Find minimum number of coins that make a given value
- Task
Find and show here on this page the minimum number of coins that can make a value of 988.
Available coins are: 1, 2, 5, 10, 20, 50, 100, and 200.
The coins that would be dispensed are:
four coins of 200 one coin of 100 one coin of 50 one coin of 20 one coin of 10 one coin of 5 one coin of 2 one coin of 1
Action!
<lang Action!>PROC Main()
DEFINE LEN="8" BYTE ARRAY coins=[200 100 50 20 10 5 2 1],count(LEN) BYTE i INT value=[988],curr,total
Zero(count,LEN) i=0 total=0 curr=value WHILE curr>0 DO IF curr>=coins(i) THEN count(i)==+1 total==+1 curr==-coins(i) ELSE i==+1 FI OD
PrintF("%I coins to make %I:%E",total,value) FOR i=0 TO LEN-1 DO IF count(i) THEN PrintF(" %B x %B%E",count(i),coins(i)) FI OD
RETURN</lang>
- Output:
Screenshot from Atari 8-bit computer
11 coins to make 988: 4 x 200 1 x 100 1 x 50 1 x 20 1 x 10 1 x 5 1 x 2 1 x 1
APL
<lang APL>coins←{
{⍺,≢⍵}⌸⍺[⍒⍺]{ coin←⊃(⍵≥⍺)/⍺ coin=0:⍬ coin,⍺∇⍵-coin }⍵
}</lang>
- Output:
(1 2 5 10 20 50 100 200) coins 988 200 4 100 1 50 1 20 1 10 1 5 1 2 1 1 1
AppleScript
<lang applescript>----------------- MINIMUM NUMBER OF COINS ----------------
-- change :: [Int] -> Int -> [(Int, Int)] on change(units, n)
if {} = units or 0 = n then {} else set {x, xs} to {item 1 of units, rest of units} set q to n div x if 0 = q then change(xs, n) else Template:Q, x & change(xs, n mod x) end if end if
end change
TEST -------------------------
on run
set coinReport to ¬ showChange({200, 100, 50, 20, 10, 5, 2, 1}) unlines(map(coinReport, {1024, 988}))
end run
-- showChange :: [Int] -> Int -> String
on showChange(units)
script on |λ|(n) script go on |λ|(qd) set {q, d} to qd (q as text) & " * " & d as text end |λ| end script unlines({("Summing to " & n as text) & ":"} & ¬ map(go, change(units, n))) & linefeed end |λ| end script
end showChange
GENERIC ------------------------
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
-- The list obtained by applying f -- to each element of xs. tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell
end map
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper. if script is class of f then f else script property |λ| : f end script end if
end mReturn
-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation -- of a list of strings with the newline character. set {dlm, my text item delimiters} to ¬ {my text item delimiters, linefeed} set s to xs as text set my text item delimiters to dlm s
end unlines</lang>
- Output:
Summing to 1024: 5 * 200 1 * 20 2 * 2 Summing to 988: 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
AWK
<lang AWK>
- syntax: GAWK -f FIND_MINIMUM_NUMBER_OF_COINS_THAT_MAKE_A_GIVEN_VALUE.AWK
BEGIN {
n = split("200,100,50,20,10,5,2,1",arr,",") main(988) main(388) main(0) exit(0)
} function main(arg1, amount,coins,denomination,i,remaining,total) {
amount = remaining = int(arg1) for (i=1; i<=n; i++) { denomination = arr[i] coins = 0 while (remaining >= denomination) { remaining -= denomination coins++ } total += coins printf("%4d x %2d = %d\n",denomination,coins,denomination*coins) } printf("%9d coins needed to disperse %s\n\n",total,arg1)
} </lang>
- Output:
200 x 4 = 800 100 x 1 = 100 50 x 1 = 50 20 x 1 = 20 10 x 1 = 10 5 x 1 = 5 2 x 1 = 2 1 x 1 = 1 11 coins needed to disperse 988 200 x 1 = 200 100 x 1 = 100 50 x 1 = 50 20 x 1 = 20 10 x 1 = 10 5 x 1 = 5 2 x 1 = 2 1 x 1 = 1 8 coins needed to disperse 388 200 x 0 = 0 100 x 0 = 0 50 x 0 = 0 20 x 0 = 0 10 x 0 = 0 5 x 0 = 0 2 x 0 = 0 1 x 0 = 0 0 coins needed to disperse 0
BASIC256
<lang BASIC256>amount = 988 sumCoins = 0 dim coins = {1, 2, 5, 10, 20, 50, 100, 200}
print "Make a value of "; amount; " using the coins 1, 2, 5, 10, 20, 50, 100 and 200:"
for n = coins[?]-1 to 0 step -1 tmp = floor(amount/coins[n]) if tmp >= 0 then print tmp; " * "; coins[n] sumCoins = sumCoins + tmp amount = amount % coins[n] end if next n end</lang>
- Output:
Igual que la entrada de FreeBASIC.
