feat(euler): 26 - reciprocal cycles

challenges/euler/pnpm-lock.yaml

@@ -1,4 +1,4 @@
-lockfileVersion: 5.3
+lockfileVersion: 5.4
 
 specifiers:
     '@swc/core': ^1.2.125
@@ -25,7 +25,7 @@ devDependencies:
     inquirer: 8.2.0
     ms: 2.1.3
     regenerator-runtime: 0.13.9
-    ts-node: 10.4.0_626351e049b80b142acb2ce48a7f5656
+    ts-node: 10.4.0_mjrvdycjxafrikwlftsiu72wky
     typescript: 4.4.4
 
 packages:
@@ -943,7 +943,7 @@ packages:
             os-tmpdir: 1.0.2
         dev: true
 
-    /ts-node/10.4.0_626351e049b80b142acb2ce48a7f5656:
+    /ts-node/10.4.0_mjrvdycjxafrikwlftsiu72wky:
         resolution:
             {
                 integrity: sha512-g0FlPvvCXSIO1JDF6S232P5jPYqBkRL9qly81ZgAOSU7rwI0stphCgd2kLiCrU9DjQCrJMWEqcNSjQL02s6d8A==

challenges/euler/readme.md

@@ -37,7 +37,7 @@ The source code can be found in the [src](src) directory. My thoughts about some
 -   [x] [23 - Non-abundant sums](src/23%20-%20Non-abundant%20sums.ts)
 -   [x] [24 - Lexicographic permutations](src/24%20-%20Lexicographic%20permutations.ts)
 -   [x] [25 - 1000-digit Fibonacci number](src/25%20-%201000-digit%20Fibonacci%20number.ts)
--   [ ] 26 - Reciprocal cycles
+-   [x] [26 - Reciprocal cycles](src/26%20-%20Reciprocal%20cycles.ts)
 -   [ ] 27 - Quadratic primes
 -   [x] [28 - Number spiral diagonals](src/28%20-%20Number%20spiral%20diagonals.ts)
 -   [ ] 29 - Distinct powers

challenges/euler/src/26 - Reciprocal cycles.ts

@@ -0,0 +1,54 @@
+// A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
+//
+// 1/2= 0.5
+// 1/3= 0.(3)
+// 1/4= 0.25
+// 1/5= 0.2
+// 1/6= 0.1(6)
+// 1/7= 0.(142857)
+// 1/8= 0.125
+// 1/9= 0.(1)
+// 1/10= 0.1
+//
+// Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
+// Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
+export = {};
+
+const cycleLength = (denominator: number, numerator: number = 1) => {
+    let dividend = numerator;
+    let position = 1;
+    let lastPosition: { [number: number]: number } = {};
+
+    while (true) {
+        const remainder = dividend % denominator;
+
+        // If the remainder is zero, there is no recurring cycle
+        if (remainder === 0) return 0;
+
+        // If the remainder has been seen before, return.
+        if (lastPosition.hasOwnProperty(remainder)) {
+            return position - lastPosition[remainder];
+        }
+
+        // Move onto the next digit
+        lastPosition[remainder] = position;
+        position++;
+        dividend = remainder * 10;
+    }
+};
+
+let longestLength = 0;
+let correspondingNumber = null;
+
+for (let i = 1; i < 1000; i++) {
+    const length = cycleLength(i);
+
+    if (length > longestLength) {
+        longestLength = length;
+        correspondingNumber = i;
+    }
+}
+
+console.log(
+    `The number with the longest recurring cycle is ${correspondingNumber} with a length of ${longestLength}.`
+);