Ex. Set of Coins - {1,2,5,10} ; MaxSum -20
We have to find a set of coins with minimum coins which can make any number up to 20.
I came up with a greedy approach depending on division of the max sum by largest coin gives remainder 0 or 1.
20/10 = 2 -- remainder =0 ; In case of zero remainder, reduce the quotient by 1 to get number of 10 coins(2-1=1) and continue with Maxsum =10(same as coin) and set{1,2,5}
Answer Set={10} (only 1 coin of 10 added - quotient-1)
10/5=2 -- remainder =0 ; Answer Set={10,5} (add only 1(quotient-1) 5-coins) MaxSum=5
Answer Set= {10,5}
set={1,2}
5/2= 2 -- remainder =1; In case of non zero remainder, add coins equal to quotient(add 2 coins of 2 ) and set Maxsum= Subtract one from Coin chosen from set(here it is 2) = 2-1 = 1.
Answer Set = {10,5,2,2} ( coins added =quotient )
Set={1}
Maxsum=1 (one subtracted from coin chosen from set)
Base Case- Set={1} and MaxSum =1 . So we need only 1 coin of 1.
Answer Set= {10,5,2,2,1}
我在很多案例中尝试过相同的逻辑。它有效，但它是否正确？