F#
<lang fsharp> //Find minimum number of coins that make a given value - Nigel Galloway: August 12th., 20 let fN g=let rec fG n g=function h::t->fG((g/h,h)::n)(g%h) t |_->n in fG [] g [200;100;50;20;10;5;2;1] fN 988|>List.iter(fun(n,g)->printfn "Take %d of %d" n g) </lang>
- Output:
Take 1 of 1 Take 1 of 2 Take 1 of 5 Take 1 of 10 Take 1 of 20 Take 1 of 50 Take 1 of 100 Take 4 of 200
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 } }
FreeBASIC
<lang freebasic>#define floor(x) ((x*2.0-0.5) Shr 1)
Dim As Integer amount = 988 Dim As Integer sumCoins = 0 Dim As Integer n, tmp Dim As Integer coins(8) = {1, 2, 5, 10, 20, 50, 100, 200}
Print "Make a value of"; amount; " using the coins 1, 2, 5, 10, 20, 50, 100 and 200:"
For n As Integer = Ubound(coins) To 0 Step -1
tmp = floor(amount/coins(n)) If tmp >= 0 Then Print tmp; " *"; coins(n) sumCoins += tmp amount Mod= coins(n) End If
Next n Sleep</lang>
- Output:
Make a value of 988 using the coins 1, 2, 5, 10, 20, 50, 100 and 200: 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
Go
<lang go>package main
import "fmt"
func main() {
denoms := []int{200, 100, 50, 20, 10, 5, 2, 1} coins := 0 amount := 988 remaining := 988 fmt.Println("The minimum number of coins needed to make a value of", amount, "is as follows:") for _, denom := range denoms { n := remaining / denom if n > 0 { coins += n fmt.Printf(" %3d x %d\n", denom, n) remaining %= denom if remaining == 0 { break } } } fmt.Println("\nA total of", coins, "coins in all.")
}</lang>
- Output:
The minimum number of coins needed to make a value of 988 is as follows: 200 x 4 100 x 1 50 x 1 20 x 1 10 x 1 5 x 1 2 x 1 1 x 1 A total of 11 coins in all.
Haskell
<lang haskell>import Data.List (mapAccumL) import Data.Tuple (swap)
FIND CHANGE ----------------------
change :: [Int] -> Int -> [(Int, Int)] change xs n = zip (snd $ mapAccumL go n xs) xs
where go m v = swap (quotRem m v)
TEST -------------------------
main :: IO () main =
mapM_ print $ change [200, 100, 50, 20, 10, 5, 2, 1] 988</lang>
- Output:
(4,200) (1,100) (1,50) (1,20) (1,10) (1,5) (1,2) (1,1)
Or as a hand-written recursion, defining a slightly more parsimonious listing, and allowing for denomination lists which are ill-sorted or incomplete.
