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refactor(euler): add problems commented in the files

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This commit is contained in:
newt 2024-10-09 18:02:40 +01:00
parent 9c510b7bc1
commit 94baabd26b
19 changed files with 332 additions and 220 deletions
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13
challenges/euler/src/1 - Multiples of 3 or 5.ts
View file

@ -1,7 +1,10 @@
// If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
// Find the sum of all the multiples of 3 or 5 below 1000.
export {}; export {};
const calcSum = (numbers: number[]) => numbers.reduce((a, b) => a + b); /**
* Figure out the multiples of two numbers below a bound
*/
const multiplesOf = (numbers: number[], upperBound: number) => { const multiplesOf = (numbers: number[], upperBound: number) => {
const results: Set<number> = new Set(); const results: Set<number> = new Set();
@ -12,4 +15,8 @@ const multiplesOf = (numbers: number[], upperBound: number) => {
return Array.from(results); return Array.from(results);
}; };
console.log(calcSum(multiplesOf([3, 5], 1000))); // Output
const multiples = multiplesOf([3, 5], 1000);
const sum = multiples.reduce((a, b) => a + b);
console.log(sum);

23
challenges/euler/src/10 - Sumation of primes.ts
View file

@ -1,36 +1,39 @@
// See https://github.com/newtykins/the-honk/tree/main/euler/thoughts/10%20-Summation%20of%29primes.md // The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
// Find the sum of all the primes below two million.
export {}; export {};
const calcSum = (numbers: number[]) => numbers.reduce((a, b) => a + b); /**
* Use the Sieve of Eratosthenes to find the sum of primes up until a limit.
// Sieve of Eratosthenes time!!! * @see https://github.com/newtykins/the-honk/tree/main/projects/euler/thoughts/10%20-Summation%20of%29primes.md
const sumOfPrimes = (upperBound: number) => { */
const sumOfPrimes = (limit: number) => {
let array: boolean[] = []; let array: boolean[] = [];
let upperLimit = Math.sqrt(upperBound); let upperLimit = Math.sqrt(limit);
let output: number[] = []; let output: number[] = [];
// Make an array from 2 to (n - 1) of truthy values // Make an array from 2 to (n - 1) of truthy values
for (var i = 0; i < upperBound; i++) { for (var i = 0; i < limit; i++) {
array.push(true); array.push(true);
} }
// Remove multiples of primes starting from 2, 3, 5,... // Remove multiples of primes starting from 2, 3, 5,...
for (var i = 2; i <= upperLimit; i++) { for (var i = 2; i <= upperLimit; i++) {
if (array[i]) { if (array[i]) {
for (var j = i * i; j < upperBound; j += i) { for (var j = i * i; j < limit; j += i) {
array[j] = false; array[j] = false;
} }
} }
} }
// All array[i] set to true are primes // All array[i] set to true are primes
for (var i = 2; i < upperBound; i++) { for (var i = 2; i < limit; i++) {
if (array[i]) { if (array[i]) {
output.push(i); output.push(i);
} }
} }
return calcSum(output); return output.reduce((a, b) => a + b);
}; };
// Output
console.log(sumOfPrimes(2000000)); console.log(sumOfPrimes(2000000));

53
challenges/euler/src/11 - Largest product in a grid.ts
View file

@ -50,30 +50,29 @@ const largestProductInGrid = (grid: number[][], adjacentDigits: number) => {
return answer; return answer;
}; };
console.log( // Output
largestProductInGrid( const grid = [
[ [8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8], [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0], [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65], [52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91], [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
[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, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
[24, 47, 32, 60, 99, 3, 45, 2, 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],
[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70], [67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21], [24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72], [21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95], [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92], [16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57], [86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58], [19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40], [4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
[4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66], [88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69], [4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
[4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36], [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16], [20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54], [1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]
[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48] ];
], const output = largestProductInGrid(grid, 4);
4
) console.log(output);
);

