== brute force ========================================
bruteforce on coinset=(1, 5, 10) with goal=24 
 number of solutions found = 9 : 
   [24, 0, 0] 
   [19, 1, 0] 
   [14, 2, 0] 
   [9, 3, 0] 
   [4, 4, 0] 
   [14, 0, 1] 
   [9, 1, 1] 
   [4, 2, 1] 
   [4, 0, 2] 
 fewest coins is 6 : [4, 0, 2] 

== greedy search ========================================
 greedy debug: coinset=(1, 5, 10), goal=24, change=None 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[0, 0, 1] 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[0, 0, 2] 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[1, 0, 2] 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[2, 0, 2] 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[3, 0, 2] 
 greedy debug: coinset=(1, 5, 10), goal=24, change=[4, 0, 2] 
greedy coinset=(1, 5, 10), goal=24 
finds 6 coins : [4, 0, 2] 

== dynamic programming ========================================
 dynamic : coinset=(1, 5, 10), goal=1, change=[1, 0, 0]) 
 dynamic : coinset=(1, 5, 10), goal=2, change=[2, 0, 0]) 
 dynamic : coinset=(1, 5, 10), goal=3, change=[3, 0, 0]) 
 dynamic : coinset=(1, 5, 10), goal=4, change=[4, 0, 0]) 
 dynamic : coinset=(1, 5, 10), goal=5, change=[0, 1, 0]) 
 dynamic : coinset=(1, 5, 10), goal=6, change=[1, 1, 0]) 
 dynamic : coinset=(1, 5, 10), goal=7, change=[2, 1, 0]) 
 dynamic : coinset=(1, 5, 10), goal=8, change=[3, 1, 0]) 
 dynamic : coinset=(1, 5, 10), goal=9, change=[4, 1, 0]) 
 dynamic : coinset=(1, 5, 10), goal=10, change=[0, 0, 1]) 
 dynamic : coinset=(1, 5, 10), goal=11, change=[1, 0, 1]) 
 dynamic : coinset=(1, 5, 10), goal=12, change=[2, 0, 1]) 
 dynamic : coinset=(1, 5, 10), goal=13, change=[3, 0, 1]) 
 dynamic : coinset=(1, 5, 10), goal=14, change=[4, 0, 1]) 
 dynamic : coinset=(1, 5, 10), goal=15, change=[0, 1, 1]) 
 dynamic : coinset=(1, 5, 10), goal=16, change=[1, 1, 1]) 
 dynamic : coinset=(1, 5, 10), goal=17, change=[2, 1, 1]) 
 dynamic : coinset=(1, 5, 10), goal=18, change=[3, 1, 1]) 
 dynamic : coinset=(1, 5, 10), goal=19, change=[4, 1, 1]) 
 dynamic : coinset=(1, 5, 10), goal=20, change=[0, 0, 2]) 
 dynamic : coinset=(1, 5, 10), goal=21, change=[1, 0, 2]) 
 dynamic : coinset=(1, 5, 10), goal=22, change=[2, 0, 2]) 
 dynamic : coinset=(1, 5, 10), goal=23, change=[3, 0, 2]) 
 dynamic : coinset=(1, 5, 10), goal=24, change=[4, 0, 2]) 

== brute force ========================================
bruteforce on coinset=(1, 6, 10) with goal=24 
 number of solutions found = 9 : 
   [24, 0, 0] 
   [18, 1, 0] 
   [12, 2, 0] 
   [6, 3, 0] 
   [0, 4, 0] 
   [14, 0, 1] 
   [8, 1, 1] 
   [2, 2, 1] 
   [4, 0, 2] 
 fewest coins is 4 : [0, 4, 0] 

== greedy search ========================================
 greedy debug: coinset=(1, 6, 10), goal=24, change=None 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[0, 0, 1] 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[0, 0, 2] 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[1, 0, 2] 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[2, 0, 2] 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[3, 0, 2] 
 greedy debug: coinset=(1, 6, 10), goal=24, change=[4, 0, 2] 
greedy coinset=(1, 6, 10), goal=24 
finds 6 coins : [4, 0, 2] 

== dynamic programming ========================================
 dynamic : coinset=(1, 6, 10), goal=1, change=[1, 0, 0]) 
 dynamic : coinset=(1, 6, 10), goal=2, change=[2, 0, 0]) 
 dynamic : coinset=(1, 6, 10), goal=3, change=[3, 0, 0]) 
 dynamic : coinset=(1, 6, 10), goal=4, change=[4, 0, 0]) 
 dynamic : coinset=(1, 6, 10), goal=5, change=[5, 0, 0]) 
 dynamic : coinset=(1, 6, 10), goal=6, change=[0, 1, 0]) 
 dynamic : coinset=(1, 6, 10), goal=7, change=[1, 1, 0]) 
 dynamic : coinset=(1, 6, 10), goal=8, change=[2, 1, 0]) 
 dynamic : coinset=(1, 6, 10), goal=9, change=[3, 1, 0]) 
 dynamic : coinset=(1, 6, 10), goal=10, change=[0, 0, 1]) 
 dynamic : coinset=(1, 6, 10), goal=11, change=[1, 0, 1]) 
 dynamic : coinset=(1, 6, 10), goal=12, change=[0, 2, 0]) 
 dynamic : coinset=(1, 6, 10), goal=13, change=[1, 2, 0]) 
 dynamic : coinset=(1, 6, 10), goal=14, change=[2, 2, 0]) 
 dynamic : coinset=(1, 6, 10), goal=15, change=[3, 2, 0]) 
 dynamic : coinset=(1, 6, 10), goal=16, change=[0, 1, 1]) 
 dynamic : coinset=(1, 6, 10), goal=17, change=[1, 1, 1]) 
 dynamic : coinset=(1, 6, 10), goal=18, change=[0, 3, 0]) 
 dynamic : coinset=(1, 6, 10), goal=19, change=[1, 3, 0]) 
 dynamic : coinset=(1, 6, 10), goal=20, change=[0, 0, 2]) 
 dynamic : coinset=(1, 6, 10), goal=21, change=[1, 0, 2]) 
 dynamic : coinset=(1, 6, 10), goal=22, change=[0, 2, 1]) 
 dynamic : coinset=(1, 6, 10), goal=23, change=[1, 2, 1]) 
 dynamic : coinset=(1, 6, 10), goal=24, change=[0, 4, 0])