<lang haskell>import Data.List (sortOn) import Data.Ord (Down (Down))
MINIMUM NUMBER OF COINS TO MAKE A SUM ---------
change :: [Int] -> Int -> Either String [(Int, Int)] change units n
| 0 == mod n m = Right $ go (sortOn Down units) (abs n) | otherwise = Left $ concat [ "Residue of ", show (mod n m), " - no denomination smaller than ", show m, "." ] where m = minimum units go _ 0 = [] go [] _ = [] go (x : xs) n | 0 == q = go xs n | otherwise = (q, x) : go xs r where (q, r) = quotRem n x
TEST -------------------------
main :: IO () main = mapM_ putStrLn $ test <$> [1024, 988]
where test n = either id ( concat . (:) ("Summing to " <> show n <> ":\n") . fmap ( \(q, v) -> concat [show q, " * ", show v, "\n"] ) ) (change [200, 100, 50, 20, 10, 5, 2, 1] n)</lang>
- Output:
Summing to 1024: 5 * 200 1 * 20 2 * 2 Summing to 988: 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
JavaScript
<lang javascript>(() => {
"use strict";
// -- MINIMUM NUMBER OF COINS TO MAKE A GIVEN VALUE --
// change :: [Int] -> Int -> [(Int, Int)] const change = denominations => { // A minimum list of (quantity, value) pairs for n. // Unused denominations are excluded from the list. const go = n => { const m = abs(n);
return 0 < denominations.length && 0 < m ? ( () => { const [h, ...t] = denominations; const q = Math.trunc(m / h);
return ( 0 < q ? [ [q, h] ] : [] ).concat(change(t)(m % h)); } )() : []; };
return go; };
// ---------------------- TEST ----------------------- // main :: IO () const main = () => { // Two sums tested with a set of denominations. const f = change([200, 100, 50, 20, 10, 5, 2, 1]);
return [1024, 988].reduce((acc, n) => { const report = f(n).reduce( (a, [q, u]) => `${a}${q} * ${u}\n`, "" );
return `${acc}Summing to ${abs(n)}:\n` + ( `${report}\n` ); }, "" ); };
// --------------------- GENERIC ---------------------
// abs :: Num -> Num const abs = // Absolute value - without the sign. x => 0 > x ? ( -x ) : x;
// MAIN --- return main();
})();</lang>
- Output:
Summing to 1024: 5 * 200 1 * 20 2 * 2 Summing to 988: 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
jq
Works with gojq, the Go implementation of jq <lang jq>
- If $details then provide {details, coins}, otherwise just the number of coins.
def minimum_number($details):
. as $amount | [200, 100, 50, 20, 10, 5, 2, 1] as $denoms | {coins: 0, remaining: 988, details: []} | label $out | foreach $denoms[] as $denom (.; ((.remaining / $denom)|floor) as $n | if $n > 0 then .coins += $n | if $details then .details += [{$denom, $n}] else . end | .remaining %= $denom
else . end;
if .remaining == 0 then ., break $out else empty end) | if $details then {details, coins} else .coins end ;
- Verbose mode:
def task:
"\nThe minimum number of coins needed to make a value of \(.) is as follows:", (minimum_number(true) | .details[], "\nA total of \(.coins) coins in all." );
988
| minimum_number(false), # illustrate minimal output
task # illustrate detailed output
</lang>
- Output:
11 The minimum number of coins needed to make a value of 988 is as follows: {"denom":200,"n":4} {"denom":100,"n":1} {"denom":50,"n":1} {"denom":20,"n":1} {"denom":10,"n":1} {"denom":5,"n":1} {"denom":2,"n":1} {"denom":1,"n":1} A total of 11 coins in all.