39
challenges/euler/src/12 - Highly divisible triangular number.ts
View file

@ -1,31 +1,51 @@
// The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
// Let us list the factors of the first seven triangle numbers:
// 1: 1
// 3: 1,3
// 6: 1,2,3,6
// 10: 1,2,5,10
// 15: 1,3,5,15
// 21: 1,3,7,21
// 28: 1,2,4,7,14,28
// We can see that 28 is the first triangle number to have over five divisors.
// What is the value of the first triangle number to have over five hundred divisors?
export {}; export {};
const factorsOf = (num: number) => { /**
const isEven = num % 2 === 0; * Find the factors of a n
const max = Math.sqrt(num); */
const factorsOf = (n: number) => {
const isEven = n % 2 === 0;
const max = Math.sqrt(n);
const inc = isEven ? 1 : 2; const inc = isEven ? 1 : 2;
const factors = [1, num]; const factors = [1, n];
for (let curFactor = isEven ? 2 : 3; curFactor <= max; curFactor += inc) { for (let curFactor = isEven ? 2 : 3; curFactor <= max; curFactor += inc) {
if (num % curFactor !== 0) continue; if (n % curFactor !== 0) continue;
factors.push(curFactor); factors.push(curFactor);
let compliment = num / curFactor; let compliment = n / curFactor;
if (compliment !== curFactor) factors.push(compliment); if (compliment !== curFactor) factors.push(compliment);
} }
return factors; return factors;
}; };
// https://www.mathsisfun.com/algebra/triangular-numbers.html /**
const nthTriangleNumber = (n: number) => (n * (n + 1)) / 2; * Find the nth triangle number
* @see https://www.mathsisfun.com/algebra/triangular-numbers.html
*/
const triangleNumber = (n: number) => (n * (n + 1)) / 2;
/**
* Find the first triangle number with over n divisors
*/
const firstTriangleWithOverNDivisors = (n: number) => { const firstTriangleWithOverNDivisors = (n: number) => {
let divisorCountFound = false; let divisorCountFound = false;
let i = 1; let i = 1;
while (!divisorCountFound) { while (!divisorCountFound) {
const triangle = nthTriangleNumber(i); const triangle = triangleNumber(i);
const factors = [...factorsOf(triangle)]; const factors = [...factorsOf(triangle)];
i++; i++;
@ -36,4 +56,5 @@ const firstTriangleWithOverNDivisors = (n: number) => {
} }
}; };
// Output
console.log(firstTriangleWithOverNDivisors(500)); console.log(firstTriangleWithOverNDivisors(500));

