Go: Project Euler 10-19

problem10.go

package main

import (
	"fmt"
	"time"
)

type primes []bool

func newPrimes(n int) (answer primes) {
	answer = make(primes, n+1)
	answer[2] = true
	for i := 3; i <= n; i += 2 {
		answer[i] = true
	}
	for p := 3; p*p <= n; p += 2 {
		if answer[p] {
			for q := p; p*q <= n; q += 2 {
				answer[p*q] = false
			}
		}
	}
	return
}

func (x primes) sum() (answer int64) {
	for i, ok := range x {
		if ok {
			answer += int64(i)
		}
	}
	return
}

func problem10() int64 {
	return newPrimes(2e6).sum()
}

func main() {
	start := time.Now()
	fmt.Println(problem10())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem11.go

package main

import (
	"fmt"
	"strings"
	"time"
)

func data() (res [][]int) {
	str := []string{
		"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08",
		"49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00",
		"81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65",
		"52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91",
		"22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80",
		"24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50",
		"32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70",
		"67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21",
		"24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72",
		"21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95",
		"78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92",
		"16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57",
		"86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58",
		"19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40",
		"04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66",
		"88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69",
		"04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36",
		"20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16",
		"20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54",
		"01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48",
	}
	for i := range str {
		s := strings.Fields(str[i])
		nums := []int{}
		for j := range s {
			var n int
			fmt.Sscanf(s[j], "%d", &n)
			nums = append(nums, n)
		}
		res = append(res, nums)
	}
	return
}

func problem11() (max int) {
	arr := data()
	for i := 3; i <= 19; i++ {
		for j := 0; j <= 16; j++ {
			x := arr[i][j] * arr[i-1][j+1] * arr[i-2][j+2] * arr[i-3][j+3]
			if x > max {
				max = x
			}
		}
	}
	for i := 0; i <= 19; i++ {
		for j := 0; j <= 16; j++ {
			x := arr[i][j] * arr[i][j+1] * arr[i][j+2] * arr[i][j+3]
			if x > max {
				max = x
			}
		}
	}
	for i := 0; i <= 16; i++ {
		for j := 0; j <= 16; j++ {
			x := arr[i][j] * arr[i+1][j+1] * arr[i+2][j+2] * arr[i+3][j+3]
			if x > max {
				max = x
			}
		}
	}
	for i := 0; i <= 16; i++ {
		for j := 0; j <= 19; j++ {
			x := arr[i][j] * arr[i+1][j] * arr[i+2][j] * arr[i+3][j]
			if x > max {
				max = x
			}
		}
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem11())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem12.go

package main

import (
	"fmt"
	"time"
)

type num int

func (x num) even() bool {
	return x%2 == 0
}

func (x num) odd() bool {
	return !x.even()
}

type primeFactors map[num]num

func newPrimeFactors(n num) (answer primeFactors) {
	answer = make(primeFactors)
	for p := num(2); p*p <= n; p++ {
		for n%p == 0 {
			answer[p]++
			n /= p
		}
	}
	if n > 1 {
		answer[n]++
	}
	return
}

func newCountFactors() func(num) num {
	m := make(map[num]num)
	f := func(n num) (answer num) {
		if v, ok := m[n]; ok {
			return v
		}
		answer++
		for _, v := range newPrimeFactors(n) {
			answer *= 1 + v
		}
		m[n] = answer
		return
	}
	return f
}

var countFactors func(num) num = newCountFactors()

type triangle struct {
	index num
	count num
}

func (t *triangle) next() {
	n := (*t).index + 1
	(*t).index = n
	switch {
	case n.odd():
		(*t).count = countFactors(n) * countFactors((n+1)/2)
	case n.even():
		(*t).count = countFactors(n/2) * countFactors(n+1)
	}
}

func (t *triangle) number() num {
	n := (*t).index
	return (n * (n + 1)) / 2
}

func problem12() num {
	t := triangle{0, 0}
	for t.count <= 500 {
		t.next()
	}
	return t.number()
}

func main() {
	start := time.Now()
	fmt.Println(problem12())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem13.go

package main

import (
	"fmt"
	"math/big"
	"time"
)

