Projecte.pdf ----> problem = 31 ---- coin sums unlimited backpack computing possible times

Problem 31

In England and the currency is made up of pound, round, and pence, P, and there are eight coins in general circulation:

1 p, 2 p, 5 p, 10 p, 20 p, 50 p, half 1 (100 P) and half 2 (200 P ).

It is possible to make every 2 in the following way:

1 × Jun 1 + 1 × 50 p + 2 × 20 p + 1 × 5 p + 1 × 2 p + 3 × 1 p

How many different ways can be used 2 be made using any number of coins?

 
Import timedef CAL (sum, Count, value): If sum = 200: Count + = 1 returnif sum> 200: returnfor I in range ): sum + = value [I] Cal (sum, Count, value) sum-= value [I] Begin = time. time () num = {100,200,}; num = List (Num) Count = 0cal (0, Count, num) End = time. time () print countprint end-begin
 

Method 1: Deep Search timeout

 
# Resolution: retrieve the largest coin value from the list each time, and obtain the upper limit of the maximum number of coins. # overlay the number, and use a smaller number. # Def CAL (value, coins): If value = 0 or Len (coins) = 1: return 1 else: coins = sorted (coins) largest = coins [-1] uses = value/largesttotal = 0for I in range (uses + 1): Total + = CAL (value-largest * I, coins [: -1]) return totalprint CAL (200, [100,200,])
 

Second, greedy and extreme value AC