223
challenges/euler/src/13 - Large sum.ts
View file

@ -1,113 +1,116 @@
// Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. (see numbers array for the numbers given)
export {}; export {};
const calcSum = (numbers: number[]) => numbers.reduce((a, b) => a + b); /**
const firstXDigits = (number: number, x: number) => * Get the first n digits of a number
parseInt(BigInt(number).toString().substr(0, x)); */
const firstDigits = (number: number, n: number) =>
parseInt(BigInt(number).toString().substring(0, n));
console.log( // Output
firstXDigits( const numbers = [
calcSum([ 37107287533902102798797998220837590246510135740250,
37107287533902102798797998220837590246510135740250, 46376937677490009712648124896970078050417018260538,
46376937677490009712648124896970078050417018260538, 74324986199524741059474233309513058123726617309629,
74324986199524741059474233309513058123726617309629, 91942213363574161572522430563301811072406154908250,
91942213363574161572522430563301811072406154908250, 23067588207539346171171980310421047513778063246676,
23067588207539346171171980310421047513778063246676, 89261670696623633820136378418383684178734361726757,
89261670696623633820136378418383684178734361726757, 28112879812849979408065481931592621691275889832738,
28112879812849979408065481931592621691275889832738, 44274228917432520321923589422876796487670272189318,
44274228917432520321923589422876796487670272189318, 47451445736001306439091167216856844588711603153276,
47451445736001306439091167216856844588711603153276, 70386486105843025439939619828917593665686757934951,
70386486105843025439939619828917593665686757934951, 62176457141856560629502157223196586755079324193331,
62176457141856560629502157223196586755079324193331, 64906352462741904929101432445813822663347944758178,
64906352462741904929101432445813822663347944758178, 92575867718337217661963751590579239728245598838407,
92575867718337217661963751590579239728245598838407, 58203565325359399008402633568948830189458628227828,
58203565325359399008402633568948830189458628227828, 80181199384826282014278194139940567587151170094390,
80181199384826282014278194139940567587151170094390, 35398664372827112653829987240784473053190104293586,
35398664372827112653829987240784473053190104293586, 86515506006295864861532075273371959191420517255829,
86515506006295864861532075273371959191420517255829, 71693888707715466499115593487603532921714970056938,
71693888707715466499115593487603532921714970056938, 54370070576826684624621495650076471787294438377604,
54370070576826684624621495650076471787294438377604, 53282654108756828443191190634694037855217779295145,
53282654108756828443191190634694037855217779295145, 36123272525000296071075082563815656710885258350721,
36123272525000296071075082563815656710885258350721, 45876576172410976447339110607218265236877223636045,
45876576172410976447339110607218265236877223636045, 17423706905851860660448207621209813287860733969412,
17423706905851860660448207621209813287860733969412, 81142660418086830619328460811191061556940512689692,
81142660418086830619328460811191061556940512689692, 51934325451728388641918047049293215058642563049483,
51934325451728388641918047049293215058642563049483, 62467221648435076201727918039944693004732956340691,
62467221648435076201727918039944693004732956340691, 15732444386908125794514089057706229429197107928209,
15732444386908125794514089057706229429197107928209, 55037687525678773091862540744969844508330393682126,
55037687525678773091862540744969844508330393682126, 18336384825330154686196124348767681297534375946515,
18336384825330154686196124348767681297534375946515, 80386287592878490201521685554828717201219257766954,
80386287592878490201521685554828717201219257766954, 78182833757993103614740356856449095527097864797581,
78182833757993103614740356856449095527097864797581, 16726320100436897842553539920931837441497806860984,
16726320100436897842553539920931837441497806860984, 48403098129077791799088218795327364475675590848030,
48403098129077791799088218795327364475675590848030, 87086987551392711854517078544161852424320693150332,
87086987551392711854517078544161852424320693150332, 59959406895756536782107074926966537676326235447210,
59959406895756536782107074926966537676326235447210, 69793950679652694742597709739166693763042633987085,
69793950679652694742597709739166693763042633987085, 41052684708299085211399427365734116182760315001271,
41052684708299085211399427365734116182760315001271, 65378607361501080857009149939512557028198746004375,
65378607361501080857009149939512557028198746004375, 35829035317434717326932123578154982629742552737307,
35829035317434717326932123578154982629742552737307, 94953759765105305946966067683156574377167401875275,
94953759765105305946966067683156574377167401875275, 88902802571733229619176668713819931811048770190271,
88902802571733229619176668713819931811048770190271, 25267680276078003013678680992525463401061632866526,
25267680276078003013678680992525463401061632866526, 36270218540497705585629946580636237993140746255962,
36270218540497705585629946580636237993140746255962, 24074486908231174977792365466257246923322810917141,
24074486908231174977792365466257246923322810917141, 91430288197103288597806669760892938638285025333403,
91430288197103288597806669760892938638285025333403, 34413065578016127815921815005561868836468420090470,
34413065578016127815921815005561868836468420090470, 23053081172816430487623791969842487255036638784583,
23053081172816430487623791969842487255036638784583, 11487696932154902810424020138335124462181441773470,
