Add Newton's Square Root Calculation Method (TheAlgorithms#357)

Author: Kalkwst

Algorithms.Tests/Numeric/NewtonSquareRootTests.cs

@@ -0,0 +1,44 @@
+using System;
+using System.Numerics;
+using NUnit.Framework;
+
+namespace Algorithms.Tests.Numeric;
+
+public class NewtonSquareRootTests
+{
+    private static readonly object[] CalculateSquareRootInput =
+    {
+        new object[] {BigInteger.One, BigInteger.One},
+        new object[] {new BigInteger(221295376), new BigInteger(14876)},
+        new object[] {new BigInteger(2530995481), new BigInteger(50309)},
+        new object[] {new BigInteger(3144293476), new BigInteger(56074)},
+        new object[] {new BigInteger(3844992064), new BigInteger(62008)},
+        new object[] {new BigInteger(5301150481), new BigInteger(72809)},
+        new object[] {new BigInteger(5551442064), new BigInteger(74508)},
+        new object[] {new BigInteger(6980435401), new BigInteger(83549)},
+        new object[] {new BigInteger(8036226025), new BigInteger(89645)},
+    };
+
+    [TestCaseSource(nameof(CalculateSquareRootInput))]
+    public void CalculateSquareRootTest(BigInteger number, BigInteger result)
+    {
+        Assert.That(NewtonSquareRoot.Calculate(number), Is.EqualTo(result));
+    }
+
+    [Test]
+    public void CalculateSquareRootOfZero()
+    {
+        Assert.That(NewtonSquareRoot.Calculate(0), Is.EqualTo(BigInteger.Zero));
+    }
+
+    [Test]
+    public void CalculateSquareRootNegativeNumber()
+    {
+        Assert.Throws(Is.TypeOf<ArgumentException>()
+            .And.Message.EqualTo("Cannot calculate the square root of a negative number."),
+            delegate
+            {
+                NewtonSquareRoot.Calculate(BigInteger.MinusOne);
+            });
+    }
+}

Algorithms/NewtonSquareRoot.cs

@@ -0,0 +1,37 @@
+using System;
+using System.Numerics;
+
+namespace Algorithms;
+
+public static class NewtonSquareRoot
+{
+    public static BigInteger Calculate(BigInteger number)
+    {
+        if (number < 0)
+        {
+            throw new ArgumentException("Cannot calculate the square root of a negative number.");
+        }
+
+        if (number == 0)
+        {
+            return BigInteger.Zero;
+        }
+
+        var bitLength = Convert.ToInt32(Math.Ceiling(BigInteger.Log(number, 2)));
+        BigInteger root = BigInteger.One << (bitLength / 2);
+
+        while (!IsSquareRoot(number, root))
+        {
+            root += number / root;
+            root /= 2;
+        }
+
+        return root;
+    }
+
+    private static bool IsSquareRoot(BigInteger number, BigInteger root)
+    {
+        var lowerBound = root * root;
+        return number >= lowerBound && number <= lowerBound + root + root;
+    }
+}

README.md

@@ -82,6 +82,7 @@ find more than one implementation for the same objective but using different alg
     * [Miller-Rabin primality check](./Algorithms/Numeric/MillerRabinPrimalityChecker.cs)
     * [KrishnamurthyNumberChecker](./Algorithms/Numeric/KrishnamurthyNumberChecker.cs)
     * [Automorphic Number](./Algorithms/Numeric/AutomorphicNumber.cs)
+    * [Newton's Square Root Calculation](./Algorithms/NewtonSquareRoot.cs)
   * [Searches](./Algorithms/Search)
     * [A-Star](./Algorithms/Search/AStar/)
     * [Binary Search](./Algorithms/Search/BinarySearcher.cs)