/
p20.go
335 lines (288 loc) · 12 KB
/
p20.go
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package main
import (
"math/big"
)
// find the max of all 4-products (in any any direction) in the grid
func problem11() string {
const max = 20
grid := [max][max]int{
[max]int{ 8, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 8},
[max]int{49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 04, 56, 62, 00},
[max]int{81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65},
[max]int{52, 70, 95, 23, 04, 60, 11, 42, 69, 24, 68, 56, 01, 32, 56, 71, 37, 02, 36, 91},
[max]int{22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80},
[max]int{24, 47, 32, 60, 99, 03, 45, 02, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50},
[max]int{32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70},
[max]int{67, 26, 20, 68, 02, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21},
[max]int{24, 55, 58, 05, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72},
[max]int{21, 36, 23, 9, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95},
[max]int{78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80, 04, 62, 16, 14, 9, 53, 56, 92},
[max]int{16, 39, 05, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57},
[max]int{86, 56, 00, 48, 35, 71, 89, 07, 05, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58},
[max]int{19, 80, 81, 68, 05, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 04, 89, 55, 40},
[max]int{04, 52, 8, 83, 97, 35, 99, 16, 07, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66},
[max]int{88, 36, 68, 87, 57, 62, 20, 72, 03, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69},
[max]int{04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36},
[max]int{20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 04, 36, 16},
[max]int{20, 73, 35, 29, 78, 31, 90, 01, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 05, 54},
[max]int{01, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 01, 89, 19, 67, 48}}
maxp := 0
for row := 0; row < max; row++ {
for col := 0; col < max; col++ {
curp := 0
if row + 3 < max {
curp = grid[row][col] * grid[row+1][col] * grid[row+2][col] * grid[row+3][col]
maxp = Max2i(maxp, curp)
}
if col + 3 < max {
curp = grid[row][col] * grid[row][col+1] * grid[row][col+2] * grid[row][col+3]
maxp = Max2i(maxp, curp)
}
if (col + 3 < max) && (row + 3 < max) {
curp = grid[row][col] * grid[row+1][col+1] * grid[row+2][col+2] * grid[row+3][col+3]
maxp = Max2i(maxp, curp)
}
if (col >= 3) && (row + 3 < max) {
curp = grid[row][col] * grid[row+1][col-1] * grid[row+2][col-2] * grid[row+3][col-3]
maxp = Max2i(maxp, curp)
}
}
}
return itoa(maxp)
}
// find the first triangle number with 500+ divisors
func problem12() string {
const max = 100000000 // just a guess
var numDivs [max]int
for i := 1; i < max; i++ {
for j := i; j < max; j += i {
numDivs[j]++
}
}
// iterate through the triangle numbers
for i, j := 2, 1; j < max; i, j = i+1, j+i {
if numDivs[j] > 500 {
return itoa(j)
}
}
return "max wasn't large enough"
}
// find the first 10 digits of the sum of 100 50-digit numbers
func problem13() string {
lines := []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"}
sum := big.NewInt(0)
cur := big.NewInt(0)
for _, line := range lines {
cur.SetString(line, 10)
sum.Add(sum, cur)
}
return sum.String()[:10]
}
// find the longest collatz sequence starting at a number 1000000
func problem14() string {
const (
max = 1000000
maxA = 10000000
)
// 10M is just a guess for maxA (takes up ~ 40MB of space);
// choosing a larger number is a memory/speed tradeoff
// (it will still compute the correct answer)
var chainLen [2*maxA+3]int
maxChain := 0
maxChainStart := -1
chainLen[0] = 0
chainLen[1] = 0
for i := 1; i < max; i++ {
if 0 == chainLen[i*2] {
chainLen[i*2 + 1] = 0 // this seq has no root
c := 1
for j := int64(i); j != 1; c++ {
// extend current chain
if 0 == (j & 1) {
j /= 2 // even
} else {
j = 3*j + 1 // odd
}
if j >= maxA {
continue // cant use array for caching, j is too big
}
k := 2*int(j)
if chainLen[k] != 0 {
// we know how long the chain is from j to 1.
c += chainLen[k] + chainLen[chainLen[k+1]*2]
break
}
chainLen[k] = -c // c steps away from root
chainLen[k+1] = i // root is 'i'
}
chainLen[i*2] = c
if c > maxChain {
maxChainStart = i
maxChain = c
}
}
}
return itoa(maxChainStart)
}
// find the sum of digits of 2^1000
func problem16() string {
return itoa(digitSum(bigExp(2, 1000).String()))
}
func problem17() string {
s1to9 := len("one"+"two"+"three"+"four"+"five"+"six"+"seven"+"eight"+"nine")
s11to19 := len("eleven"+"twelve"+"thirteen"+"fourteen"+"fifteen"+"sixteen"+"seventeen"+"eighteen"+"nineteen")
s20to90by10 := len("twenty"+"thirty"+"forty"+"fifty"+"sixty"+"seventy"+"eighty"+"ninety")
s1to99 := s1to9 + len("ten") + s11to19 + (s20to90by10 * 10) + (s1to9 * 8)
s1to999 := (10 * s1to99) + ((s1to9 + 9*len("hundred"+"and")) * 100) - 9*len("and") // e.g. 200 has no 'and'
s1to1000 := s1to999 + len("one"+"thousand")
return itoa(s1to1000)
}
func sumMax(grid [][]int64) int64 {
for row := len(grid) - 2; row >= 0; row-- {
for col := range grid[row] {
grid[row][col] += Max2l(grid[row+1][col], grid[row+1][col+1])
}
}
return grid[0][0]
}
func problem18() string {
return i64toa(sumMax(ReadGrid("data/p18.txt")))
}
// count the number of 1st of months were Sundays from 1/1/1901 to 31/12/2000
func problem19() string {
numDaysInMonth := []int{31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
// if the first day of the year is Sunday, determine the day of week for the first of each month
var dayOfWkOffset [12]int
dayOfWkOffset[0] = 0
for i := 1; i < 12; i++ {
dayOfWkOffset[i] = (dayOfWkOffset[i-1] + numDaysInMonth[i]) % 7
}
var numSundays [7]int
for i := 0; i < 12; i++ {
numSundays[dayOfWkOffset[i]]++
}
// adjust for leap years
for i := 2; i < 12; i++ {
dayOfWkOffset[i] = (dayOfWkOffset[i] + 1) % 7
}
var numSundaysLeap [7]int
for i := 0; i < 12; i++ {
numSundaysLeap[dayOfWkOffset[i]]++
}
// first day of 1901 is Wed (day = 3)
countSundays := 0
for day, year := 3, 1901; year <= 2000; day, year = (day + 365) % 7, year + 1 {
isLeapYear := (year % 4) == 0
if isLeapYear {
countSundays += numSundaysLeap[day]
day++
} else {
countSundays += numSundays[day]
}
}
return itoa(countSundays)
}
// find the sum of the digits in 100!
func problem20() string {
return itoa(digitSum(prod(1, 100).String()))
}