11487696932154902810424020138335124462181441773470, 63783299490636259666498587618221225225512486764533,
63783299490636259666498587618221225225512486764533, 67720186971698544312419572409913959008952310058822,
67720186971698544312419572409913959008952310058822, 95548255300263520781532296796249481641953868218774,
95548255300263520781532296796249481641953868218774, 76085327132285723110424803456124867697064507995236,
76085327132285723110424803456124867697064507995236, 37774242535411291684276865538926205024910326572967,
37774242535411291684276865538926205024910326572967, 23701913275725675285653248258265463092207058596522,
23701913275725675285653248258265463092207058596522, 29798860272258331913126375147341994889534765745501,
29798860272258331913126375147341994889534765745501, 18495701454879288984856827726077713721403798879715,
18495701454879288984856827726077713721403798879715, 38298203783031473527721580348144513491373226651381,
38298203783031473527721580348144513491373226651381, 34829543829199918180278916522431027392251122869539,
34829543829199918180278916522431027392251122869539, 40957953066405232632538044100059654939159879593635,
40957953066405232632538044100059654939159879593635, 29746152185502371307642255121183693803580388584903,
29746152185502371307642255121183693803580388584903, 41698116222072977186158236678424689157993532961922,
41698116222072977186158236678424689157993532961922, 62467957194401269043877107275048102390895523597457,
62467957194401269043877107275048102390895523597457, 23189706772547915061505504953922979530901129967519,
23189706772547915061505504953922979530901129967519, 86188088225875314529584099251203829009407770775672,
86188088225875314529584099251203829009407770775672, 11306739708304724483816533873502340845647058077308,
11306739708304724483816533873502340845647058077308, 82959174767140363198008187129011875491310547126581,
82959174767140363198008187129011875491310547126581, 97623331044818386269515456334926366572897563400500,
97623331044818386269515456334926366572897563400500, 42846280183517070527831839425882145521227251250327,
42846280183517070527831839425882145521227251250327, 55121603546981200581762165212827652751691296897789,
55121603546981200581762165212827652751691296897789, 32238195734329339946437501907836945765883352399886,
32238195734329339946437501907836945765883352399886, 75506164965184775180738168837861091527357929701337,
75506164965184775180738168837861091527357929701337, 62177842752192623401942399639168044983993173312731,
62177842752192623401942399639168044983993173312731, 32924185707147349566916674687634660915035914677504,
32924185707147349566916674687634660915035914677504, 99518671430235219628894890102423325116913619626622,
99518671430235219628894890102423325116913619626622, 73267460800591547471830798392868535206946944540724,
73267460800591547471830798392868535206946944540724, 76841822524674417161514036427982273348055556214818,
76841822524674417161514036427982273348055556214818, 97142617910342598647204516893989422179826088076852,
97142617910342598647204516893989422179826088076852, 87783646182799346313767754307809363333018982642090,
87783646182799346313767754307809363333018982642090, 10848802521674670883215120185883543223812876952786,
10848802521674670883215120185883543223812876952786, 71329612474782464538636993009049310363619763878039,
71329612474782464538636993009049310363619763878039, 62184073572399794223406235393808339651327408011116,
62184073572399794223406235393808339651327408011116, 66627891981488087797941876876144230030984490851411,
66627891981488087797941876876144230030984490851411, 60661826293682836764744779239180335110989069790714,
60661826293682836764744779239180335110989069790714, 85786944089552990653640447425576083659976645795096,
85786944089552990653640447425576083659976645795096, 66024396409905389607120198219976047599490197230297,
66024396409905389607120198219976047599490197230297, 64913982680032973156037120041377903785566085089252,
64913982680032973156037120041377903785566085089252, 16730939319872750275468906903707539413042652315011,
16730939319872750275468906903707539413042652315011, 94809377245048795150954100921645863754710598436791,
94809377245048795150954100921645863754710598436791, 78639167021187492431995700641917969777599028300699,
78639167021187492431995700641917969777599028300699, 15368713711936614952811305876380278410754449733078,
15368713711936614952811305876380278410754449733078, 40789923115535562561142322423255033685442488917353,
40789923115535562561142322423255033685442488917353, 44889911501440648020369068063960672322193204149535,
44889911501440648020369068063960672322193204149535, 41503128880339536053299340368006977710650566631954,
41503128880339536053299340368006977710650566631954, 81234880673210146739058568557934581403627822703280,
81234880673210146739058568557934581403627822703280, 82616570773948327592232845941706525094512325230608,
82616570773948327592232845941706525094512325230608, 22918802058777319719839450180888072429661980811197,
22918802058777319719839450180888072429661980811197, 77158542502016545090413245809786882778948721859617,
77158542502016545090413245809786882778948721859617, 72107838435069186155435662884062257473692284509516,
72107838435069186155435662884062257473692284509516, 20849603980134001723930671666823555245252804609722,
20849603980134001723930671666823555245252804609722, 53503534226472524250874054075591789781264330331690
53503534226472524250874054075591789781264330331690 ];
]), const sum = numbers.reduce((a, b) => a + b);
10 const output = firstDigits(sum, 10);
)
); console.log(output);