Julia
Long version
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
Brief REPL command version
julia> accumulate((x, y) -> (x[1] % y, (y, x[1] ÷ y)), [200, 100, 50, 20, 10, 5, 2, 1], init=(988, 0)) 8-element Vector{Tuple{Int64, Tuple{Int64, Int64}}}: (188, (200, 4)) (88, (100, 1)) (38, (50, 1)) (18, (20, 1)) (8, (10, 1)) (3, (5, 1)) (1, (2, 1)) (0, (1, 1))
Mathematica/Wolfram Language
<lang Mathematica>coins = {1, 2, 5, 10, 20, 50, 100, 200}; out = v /. ConvexOptimization[Total[v], coins . v == 988, v \[Element] Vectors[8, NonNegativeIntegers]]; MapThread[Row[{#1, " x ", #2}] &, {out, coins}] // Column</lang>
- Output:
1 x 1 1 x 2 1 x 5 1 x 10 1 x 20 1 x 50 1 x 100 4 x 200
MiniZinc
<lang MiniZinc> %Find minimum number of coins that make a given value. Nigel Galloway, August 11th., 2021 int: N=988; array [1..8] of int: coinValue=[1,2,5,10,20,50,100,200]; array [1..8] of var 0..N: take; constraint sum(n in 1..8)(take[n]*coinValue[n])=N; solve minimize sum(n in 1..8)(take[n]); output(["Take "++show(take[n])++" of "++show(coinValue[n])++"\n" | n in 1..8]) </lang>
- Output:
Take 1 of 1 Take 1 of 2 Take 1 of 5 Take 1 of 10 Take 1 of 20 Take 1 of 50 Take 1 of 100 Take 4 of 200 ---------- ========== Finished in 196msec
Nim
<lang Nim>import strformat
const
Coins = [200, 100, 50, 20, 10, 5, 2, 1] Target = 988
echo &"Minimal number of coins to make a value of {Target}:" var count = 0 var remaining = Target for coin in Coins:
let n = remaining div coin if n != 0: inc count, n echo &"coins of {coin:3}: {n}" dec remaining, n * coin if remaining == 0: break
echo "\nTotal: ", count</lang>
- Output:
Minimal number of coins to make a value of 988: coins of 200: 4 coins of 100: 1 coins of 50: 1 coins of 20: 1 coins of 10: 1 coins of 5: 1 coins of 2: 1 coins of 1: 1 Total: 11
Perl
<lang perl>use strict; use warnings;
my @denominations = <200 100 50 20 10 5 2 1>;
sub change {
my $n = shift; my @a; push(@a, int $n/$_) and $n %= $_ for @denominations; @a
}
my @amounts = change 988; for (0 .. $#amounts) {
printf "%1d * %3d\n", $amounts[$_], $denominations[$_]
}</lang>
- Output:
4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
Phix
with javascript_semantics requires("1.0.1") -- (lastdelim added to the join() function) sequence coins = {1,2,5,10,20,50,100,200} string strc = join(apply(coins,sprint),", ", ", and ") atom total = 988 printf(1,"Make a value of %d using the coins %s:\n",{total,strc}) integer count = 0 for i=length(coins) to 1 by -1 do integer ci = coins[i], c = floor(total/ci) if c then printf(1,"%6s coin%s of %3d\n",{ordinal(c,true),iff(c>1?"s":" "),ci}) count += c total = remainder(total,ci) if total=0 then exit end if end if end for printf(1,"%s coins were used.\n",{proper(ordinal(count,true))})
- Output:
Make a value of 988 using the coins 1, 2, 5, 10, 20, 50, 100, and 200: four coins of 200 one coin of 100 one coin of 50 one coin of 20 one coin of 10 one coin of 5 one coin of 2 one coin of 1 Eleven coins were used.
Python
Python :: Procedural
<lang python>def makechange(denominations = [1,2,5,10,20,50,100,200], total = 988):
print(f"Available denominations: {denominations}. Total is to be: {total}.") coins, remaining = sorted(denominations, reverse=True), total for n in range(len(coins)): coinsused, remaining = divmod(remaining, coins[n]) if coinsused > 0: print(" ", coinsused, "*", coins[n])
makechange()
</lang>
- Output:
Available denominations: [1, 2, 5, 10, 20, 50, 100, 200]. Total is to be: 988. 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
Python :: Functional
<lang python>Minimum number of coins to make a given value
- change :: [Int] -> Int -> [(Int, Int)]
def change(xs):
A list of (quantity, denomination) pairs. Unused denominations are excluded from the list. def go(n): if xs and n: h, *t = xs q, r = divmod(n, h)
return ([(q, h)] if q else []) + ( change(t)(r) ) else: return []
return go
- ------------------------- TEST -------------------------
- main :: IO ()
def main():
Testing a set of denominations with two sums
f = change([200, 100, 50, 20, 10, 5, 2, 1]) print( "\n".join([ f'Summing to {n}:\n' + "\n".join([ f'{qu[0]} * {qu[1]}' for qu in f(n)] ) + "\n" for n in [1024, 988] ]) )
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Summing to 1024: 5 * 200 1 * 20 2 * 2 Summing to 988: 4 * 200 1 * 100 1 * 50 1 * 20 1 * 10 1 * 5 1 * 2 1 * 1
Raku
Since unit denominations are possible, don't bother to check to see if an exact pay-out isn't possible.
