n = int(first_multiple_input[0])
+
+    m = int(first_multiple_input[1])
+
+    c = list(map(int, input().rstrip().split()))
+
+    # Print the number of ways of making change for 'n' units using coins having the values given by 'c'
+
+    ways = getWays(n, c)
+
+    fptr.write(str(ways) + '\n')
+
+    fptr.close()