27
challenges/euler/src/14 - Longest Collatz sequence.ts
View file

@ -1,18 +1,22 @@
// n -> n/2 (if n is even) // The following iterative sequence is defined for the set of positive integers:
// n -> 3n + 1 (if n is odd) // n → n/2 (n is even)
// Start at a number, iterate until 1 // n → 3n + 1 (n is odd)
// Which starting number under one million has the longest chain?
// Using the rule above and starting with 13, we generate the following sequence:
// 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
// It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
// Which starting number, under one million, produces the longest chain?
// NOTE: Once the chain starts the terms are allowed to go above one million.
export {}; export {};
const isEven = (n: number) => n % 2 === 0; const calculateSequence = (startNumber: number) => {
const collatzSequence = (startNumber: number) => {
let currentNumber = startNumber; let currentNumber = startNumber;
let sequence = [startNumber]; let sequence = [startNumber];
while (currentNumber > 1) { while (currentNumber > 1) {
if (isEven(currentNumber)) currentNumber = currentNumber / 2; if (currentNumber % 2 === 0) currentNumber = currentNumber / 2;
else currentNumber = currentNumber * 3 + 1; else currentNumber = currentNumber * 3 + 1;
sequence.push(currentNumber); sequence.push(currentNumber);
@ -21,12 +25,12 @@ const collatzSequence = (startNumber: number) => {
return sequence; return sequence;
}; };
const longestCollatzUnderLimit = (limit: number) => { const longestSequenceUnderLimit = (limit: number) => {
let longestStartingNumber = -1; let longestStartingNumber = -1;
let longestStartingNumberLength = -1; let longestStartingNumberLength = -1;
for (let i = 1; i < limit; i++) { for (let i = 1; i < limit; i++) {
const sequence = collatzSequence(i); const sequence = calculateSequence(i);
if (sequence.length > longestStartingNumberLength) { if (sequence.length > longestStartingNumberLength) {
longestStartingNumber = i; longestStartingNumber = i;
@ -37,4 +41,5 @@ const longestCollatzUnderLimit = (limit: number) => {
return longestStartingNumberLength; return longestStartingNumberLength;
}; };
console.log(longestCollatzUnderLimit(1000000)); // Output
console.log(longestSequenceUnderLimit(1000000));

10
challenges/euler/src/15 - Lattice paths.ts
View file

@ -1,12 +1,20 @@
// See https://github.com/newtykins/the-honk/tree/main/euler/thoughts/15%20-Lattice%20paths.md // Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
// How many such routes are there through a 20×20 grid?
export {}; export {};
/**
* Calculate n!
*/
const factorial = (n: number) => { const factorial = (n: number) => {
if (n < 0) return -1; if (n < 0) return -1;
else if (n === 0) return 1; else if (n === 0) return 1;
else return n * factorial(n - 1); else return n * factorial(n - 1);
}; };
/**
* Count the lattice paths using the formula shown in the thoughts document.
* @see https://github.com/newtykins/the-honk/tree/main/projects/euler/thoughts/15%20-Lattice%20paths.md
*/
const countLatticePaths = (width: number, height: number) => { const countLatticePaths = (width: number, height: number) => {
return factorial(width + height) / (factorial(width) * factorial(height)); return factorial(width + height) / (factorial(width) * factorial(height));
}; };

2
challenges/euler/src/16 - Power digit sum.ts
View file

@ -1,3 +1,5 @@
// 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
// What is the sum of the digits of the number 2^1000?
export {}; export {};
const powerDigitSum = (base: number, power: number) => { const powerDigitSum = (base: number, power: number) => {

