Prime Mover

ardallie · ardallie · Aug 17, 2021 · Aug 16, 2021 · Aug 16, 2021 · Aug 16, 2021
commit c50806a3af24e20ae2119cc858fff601decce066
diff --git a/src/medium/PrimeMover.java b/src/medium/PrimeMover.java
@@ -0,0 +1,77 @@
+package medium;
+
+/**
+ * Have the function PrimeMover(num) return the numth prime number.
+ * The range will be from 1 to 10^4.
+ * ---
+ * For example: if num is 16 the output should be 53 as 53 is the 16th prime number.
+ */
+public class PrimeMover {
+
+  /**
+   * Check if a given number is a prime number.
+   *
+   * @param num input number
+   * @return true if is a prime number
+   */
+  private static boolean isPrimeNumber(int num) {
+    // prime numbers are greater than 1
+    if (num <= 1) {
+      return false;
+    }
+    // 2 is an only even prime number
+    // http://mathworld.wolfram.com/EvenPrime.html
+    if (num == 2) {
+      return true;
+    }
+    // eliminate all even numbers to reduce time complexity
+    // (cannot be a prime number if is divisible by 2)
+    if (num % 2 == 0) {
+      return false;
+    }
+    // no need to check the entire range from 0 to num
+    // (square root of num) + 1 is the sufficient upper limit
+    // which greatly reduces time complexity
+    double upper = Math.sqrt(num) + 1;
+    // since the even numbers are eliminated, we can check the odd numbers only
+    for (int i = 3; i < upper; i += 2) {
+      if (num % i == 0) {
+        // not a prime number
+        return false;
+      }
+    }
+    // must be a prime number!
+    return true;
+  }
+
+  /**
+   * Prime Mover function.
+   *
+   * @param num input number
+   * @return Nth prime number where N = num
+   */
+  private static int primeMover(int num) {
+    int i = 1;
+    int primes = 0;
+    while (primes < num) {
+      if (isPrimeNumber(i)) {
+        primes++;
+      }
+      i++;
+    }
+    return i - 1;
+  }
+
+  /**
+   * Entry point.
+   *
+   * @param args command line arguments
+   */
+  public static void main(String[] args) {
+    int result1 = primeMover(9);
+    System.out.println(result1);
+    int result2 = primeMover(100);
+    System.out.println(result2);
+  }
+
+}