allPrimesLessThanN

Author: Wakidur Rahaman

src/exercises/number/modularExponentiation.ts

@@ -1,3 +1,59 @@
+/**
+ * 1.
+ * Given three numbers x, y, and p, compute (xˆy) % p. (This is modular exponentiation.)
+ * Here, x is the base, y is exponent, and p is the modulus.
+ * Modular exponentiation is a type of exponentiation performed over a modulus,
+ * which is useful in computer science and used in the field of public-key encryption algorithms
+ *
+ * @param base
+ * @param exponent
+ * @param modulus
+ * @returns
+ */
 function modularExponentiation(base: number, exponent: number, modulus: number): number {
   return Math.pow(base, exponent) % modulus;
 }
+
+function modularExponentiation01(base: number, exponent: number, modulus: number): number {
+  if (modulus == 1) return 0;
+
+  let value = 1;
+
+  for (let i = 0; i < exponent; i++) {
+    value = (value * base) % modulus;
+  }
+
+  return value;
+}
+
+/**
+ * 2.
+ * Print all primes lass than n.
+ *
+ * Simply iterate from 0 to n and print any prime numbers where isPrime() evaluates to true.
+ *
+ */
+
+function allPrimesLessThanN(n: number): void {
+  for (let i = 0; i < n; i++) {
+    if (isPrimeNumber(i)) {
+      console.log(i);
+    }
+  }
+} // time complexity of O(n sqrt(n)) is run n times.
+
+function isPrimeNumber(number: number): boolean {
+  if (number <= 1) return false;
+  if (number <= 3) return true;
+
+  // This is checked so that we can skip
+  // middle five number in below loop
+
+  for (let i = 5; i * i < number; i = i + 6) {
+    if (number % i == 0 || number % (i + 2) == 0) {
+      return false;
+    }
+  }
+
+  return true;
+} // time complexity of O(sqrt(n)) is run n times.