9
challenges/euler/src/17 - Number letter counts.ts
View file

@ -1,3 +1,7 @@
// If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.
// If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
// NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.
export {}; export {};
const translations = { const translations = {
@ -30,7 +34,9 @@ const translations = {
90: 'ninety' 90: 'ninety'
}; };
// works for what we need, could be improved /**
* Converts numbers to words, could be improved.
*/
const numberToWords = (n: number): string => { const numberToWords = (n: number): string => {
let out = ''; let out = '';
@ -72,6 +78,7 @@ const numberToWords = (n: number): string => {
return out; return out;
}; };
// Output
let sum = 0; let sum = 0;
for (let i = 1; i <= 1000; i++) { for (let i = 1; i <= 1000; i++) {

47
challenges/euler/src/18 - Maximum path sum I.ts
View file

@ -1,3 +1,10 @@
// By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
// 3
// 7 4
// 2 4 6
// 8 5 9 3
// That is, 3 + 7 + 4 + 9 = 23.
// Find the maximum total from top to bottom of the triangle below (see triangle variable)
export {}; export {};
const maximumPathSum = (triangle: number[][]) => { const maximumPathSum = (triangle: number[][]) => {
@ -13,22 +20,24 @@ const maximumPathSum = (triangle: number[][]) => {
return triangle[0][0]; return triangle[0][0];
}; };
console.log( // Output
maximumPathSum([ const triangle = [
[75], [75],
[95, 64], [95, 64],
[17, 47, 82], [17, 47, 82],
[18, 35, 87, 10], [18, 35, 87, 10],
[20, 4, 82, 47, 65], [20, 4, 82, 47, 65],
[19, 1, 23, 75, 3, 34], [19, 1, 23, 75, 3, 34],
[88, 2, 77, 73, 7, 63, 67], [88, 2, 77, 73, 7, 63, 67],
[99, 65, 4, 28, 6, 16, 70, 92], [99, 65, 4, 28, 6, 16, 70, 92],
[41, 41, 26, 56, 83, 40, 80, 70, 33], [41, 41, 26, 56, 83, 40, 80, 70, 33],
[41, 48, 72, 33, 47, 32, 37, 16, 94, 29], [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
[53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14], [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
[70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57], [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], [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
[63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31], [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
[4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23] [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]
]) ];
); const maximumSum = maximumPathSum(triangle);
console.log(maximumSum);

23
challenges/euler/src/2 - Even Fibonacci numbers.ts
View file

@ -1,12 +1,15 @@
// Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
// By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
export {}; export {};
const calcSum = (numbers: number[]) => numbers.reduce((a, b) => a + b); /**
* Calculate the Fibonacci sequence up until a limit
const fibonacciNumbers = (upperBound: number) => { */
const calculateFibonacci = (limit: number) => {
const sequence = [1, 2]; const sequence = [1, 2];
// Keep making new numbers in the sequence until we hit the upper bound // Keep making new numbers in the sequence until we hit the upper bound
while (sequence[sequence.length - 1] < upperBound) { while (sequence[sequence.length - 1] < limit) {
const newValue = sequence[sequence.length - 1] + sequence[sequence.length - 2]; const newValue = sequence[sequence.length - 1] + sequence[sequence.length - 2];
sequence.push(newValue); sequence.push(newValue);
} }
@ -14,11 +17,9 @@ const fibonacciNumbers = (upperBound: number) => {
return sequence; return sequence;
}; };
const evenFibonacciNumbers = (upperBound: number) => { // Output
const sequence = fibonacciNumbers(upperBound); const fibonacci = calculateFibonacci(4000000);
const even = sequence.filter(n => n % 2 === 0); const even = fibonacci.filter(n => n % 2 === 0);
const evenSum = even.reduce((a, b) => a + b);
return even; console.log(evenSum);
};
console.log(calcSum(evenFibonacciNumbers(4000000)));

6
challenges/euler/src/3 - Largest prime factor.ts
View file

@ -1,5 +1,10 @@
// The prime factors of 13195 are 5, 7, 13 and 29.
// What is the largest prime factor of the number 600851475143?
export {}; export {};
/**
* Work out the largest prime factor of a number
*/
const largestPrimeFactor = (number: number) => { const largestPrimeFactor = (number: number) => {
let i = 2; let i = 2;
@ -11,4 +16,5 @@ const largestPrimeFactor = (number: number) => {
return number; return number;
}; };
// Output
console.log(largestPrimeFactor(600851475143)); console.log(largestPrimeFactor(600851475143));

