New helper: prime factors

src/helpers/divisors.test.ts

@@ -1,6 +1,12 @@
-import { divisors } from './divisors';
+import { divisors, nextPrimeFactor, primeFactors } from './divisors';
 
 describe('divisors of a number', () => {
+  it('divisors of one', () => {
+    expect.assertions(1);
+
+    expect(divisors(1)).toStrictEqual([1]);
+  });
+
   it('divisors of a number', () => {
     expect.assertions(5);
 
@@ -10,4 +16,50 @@ describe('divisors of a number', () => {
     expect(divisors(9)).toStrictEqual([1, 3, 9]);
     expect(divisors(16)).toStrictEqual([1, 2, 4, 8, 16]);
   });
+
+  it('next prime factor of a target number', () => {
+    expect.assertions(5);
+
+    expect(nextPrimeFactor(1)).toStrictEqual({
+      factor: 1,
+      carry: 1,
+      cycles: 0
+    });
+    expect(nextPrimeFactor(2)).toStrictEqual({
+      factor: 2,
+      carry: 1,
+      cycles: 1
+    });
+    expect(nextPrimeFactor(4)).toStrictEqual({
+      factor: 2,
+      carry: 2,
+      cycles: 1
+    });
+    expect(nextPrimeFactor(9)).toStrictEqual({
+      factor: 3,
+      carry: 3,
+      cycles: 2
+    });
+    expect(nextPrimeFactor(7)).toStrictEqual({
+      factor: 7,
+      carry: 1,
+      cycles: 6
+    });
+  });
+
+  it('prime factors of number', () => {
+    expect.assertions(5);
+
+    expect(primeFactors(1)).toStrictEqual({ factors: [1], cycles: 1 });
+    expect(primeFactors(2)).toStrictEqual({ factors: [2], cycles: 1 });
+    expect(primeFactors(6)).toStrictEqual({ factors: [2, 3], cycles: 3 });
+    expect(primeFactors(12)).toStrictEqual({
+      factors: [2, 2, 3],
+      cycles: 4
+    });
+    expect(primeFactors(120)).toStrictEqual({
+      factors: [2, 2, 2, 3, 5],
+      cycles: 9
+    });
+  });
 });

src/helpers/divisors.ts

@@ -38,6 +38,66 @@ export const divisors = (target: number): number[] => {
   return divs;
 };
 
+export interface PrimeFactor {
+  factor: number;
+  carry: number;
+  cycles: number;
+}
+
+export const nextPrimeFactor = (_target: number): PrimeFactor => {
+  const top = Math.abs(_target);
+  let cycles = 0;
+
+  if (top === 1) {
+    return {
+      factor: 1,
+      carry: 1,
+      cycles: cycles
+    };
+  }
+
+  let i = 2;
+  while (i < top) {
+    cycles += 1;
+    if (top % i === 0) {
+      return {
+        factor: i,
+        carry: top / i,
+        cycles: cycles
+      };
+    }
+    i += 1;
+  }
+
+  return {
+    factor: i,
+    carry: top / i,
+    cycles: cycles + 1
+  };
+};
+
+export const primeFactors = (target: number) => {
+  const factors = [];
+  let cycles = 0;
+
+  if (target === 1) {
+    return { factors: [1], cycles: 1 };
+  }
+
+  let factor = target;
+  while (factor !== 1) {
+    const partial = nextPrimeFactor(factor);
+    cycles += partial.cycles;
+
+    factors.push(partial.factor);
+    factor = partial.carry;
+  }
+
+  return { factors: factors, cycles: cycles };
+};
+
 export default {
-  divisors
+  divisors,
+  primeFactors,
+  nextPrimeFactor
 };

src/helpers/index.ts

@@ -1,6 +1,6 @@
 type nullable<T> = T | null | undefined;
 
-export { divisors } from './divisors';
+export { divisors, primeFactors, nextPrimeFactor } from './divisors';
 export { isPrime } from './prime';
 export { isPalindrome } from './isPalindrome';
 export { nullable };