func problem13() (answer *big.Int) {
	str := []string{
		"37107287533902102798797998220837590246510135740250",
		"46376937677490009712648124896970078050417018260538",
		"74324986199524741059474233309513058123726617309629",
		"91942213363574161572522430563301811072406154908250",
		"23067588207539346171171980310421047513778063246676",
		"89261670696623633820136378418383684178734361726757",
		"28112879812849979408065481931592621691275889832738",
		"44274228917432520321923589422876796487670272189318",
		"47451445736001306439091167216856844588711603153276",
		"70386486105843025439939619828917593665686757934951",
		"62176457141856560629502157223196586755079324193331",
		"64906352462741904929101432445813822663347944758178",
		"92575867718337217661963751590579239728245598838407",
		"58203565325359399008402633568948830189458628227828",
		"80181199384826282014278194139940567587151170094390",
		"35398664372827112653829987240784473053190104293586",
		"86515506006295864861532075273371959191420517255829",
		"71693888707715466499115593487603532921714970056938",
		"54370070576826684624621495650076471787294438377604",
		"53282654108756828443191190634694037855217779295145",
		"36123272525000296071075082563815656710885258350721",
		"45876576172410976447339110607218265236877223636045",
		"17423706905851860660448207621209813287860733969412",
		"81142660418086830619328460811191061556940512689692",
		"51934325451728388641918047049293215058642563049483",
		"62467221648435076201727918039944693004732956340691",
		"15732444386908125794514089057706229429197107928209",
		"55037687525678773091862540744969844508330393682126",
		"18336384825330154686196124348767681297534375946515",
		"80386287592878490201521685554828717201219257766954",
		"78182833757993103614740356856449095527097864797581",
		"16726320100436897842553539920931837441497806860984",
		"48403098129077791799088218795327364475675590848030",
		"87086987551392711854517078544161852424320693150332",
		"59959406895756536782107074926966537676326235447210",
		"69793950679652694742597709739166693763042633987085",
		"41052684708299085211399427365734116182760315001271",
		"65378607361501080857009149939512557028198746004375",
		"35829035317434717326932123578154982629742552737307",
		"94953759765105305946966067683156574377167401875275",
		"88902802571733229619176668713819931811048770190271",
		"25267680276078003013678680992525463401061632866526",
		"36270218540497705585629946580636237993140746255962",
		"24074486908231174977792365466257246923322810917141",
		"91430288197103288597806669760892938638285025333403",
		"34413065578016127815921815005561868836468420090470",
		"23053081172816430487623791969842487255036638784583",
		"11487696932154902810424020138335124462181441773470",
		"63783299490636259666498587618221225225512486764533",
		"67720186971698544312419572409913959008952310058822",
		"95548255300263520781532296796249481641953868218774",
		"76085327132285723110424803456124867697064507995236",
		"37774242535411291684276865538926205024910326572967",
		"23701913275725675285653248258265463092207058596522",
		"29798860272258331913126375147341994889534765745501",
		"18495701454879288984856827726077713721403798879715",
		"38298203783031473527721580348144513491373226651381",
		"34829543829199918180278916522431027392251122869539",
		"40957953066405232632538044100059654939159879593635",
		"29746152185502371307642255121183693803580388584903",
		"41698116222072977186158236678424689157993532961922",
		"62467957194401269043877107275048102390895523597457",
		"23189706772547915061505504953922979530901129967519",
		"86188088225875314529584099251203829009407770775672",
		"11306739708304724483816533873502340845647058077308",
		"82959174767140363198008187129011875491310547126581",
		"97623331044818386269515456334926366572897563400500",
		"42846280183517070527831839425882145521227251250327",
		"55121603546981200581762165212827652751691296897789",
		"32238195734329339946437501907836945765883352399886",
		"75506164965184775180738168837861091527357929701337",
		"62177842752192623401942399639168044983993173312731",
		"32924185707147349566916674687634660915035914677504",
		"99518671430235219628894890102423325116913619626622",
		"73267460800591547471830798392868535206946944540724",
		"76841822524674417161514036427982273348055556214818",
		"97142617910342598647204516893989422179826088076852",
		"87783646182799346313767754307809363333018982642090",
		"10848802521674670883215120185883543223812876952786",
		"71329612474782464538636993009049310363619763878039",
		"62184073572399794223406235393808339651327408011116",
		"66627891981488087797941876876144230030984490851411",
		"60661826293682836764744779239180335110989069790714",
		"85786944089552990653640447425576083659976645795096",
		"66024396409905389607120198219976047599490197230297",
		"64913982680032973156037120041377903785566085089252",
		"16730939319872750275468906903707539413042652315011",
		"94809377245048795150954100921645863754710598436791",
		"78639167021187492431995700641917969777599028300699",
		"15368713711936614952811305876380278410754449733078",
		"40789923115535562561142322423255033685442488917353",
		"44889911501440648020369068063960672322193204149535",
		"41503128880339536053299340368006977710650566631954",
		"81234880673210146739058568557934581403627822703280",
		"82616570773948327592232845941706525094512325230608",
		"22918802058777319719839450180888072429661980811197",
		"77158542502016545090413245809786882778948721859617",
		"72107838435069186155435662884062257473692284509516",
		"20849603980134001723930671666823555245252804609722",
		"53503534226472524250874054075591789781264330331690",
	}
	answer = new(big.Int)
	num := new(big.Int)
	for i := range str {
		num.SetString(str[i], 10)
		answer.Add(answer, num)
	}
	limit := big.NewInt(10000000000)
	ten := big.NewInt(10)
	for answer.Cmp(limit) == 1 {
		answer.Div(answer, ten)
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem13())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem14.go

package main

import (
	"fmt"
	"time"
)

const limit = 1e6

func collatz() (xs []int) {
	xs = make([]int, limit)
	xs[1] = 1
	for x := int64(2); x < limit; x++ {
		y, step := x, 0
		for x <= y {
			step++
			if y%2 == 0 {
				y /= 2
			} else {
				y = 3*y + 1
			}
		}
		xs[int(x)] = xs[int(y)] + step
	}
	return
}