9
challenges/euler/src/4 - Largest pallindrome product.ts
View file

@ -1,6 +1,11 @@
// A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
// Find the largest palindrome made from the product of two 3-digit numbers.
export {}; export {};
const largestPallidromeNumber = (lowerBound: number, upperBound: number) => { /**
* Work out the largest pallindromic number between a lower and upper bound.
*/
const largestPallindromicNumber = (lowerBound: number, upperBound: number) => {
// Work out all of the products of 3 digit numbers // Work out all of the products of 3 digit numbers
const products: number[] = []; const products: number[] = [];
@ -20,4 +25,4 @@ const largestPallidromeNumber = (lowerBound: number, upperBound: number) => {
return sorted[0]; return sorted[0];
}; };
console.log(largestPallidromeNumber(100, 999)); console.log(largestPallindromicNumber(100, 999));

10
challenges/euler/src/5 - Smallest multiple.ts
View file

@ -1,9 +1,8 @@
// 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
// What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
export {}; export {};
/** const canBeDivided = (x: number, n: number) => {
* Is x disible to n?
*/
const isDivisibleTo = (x: number, n: number) => {
for (; n > 0; n -= 1) { for (; n > 0; n -= 1) {
if (x % n !== 0) return false; if (x % n !== 0) return false;
} }
@ -14,8 +13,9 @@ const isDivisibleTo = (x: number, n: number) => {
const divisibleTo = (n: number) => { const divisibleTo = (n: number) => {
if (n === 1) return 1; if (n === 1) return 1;
for (var step = divisibleTo(n - 1), i = step; !isDivisibleTo(i, n); i += step); for (var step = divisibleTo(n - 1), i = step; !canBeDivided(i, n); i += step);
return i; return i;
}; };
// Output
console.log(divisibleTo(20)); console.log(divisibleTo(20));

19
challenges/euler/src/6 - Sum square difference.ts
View file

@ -1,7 +1,12 @@
// The sum of the squares of the first ten natural numbers is 1^2 + 2^2 + ... + 10^2 = 385
// The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)^2 = 55^2 = 3025
// Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.
// Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
export {}; export {};
const calcSum = (numbers: number[]) => numbers.reduce((a, b) => a + b); /**
* Calculate the sum of the squares between a lower and upper bound.
*/
const sumOfSquares = (lowerBound: number, upperBound: number) => { const sumOfSquares = (lowerBound: number, upperBound: number) => {
// Calculate the square number of all the numbers between the bounds // Calculate the square number of all the numbers between the bounds
const squares: number[] = []; const squares: number[] = [];
@ -11,9 +16,12 @@ const sumOfSquares = (lowerBound: number, upperBound: number) => {
} }
// Return the sum // Return the sum
return calcSum(squares); return squares.reduce((a, b) => a + b);
}; };
/**
* Square the sum of the numbers between a lower and upper bound, and return it.
*/
const squareOfSum = (lowerBound: number, upperBound: number) => { const squareOfSum = (lowerBound: number, upperBound: number) => {
// Get the sum of all of the numbers between the bounds // Get the sum of all of the numbers between the bounds
const numbers: number[] = []; const numbers: number[] = [];
@ -22,10 +30,9 @@ const squareOfSum = (lowerBound: number, upperBound: number) => {
numbers.push(i); numbers.push(i);
} }
const sum = calcSum(numbers);
// Square the sum // Square the sum
return sum ** 2; return numbers.reduce((a, b) => a + b) ** 2;
}; };
// Output
console.log(squareOfSum(1, 100) - sumOfSquares(1, 100)); console.log(squareOfSum(1, 100) - sumOfSquares(1, 100));

