Solving coin problems: Difference between revisions
→{{header|Go}}: Extended to solve 3 coin problems.
(→{{header|Go}}: Extended to solve 3 coin problems.) |
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=={{header|Go}}==
This relatively simple program can only solve problems with 2 types of coins (or other objects)
<lang go>package main
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value float64
number int
}
// variable1 = constant1 * variable2 + constant2
type relation struct {
variable1 string
variable2 string
constant1 float64
constant2 float64
}
var nums = map[string]string{
"
"six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
"thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
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var coins = map[string]float64{
"pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-
"one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00}
var bills = map[string]string{
"$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"}
var (
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rx2 = regexp.MustCompile(`\b(pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar)\b`)
rx3 = regexp.MustCompile(`\s(\d+)\s`)
rx4 = regexp.MustCompile(`(\d+) times as many ([-\w]+) as (s?he (does|has) )?([-\w]+)`)
rx5 = regexp.MustCompile(`(\d+) more ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
rx6 = regexp.MustCompile(`(\d+) less ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
rx7 = regexp.MustCompile(`(\d+) dollars`)
)
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// Gets the 'kinds' for the problem.
func getKinds(
num, _ := strconv.Atoi(a[1])
kinds := []kind{{a[2], 0, 0}, {a[
areCoins := false
for i := range kinds {
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}
return num, kinds
}
// Checks if the problem involves 3 coins and
// also returns their names and the name of the coin which occurs most.
func hasThreeCoins(q string) ([]string, string, bool) {
q = strings.ReplaceAll(q, ".", "")
q = strings.ReplaceAll(q, ",", "")
words := strings.Split(q, " ")
coinMap := make(map[string]int)
for _, word := range words {
if _, ok := coins[word]; ok {
coinMap[word]++
}
}
if len(coinMap) != 3 {
return nil, "", false
}
maxNum, maxName := 0, ""
var names []string
for k, v := range coinMap {
names = append(names, k)
if v > maxNum {
maxNum, maxName = v, k
}
}
return names, maxName, true
}
// Processes a problem which involves 3 coins.
func threeCoins(p, q string, names []string, maxName string) {
var relations []relation
am := rx4.FindAllStringSubmatch(q, -1)
for i := 0; i < len(am); i++ {
mult, kinds := getKinds(am[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, float64(mult), 0})
}
mt := rx5.FindAllStringSubmatch(q, -1)
for i := 0; i < len(mt); i++ {
plus, kinds := getKinds(mt[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, float64(plus)})
}
lt := rx6.FindAllStringSubmatch(q, -1)
for i := 0; i < len(lt); i++ {
minus, kinds := getKinds(lt[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, -float64(minus)})
}
le := len(relations)
if le > 2 {
errorMsg(p)
return
}
if le == 0 { // numbers of each coin must be the same
sum := 0.0
for _, name := range names {
sum += coins[name]
}
res := getValues(q)
tv := res[len(res)-1]
n := int(tv/sum + 0.5)
var kinds []kind
for _, name := range names {
kinds = append(kinds, kind{name, 0, n})
}
printAnswers(p, kinds)
} else {
for i := 0; i < le; i++ {
if relations[i].constant1 == 0 {
relations[i].constant1 = 0.5 // deals with 'one-half' cases
}
if le == 2 && maxName == relations[i].variable1 {
v := relations[i].variable2
relations[i].variable1, relations[i].variable2 = v, maxName
relations[i].constant1 = 1 / relations[i].constant1
relations[i].constant2 = -relations[i].constant2
}
}
res := getValues(q)
tv := res[len(res)-1]
var v1, v2, v3 string
var n1, n2, n3 int
if le == 2 {
tmc := coins[relations[0].variable1]*relations[0].constant1 +
coins[relations[1].variable1]*relations[1].constant1 + coins[maxName]
tv -= coins[relations[0].variable1]*relations[0].constant2 +
coins[relations[1].variable1]*relations[1].constant2
v1, v2, v3 = maxName, relations[0].variable1, relations[1].variable1
n1 = int(tv/tmc + 0.5)
n2 = int(relations[0].constant1*float64(n1) + relations[0].constant2 + 0.5)
n3 = int(relations[1].constant1*float64(n1) + relations[1].constant2 + 0.5)
} else {
res2 := getNumbers(q)
tn := float64(res2[len(res2)-1])
v1, v2 = relations[0].variable1, relations[0].variable2
for _, name := range names {
if name != v1 && name != v2 {
v3 = name
break
}
}
mult1, mult2, mult3 := coins[v1], coins[v2], coins[v3]
n2 = int(((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5)
n1 = int(float64(n2)*relations[0].constant1 + relations[0].constant2 + 0.5)
n3 = int(tn) - n1 - n2
}
kinds := []kind{kind{v1, 0, n1}, kind{v2, 0, n2}, kind{v3, 0, n3}}
printAnswers(p, kinds)
}
return
}
func printAnswers(p string, kinds []kind) {
fmt.Println(p)
fmt.Print("ANSWER:")
for i, kind := range kinds {
if i > 0 {
fmt.Print(",")
}
fmt.Printf(" %d %s", kind.number, kind.name)
}
fmt.Println("\n")
}
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"A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
"A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
"A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
"In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
"A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
"A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
"An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
"A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
"A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
"A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
"A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
"A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
"A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
"A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
"Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
"A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
"A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
"Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
"Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
"In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
"Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
"A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
"Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
"Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
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}
for k, v := range nums {
q = strings.ReplaceAll(q, k+" ", v+" ")
}
for k, v := range bills {
q = strings.ReplaceAll(q, k+" ", v+" ")
}
q = strings.ReplaceAll(q, " bills", "")
q = strings.ReplaceAll(q, " bill", "")
// check if there are 3 coins involved
if names, maxName, ok := hasThreeCoins(q); ok {
threeCoins(p, q, names, maxName)
continue
}
am := rx4.FindAllStringSubmatch(q, -1)
if len(am) == 1 {
mult, kinds := getKinds(am[0])
if kinds == nil {
errorMsg(p)
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mt := rx5.FindAllStringSubmatch(q, -1)
if len(mt) == 1 {
plus, kinds := getKinds(mt[0])
if kinds == nil {
errorMsg(p)
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lt := rx6.FindAllStringSubmatch(q, -1)
if len(lt) == 1 {
minus, kinds := getKinds(lt[0])
if kinds == nil {
errorMsg(p)
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A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
ANSWER: 21 nickels, 11 quarters
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
ANSWER: 7 pennies, 14 dimes, 10 nickels
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
ANSWER: 3 half-dollars, 9 quarters, 9 dimes
A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
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An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
ANSWER: 7 $1.59 item, 2 $2.29 item
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
ANSWER: 5 dimes, 3 quarters
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
ANSWER: 3 nickels, 9 dimes, 8 pennies
A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
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A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
ANSWER: 5
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 nickels, 9 dimes
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
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Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
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