Find minimum number of coins that make a given value
- Task
- Find minimum number of coins that make a given value
coins = [1,2,5,10,20,50,100,200]
value = 988
Coins are:
4*200
1*100
1*50
1*20
1*10
1*5
1*2
1*1
Factor
<lang factor>USING: assocs kernel math math.order prettyprint sorting ;
- make-change ( value coins -- assoc )
[ >=< ] sort [ /mod swap ] zip-with nip ;
988 { 1 2 5 10 20 50 100 200 } make-change .</lang>
- Output:
{
{ 200 4 }
{ 100 1 }
{ 50 1 }
{ 20 1 }
{ 10 1 }
{ 5 1 }
{ 2 1 }
{ 1 1 }
}
Julia
Using a linear optimizer for this is serious overkill, but why not? <lang julia>using JuMP, GLPK
model = Model(GLPK.Optimizer) @variable(model, ones, Int) @variable(model, twos, Int) @variable(model, fives, Int) @variable(model, tens, Int) @variable(model, twenties, Int) @variable(model, fifties, Int) @variable(model, onehundreds, Int) @variable(model, twohundreds, Int) @constraint(model, ones >= 0) @constraint(model, twos >= 0) @constraint(model, fives >= 0) @constraint(model, tens >= 0) @constraint(model, twenties >= 0) @constraint(model, fifties >= 0) @constraint(model, onehundreds >= 0) @constraint(model, twohundreds >= 0) @constraint(model, 988 == 1ones +2twos + 5fives + 10tens + 20twenties + 50fifties + 100onehundreds + 200twohundreds)
@objective(model, Min, ones + twos + fives + tens + twenties + fifties + onehundreds + twohundreds)
optimize!(model) println("Optimized total coins: ", objective_value(model)) for val in [ones, twos, fives, tens, twenties, fifties, onehundreds, twohundreds]
println("Value of ", string(val), " is ", value(val))
end
</lang>
- Output:
Optimized total coins: 11.0 Value of ones is 1.0 Value of twos is 1.0 Value of fives is 1.0 Value of tens is 1.0 Value of twenties is 1.0 Value of fifties is 1.0 Value of onehundreds is 1.0 Value of twohundreds is 4.0
REXX
<lang rexx>/*REXX pgm finds & displays the minimum number of coins which total to a specified value*/ parse arg $ coins /*obtain optional arguments from the CL*/ if $= | $="," then $= 988 /*Not specified? Then use the default.*/ if coins= | coins="," then coins= 1 2 5 10 20 50 100 200 /* ... " " " " */
- = words(coins) /*#: is the number of allowable coins.*/
w= 0 /*width of largest coin (for alignment)*/
do j=1 for #; @.j= word(coins, j) /*assign all coins to an array (@.). */
w= max(w, length(@.j) ) /*find the width of the largest coin. */
end /*j*/
say 'available coin denominations: ' coins /*shown list of available denominations*/ say say center(' making change for ' $, 30 ) /*display title for the upcoming output*/ say center( , 30, "─") /* " sep " " " " */ paid= 0 /*the total amount of money paid so far*/
do k=# by -1 for #; z= $ % @.k /*start with largest coin for payout. */
if z<1 then iterate /*if Z is not positive, then skip coin.*/
paid= z * @.k /*pay out a number of coins. */
$= $ - paid /*subtract the pay─out from the $ total*/
say right(z,9) ' of coin ' right(@.k, w) /*display how many coins were paid out.*/
end /*k*/
if $>0 then say 'exact payout not possible.' /*There a residue? Payout not possible*/ exit 0 /*stick a fork in it, we're all done. */</lang>
- output when using the default inputs:
available coin denominations: 1 2 5 10 20 50 100 200
making change for 988
──────────────────────────────
4 of coin 200
1 of coin 100
1 of coin 50
1 of coin 20
1 of coin 10
1 of coin 5
1 of coin 2
1 of coin 1
Ring
<lang ring> load "stdlib.ring"
see "working..." + nl see "Coins are:" + nl sum = 988
sumCoins = 0 coins = [1,2,5,10,20,50,100,200] coins = reverse(coins)
for n = 1 to len(coins)
nr = floor(sum/coins[n])
if nr > 0
sumCoins= nr*coins[n]
sum -= sumCoins
see "" + nr + "*" + coins[n] + nl
ok
next
see "done..." + nl </lang>
- Output:
working... Coins are: 4*200 1*100 1*50 1*20 1*10 1*5 1*2 1*1 done...