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‎Maths/ModularArithmetic.js‎
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‎Maths/ModularArithmetic.js‎
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+56Lines changed: 56 additions & 0 deletions
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‎Maths/test/ModularArithmetic.test.js‎
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‎Maths/test/ModularArithmetic.test.js‎
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+45Lines changed: 45 additions & 0 deletions
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+import { extendedEuclideanGCD } from './ExtendedEuclideanGCD'
+
+/**
+ * https://brilliant.org/wiki/modular-arithmetic/
+ * @param {Number} arg1 first argument
+ * @param {Number} arg2 second argument
+ * @returns {Number}
+ */
+
+export class ModRing {
+  constructor (MOD) {
+    this.MOD = MOD
+  }
+
+  isInputValid = (arg1, arg2) => {
+    if (!this.MOD) {
+      throw new Error('Modulus must be initialized in the object constructor')
+    }
+    if (typeof arg1 !== 'number' || typeof arg2 !== 'number') {
+      throw new TypeError('Input must be Numbers')
+    }
+  }
+  /**
+   * Modulus is Distributive property,
+   * As a result, we separate it into numbers in order to keep it within MOD's range
+  */
+
+  add = (arg1, arg2) => {
+    this.isInputValid(arg1, arg2)
+    return ((arg1 % this.MOD) + (arg2 % this.MOD)) % this.MOD
+  }
+
+  subtract = (arg1, arg2) => {
+    this.isInputValid(arg1, arg2)
+    // An extra MOD is added to check negative results
+    return ((arg1 % this.MOD) - (arg2 % this.MOD) + this.MOD) % this.MOD
+  }
+
+  multiply = (arg1, arg2) => {
+    this.isInputValid(arg1, arg2)
+    return ((arg1 % this.MOD) * (arg2 % this.MOD)) % this.MOD
+  }
+
+  /**
+   *
+   * It is not Possible to find Division directly like the above methods,
+   * So we have to use the Extended Euclidean Theorem for finding Multiplicative Inverse
+   * https://github.com/TheAlgorithms/JavaScript/blob/master/Maths/ExtendedEuclideanGCD.js
+   */
+
+  divide = (arg1, arg2) => {
+    // 1st Index contains the required result
+    // The theorem may have return Negative value, we need to add MOD to make it Positive
+    return (extendedEuclideanGCD(arg1, arg2)[1] + this.MOD) % this.MOD
+  }
+}
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+import { ModRing } from '../ModularArithmetic'
+
+describe('Modular Arithmetic', () => {
+  const MOD = 10000007
+  let ring
+  beforeEach(() => {
+    ring = new ModRing(MOD)
+  })
+
+  describe('add', () => {
+    it('Should return 9999993 for 10000000 and 10000000', () => {
+      expect(ring.add(10000000, 10000000)).toBe(9999993)
+    })
+    it('Should return 9999986 for 10000000 and 20000000', () => {
+      expect(ring.add(10000000, 20000000)).toBe(9999986)
+    })
+  })
+
+  describe('subtract', () => {
+    it('Should return 1000000 for 10000000 and 9000000', () => {
+      expect(ring.subtract(10000000, 9000000)).toBe(1000000)
+    })
+    it('Should return 7 for 10000000 and 20000000', () => {
+      expect(ring.subtract(10000000, 20000000)).toBe(7)
+    })
+  })
+
+  describe('multiply', () => {
+    it('Should return 1000000 for 100000 and 10000', () => {
+      expect(ring.multiply(100000, 10000)).toBe(9999307)
+    })
+    it('Should return 7 for 100000 and 10000100', () => {
+      expect(ring.multiply(10000000, 20000000)).toBe(98)
+    })
+  })
+
+  describe('divide', () => {
+    it('Should return 4 for 3 and 11', () => {
+      expect(ring.divide(3, 11)).toBe(4)
+    })
+    it('Should return 2 for 18 and 7', () => {
+      expect(ring.divide(18, 7)).toBe(2)
+    })
+  })
+})