type max struct {
	index int
	value int
}

func (x *max) set(i, v int) {
	if v > (*x).value {
		*x = max{i, v}
	}
}

func (x *max) String() string {
	return fmt.Sprint((*x).index)
}

func problem14() (answer *max) {
	answer = new(max)
	for i, v := range collatz() {
		answer.set(i, v)
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem14())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem15.go

package main

import (
	"fmt"
	"math/big"
	"time"
)

func problem15() *big.Int {
	return new(big.Int).Binomial(40, 20)
}

func main() {
	start := time.Now()
	fmt.Println(problem15())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem16.go

package main

import (
	"fmt"
	"math/big"
	"time"
)

func problem16() (answer *big.Int) {
	answer = new(big.Int)
	x := new(big.Int).Exp(big.NewInt(2), big.NewInt(1000), nil)
	y := new(big.Int)
	zero := big.NewInt(0)
	ten := big.NewInt(10)
	for x.Cmp(zero) == 1 {
		x.DivMod(x, ten, y)
		answer.Add(answer, y)
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem16())
	fmt.Println(time.Now().Sub(start).Seconds())
}

// by digits

package main

import (
	"fmt"
	"time"
)

type digits []int

func (x *digits) multi(n int) {
	carry := 0
	for i, v := range *x {
		w := v*n + carry
		(*x)[i] = w % 10
		carry = w / 10
	}
	for carry > 0 {
		*x = append(*x, carry%10)
		carry /= 10
	}
}

func (x *digits) sum() (answer int) {
	for _, v := range *x {
		answer += v		
	}
	return
}

func problem16() int {
	d := digits{1}
	for i := 1; i <= 1000; i++ {
		d.multi(2)
	}
	return d.sum()
}

func main() {
	start := time.Now()
	fmt.Println(problem16())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem17.go

package main

import (
	"fmt"
	"time"
)

func spell(n int) (s string) {
	s0 := []string{
		"", "One", "Two", "Three", "Four", "Five",
		"Six", "Seven", "Eight", "Nine", "Ten",
		"Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen",
		"Sixteen", "Seventeen", "Eighteen", "Nineteen",
	}
	s1 := []string{
		"", "", "Twenty", "Thirty", "Forty", "Fifty",
		"Sixty", "Seventy", "Eighty", "Ninety",
	}
	for {
		switch {
		case n < 20:
			s += s0[n]
			return
		case n < 100:
			s += s1[n/10] + s0[n%10]
			return
		case n == 1000:
			return "OneThousand"
		case n%100 == 0:
			return s0[n/100] + "Hundred"
		default:
			s += s0[n/100] + "HundredAnd"
			n %= 100
		}
	}
	return
}

func problem17() (anser int) {
	for n := 1; n <= 1000; n++ {
		anser += len(spell(n))
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem17())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem18.go

package main

import (
	"fmt"
	"strings"
	"time"
)

func data() (answer [][]int) {
	lines := []string{
		"75",
		"95 64",
		"17 47 82",
		"18 35 87 10",
		"20 04 82 47 65",
		"19 01 23 75 03 34",
		"88 02 77 73 07 63 67",
		"99 65 04 28 06 16 70 92",
		"41 41 26 56 83 40 80 70 33",
		"41 48 72 33 47 32 37 16 94 29",
		"53 71 44 65 25 43 91 52 97 51 14",
		"70 11 33 28 77 73 17 78 39 68 17 57",
		"91 71 52 38 17 14 91 43 58 50 27 29 48",
		"63 66 04 68 89 53 67 30 73 16 69 87 40 31",
		"04 62 98 27 23 09 70 98 73 93 38 53 60 04 23",
	}
	answer = make([][]int, len(lines))
	for i, line := range lines {
		xs := strings.Fields(line)
		ys := make([]int, len(xs))
		for j, str := range xs {
			fmt.Sscanf(str, "%d", &ys[j])
		}
		answer[i] = ys
	}
	return
}

func join(x, y []int) (answer []int) {
	answer = make([]int, len(x))
	for i, v := range x {
		j := i+1
		if y[i] > y[j] {
			answer[i] = v+y[i]
		} else {
			answer[i] = v+y[j]
		}
	}
	return
}

func problem18() int {
	xss := data()
	xs := xss[len(xss)-1]
	for i := len(xss) - 2; i >= 0; i-- {
		xs = join(xss[i], xs)
	}
	return xs[0]
}

func main() {
	start := time.Now()
	fmt.Println(problem18())
	fmt.Println(time.Now().Sub(start).Seconds())
}

problem19.go

package main

import (
	"fmt"
	"time"
)

func fstDay(year, month int) time.Time {
	return time.Date(year, time.Month(month), 1, 0, 0, 0, 0, time.UTC)
}

func problem19() (answer int) {
	for year := 1901; year <= 2000; year++ {
		for month := 1; month <= 12; month++ {
			t := fstDay(year, month)
			if t.Weekday() == 0 {
				answer++
			}
		}
	}
	return
}

func main() {
	start := time.Now()
	fmt.Println(problem19())
	fmt.Println(time.Now().Sub(start).Seconds())
}