<lang perl6>my @denominations = 200, 100, 50, 20, 10, 5, 2, 1;
sub change (Int $n is copy where * >= 0) { gather for @denominations { take $n div $_; $n %= $_ } }
for 988, 1307, 37511, 0 -> $amount {
say "\n$amount:"; printf "%d × %d\n", |$_ for $amount.&change Z @denominations;
}</lang>
- Output:
988: 4 × 200 1 × 100 1 × 50 1 × 20 1 × 10 1 × 5 1 × 2 1 × 1 1307: 6 × 200 1 × 100 0 × 50 0 × 20 0 × 10 1 × 5 1 × 2 0 × 1 37511: 187 × 200 1 × 100 0 × 50 0 × 20 1 × 10 0 × 5 0 × 2 1 × 1 0: 0 × 200 0 × 100 0 × 50 0 × 20 0 × 10 0 × 5 0 × 2 0 × 1
REXX
A check was made to see if an exact pay─out isn't possible.
The total number of coins paid out is also shown. <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 " " " " */ koins= 0 /*the total number of coins dispensed. */ 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.*/ koins= koins + z 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*/
say center( , 30, "─") /* " sep " " " " */ say say 'number of coins dispensed: ' koins 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 ────────────────────────────── number of coins dispensed: 11
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...
Rust
<lang rust> fn main() {
let denoms = vec![200, 100, 50, 20, 10, 5, 2, 1]; let mut coins = 0; let amount = 988; let mut remaining = 988; println!("The minimum number of coins needed to make a value of {} is as follows:", amount); for denom in denoms.iter() { let n = remaining / denom; if n > 0 { coins += n; println!(" {} x {}", denom, n); remaining %= denom; if remaining == 0 { break; } } } println!("\nA total of {} coins in all.", coins);
} </lang>
- Output:
The minimum number of coins needed to make a value of 988 is as follows: 200 x 4 100 x 1 50 x 1 20 x 1 10 x 1 5 x 1 2 x 1 1 x 1 A total of 11 coins in all.
Wren
As there is, apparently, an unlimited supply of coins of each denomination, it follows that any amount can be made up. <lang ecmascript>import "/fmt" for Fmt
var denoms = [200, 100, 50, 20, 10, 5, 2, 1] var coins = 0 var amount = 988 var remaining = 988 System.print("The minimum number of coins needed to make a value of %(amount) is as follows:") for (denom in denoms) {
var n = (remaining / denom).floor if (n > 0) { coins = coins + n Fmt.print(" $3d x $d", denom, n) remaining = remaining % denom if (remaining == 0) break }
} System.print("\nA total of %(coins) coins in all.")</lang>
- Output:
The minimum number of coins needed to make a value of 988 is as follows: 200 x 4 100 x 1 50 x 1 20 x 1 10 x 1 5 x 1 2 x 1 1 x 1 A total of 11 coins in all.
XPL0
<lang XPL0>int Denom, Denoms, Coins, Amount, Remaining, I, N; [Denoms:= [200, 100, 50, 20, 10, 5, 2, 1]; Coins:= 0; Amount:= 988; Remaining:= 988; Text(0, "The minimum number of coins needed to make a value of "); IntOut(0, Amount); Text(0, " is as follows: "); Format(3, 0); for I:= 0 to 7 do
[Denom:= Denoms(I); N:= Remaining/Denom; if N > 0 then [Coins:= Coins + N; RlOut(0, float(Denom)); Text(0, " x "); IntOut(0, N); CrLf(0); Remaining:= rem(Remaining/Denom); if Remaining = 0 then I:= 7; ]; ];
Text(0, " A total of "); IntOut(0, Coins); Text(0, " coins in all. "); ]</lang>
- Output:
The minimum number of coins needed to make a value of 988 is as follows: 200 x 4 100 x 1 50 x 1 20 x 1 10 x 1 5 x 1 2 x 1 1 x 1 A total of 11 coins in all.