16
challenges/euler/src/67 - Maximum path sum II.ts
View file

@ -1,9 +1,17 @@
// By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
// 3
// 7 4
// 2 4 6
// 8 5 9 3
// That is, 3 + 7 + 4 + 9 = 23.
// Find the maximum total from top to bottom in p067_triangle.txt, a 15K text file containing a triangle with one-hundred rows.
import fs from 'fs'; import fs from 'fs';
import path from 'path'; import path from 'path';
import { resources } from '../constants'; import { resources } from '../constants';
export {}; export {};
// Same method as 18 - Maximum path sum I
const maximumPathSum = (triangle: number[][]) => { const maximumPathSum = (triangle: number[][]) => {
let row = triangle.length - 1; let row = triangle.length - 1;
@ -17,13 +25,15 @@ const maximumPathSum = (triangle: number[][]) => {
return triangle[0][0]; return triangle[0][0];
}; };
// Output
const data = fs const data = fs
.readFileSync(path.join(resources, 'p067_triangle.txt')) .readFileSync(path.join(resources, 'p067_triangle.txt')) // https://github.com/newtykins/the-honk/tree/main/challenges/euler/resources/p067_triangle.txt
.toString() .toString()
.split('\n') .split('\n')
.map(row => { .map(row => {
const values = row.split(' '); const values = row.split(' ');
return values.map(v => parseInt(v)); return values.map(v => parseInt(v));
}); });
const maximumSum = maximumPathSum(data);
console.log(maximumPathSum(data)); console.log(maximumSum);

9
challenges/euler/src/7 - 10001st Prime.ts
View file

@ -1,5 +1,10 @@
// By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
// What is the 10 001st prime number?
export {}; export {};
/**
* Is this number prime?
*/
const isPrime = (number: number) => { const isPrime = (number: number) => {
for (var i = 2; i < number; i++) { for (var i = 2; i < number; i++) {
if (number % i === 0) return false; if (number % i === 0) return false;
@ -8,6 +13,9 @@ const isPrime = (number: number) => {
return true; return true;
}; };
/**
* Calculate the nth prime number.
*/
const nthPrime = (n: number) => { const nthPrime = (n: number) => {
const primes: number[] = []; const primes: number[] = [];
let number = 2; let number = 2;
@ -20,4 +28,5 @@ const nthPrime = (n: number) => {
return primes[n - 1]; return primes[n - 1];
}; };
// Output
console.log(nthPrime(10001)); console.log(nthPrime(10001));

3
challenges/euler/src/8 - Largest product in a series.ts
View file

@ -1,3 +1,5 @@
// The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.
// Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
export {}; export {};
const largestProduct = (number: bigint | number, adjacentDigits: number) => { const largestProduct = (number: bigint | number, adjacentDigits: number) => {
@ -31,6 +33,7 @@ const largestProduct = (number: bigint | number, adjacentDigits: number) => {
return products.sort((a, b) => b - a)[0]; return products.sort((a, b) => b - a)[0];
}; };
// Output
const number = BigInt( const number = BigInt(
'7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450' '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
); );

11
challenges/euler/src/9 - Special Pythagorean triplet.ts
View file

@ -1,6 +1,13 @@
// See https://github.com/newtykins/the-honk/tree/main/euler/thoughts/9%20-Special%20Pythagorean%29triplet.md // A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a^2 + b^2 = c^2
// For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2
// There exists exactly one Pythagorean triplet for which a + b + c = 1000.
// Find the product abc.
export {}; export {};
/**
* Find a Pythagorean triplet based on its sum
* @see // See https://github.com/newtykins/the-honk/tree/main/projects/euler/thoughts/9%20-Special%20Pythagorean%29triplet.md
*/
const pythagoreanTriplet = (sum: number) => { const pythagoreanTriplet = (sum: number) => {
let a: number, let a: number,
b = 1, b = 1,
@ -18,6 +25,6 @@ const pythagoreanTriplet = (sum: number) => {
return { a, b, c }; return { a, b, c };
}; };
// Output
const triplet = pythagoreanTriplet(1000); const triplet = pythagoreanTriplet(1000);
console.log(triplet);
console.log(triplet.a * triplet.b * triplet.c); console.log(triplet.a * triplet.b * triplet.c);