algorithm-in-python/dynamicProgramming/splitStripe.py

''' mbinary
#########################################################################
# File : splitStripe.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-08-24  17:07
# Description:
#########################################################################
'''

'''
    There is stripe which length is n, 
    priceMap contains a map for different length of stripe and its price
    then find the maximum price to split the stripe in different shorter stripes
    ( including  the original length if possible)
'''


def count(n, prices):
    def best(cur):
        # note that copying the list or create a new list in the following new_stripes codes
        if cur in values:
            return values[cur], stripes[cur]
        maxPrice = 0
        new_stripes = []
        for i, j in prices.items():
            if i <= cur:
                p, tmp = best(cur-i)
                if maxPrice < p+j:
                    # if the list is not copyed, create a new list, don't use append
                    new_stripes = tmp+[i]
                    maxPrice = p+j
        values[cur] = maxPrice
        stripes[cur] = new_stripes
        return maxPrice, new_stripes
    values = {0: 0}
    stripes = {0: []}
    return best(n)


if __name__ == '__main__':
    li = [(1, 1), (2, 5), (3, 8), (4, 9), (5, 10),
          (6, 17), (7, 17), (8, 20), (9, 24), (10, 30)]
    prices = {i: j for i, j in li}
    n = 40

    d = {i: count(i, prices) for i in range(n+1)}
    for i in range(n+1):
        print(i, d[i])