The Change Problem

Solution to Rosalind Textbook Track Problem 5A: The Change Problem

Textbook_05A.py

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+#!/usr/bin/env python
+'''
+A solution to a code challenges that accompanies Bioinformatics Algorithms: An Active-Learning Approach by Phillip Compeau & Pavel Pevzner.
+The textbook is hosted on Stepic and the problem is listed on ROSALIND under the Textbook Track.
+
+Problem Title: The Change Problem
+Assignment #: 05
+Problem ID: A
+URL: http://rosalind.info/problems/5a/
+'''
+
+
+def dp_change(amount, coin_list):
+    '''Gives the minimum number of coins of denomination in coint_list necessary to create the given amount.'''
+    # Initiate the amounts larger than zero as a number greater than the upper bound.
+    min_coins = [0]+[(amount/min(coin_list))+1]*amount
+
+    # Use dynamic programming to build up to the desired amount.
+    for m in xrange(1,amount+1):
+        for coin in coin_list:
+            if m >= coin:
+                if min_coins[m-coin] + 1 < min_coins[m]:
+                    min_coins[m] = min_coins[m-coin] + 1
+    return min_coins[amount]
+
+
+def main():
+    '''Main call. Reads, runs, and saves problem specific data.'''
+    # Read the input data.
+    with open('data/textbook/rosalind_5a.txt') as input_data:
+        amount = int(input_data.readline().strip())
+        coin_list = map(int, input_data.readline().strip().split(','))
+
+    # Get the desired minimum number of coins.
+    min_number = str(dp_change(amount, coin_list))
+
+    # Print and save the answer.
+    print min_number
+    with open('output/textbook/Textbook_05A.txt', 'w') as output_data:
+        output_data.write(min_number)
+
+if __name__ == '__main__':
+    main()

data/textbook/rosalind_5a.txt

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+17369
+1,3,5,9,11,14,18,19,24

output/textbook/Textbook_05A.txt

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+725