Data update

Task/Combinations-and-permutations/C-sharp/combinations-and-permutations.cs

@@ -0,0 +1,94 @@
+using System;
+using System.Numerics;
+
+class CombinationsAndPermutations
+{
+	public static void Main(string[] args)
+	{
+		Console.WriteLine(double.MaxValue);
+		Console.WriteLine("A sample of permutations from 1 to 12 with exact Integer arithmetic:");
+		for (int n = 1; n <= 12; n++)
+		{
+			int k = n / 2;
+			Console.WriteLine($"{n} P {k} = {Permutation(n, k)}");
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("A sample of combinations from 10 to 60 with exact Integer arithmetic:");
+		for (int n = 10; n <= 60; n += 5)
+		{
+			int k = n / 2;
+			Console.WriteLine($"{n} C {k} = {Combination(n, k)}");
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("A sample of permutations from 5 to 15000 displayed in floating point arithmetic:");
+		Console.WriteLine($"{5} P {2} = {Display(Permutation(5, 2), 50)}");
+		for (int n = 1000; n <= 15000; n += 1000)
+		{
+			int k = n / 2;
+			Console.WriteLine($"{n} P {k} = {Display(Permutation(n, k), 50)}");
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("A sample of combinations from 100 to 1000 displayed in floating point arithmetic:");
+		for (int n = 100; n <= 1000; n += 100)
+		{
+			int k = n / 2;
+			Console.WriteLine($"{n} C {k} = {Display(Combination(n, k), 50)}");
+		}
+	}
+
+	private static string Display(BigInteger val, int precision)
+	{
+		string s = val.ToString();
+		// Ensure that we don't try to take a substring longer than what's available.
+		int actualPrecision = Math.Min(precision, s.Length - 1); // Adjusted to ensure it doesn't exceed string length
+		System.Text.StringBuilder sb = new System.Text.StringBuilder();
+		if (s.Length > 1) // Check if the string has more than one character
+		{
+			sb.Append(s.Substring(0, 1));
+			sb.Append(".");
+			sb.Append(s.Substring(1, actualPrecision-1));
+		}
+		else
+		{
+			// If the string is only one digit, no need to insert a decimal point.
+			sb.Append(s);
+		}
+
+		sb.Append(" * 10^");
+		sb.Append(s.Length - 1);
+		return sb.ToString();
+	}
+
+	public static BigInteger Combination(int n, int k)
+	{
+		// Select value with smallest intermediate results
+		// combination(n, k) = combination(n, n-k)
+		if (n - k < k)
+		{
+			k = n - k;
+		}
+
+		BigInteger result = Permutation(n, k);
+		while (k > 0)
+		{
+			result = result / k;
+			k--;
+		}
+
+		return result;
+	}
+
+	public static BigInteger Permutation(int n, int k)
+	{
+		BigInteger result = BigInteger.One;
+		for (int i = n; i >= n - k + 1; i--)
+		{
+			result = result * i;
+		}
+
+		return result;
+	}
+}

Task/Combinations-and-permutations/Lua/combinations-and-permutations.lua

@@ -0,0 +1,61 @@
+-- Helper function to display results in scientific notation corrected
+function eshow(x)
+    local e = math.floor(x / math.log(10))
+    local exponentiated = math.exp(x - e * math.log(10))
+    -- Corrected format specifier from %.8Fe%+d to %.8e, and manually constructing the scientific notation if needed
+    return string.format("%.8e", exponentiated) .. "e" .. tostring(e)
+end
+
+-- The rest of the functions remain the same
+
+-- Define the factorial function for permutations
+function P(n, k)
+    local x = 1
+    for i = n - k + 1, n do
+        x = x * i
+    end
+    return x
+end
+
+-- Define the function for big permutations using logarithms
+function P_big(n, k)
+    local x = 0
+    for i = n - k + 1, n do
+        x = x + math.log(i)
+    end
+    return eshow(x)
+end
+
+-- Define the combinations function
+function C(n, k)
+    local x = 1
+    for i = 1, k do
+        x = x * (n - i + 1) / i
+    end
+    return x
+end
+
+-- Define the function for big combinations using logarithms
+function C_big(n, k)
+    local x = 0
+    for i = 1, k do
+        x = x + math.log(n - i + 1) - math.log(i)
+    end
+    return math.exp(x)
+end
+
+-- Function to showcase the calculations
+function showoff(text, code, fname, ...)
+    local n = {...}
+    print("\nA sample of " .. text .. " from " .. n[1] .. " to " .. n[#n] .. "")
+    for _, v in ipairs(n) do
+        local k = math.floor(v / 3)
+        print(v, fname .. " " .. k .. " = ", code(v, k))
+    end
+end
+
+-- Examples of usage
+showoff("Permutations", P, "P", 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
+showoff("Combinations", C, "C", 10, 20, 30, 40, 50, 60)
+showoff("Permutations", P_big, "P", 5, 50, 500, 1000, 5000, 15000)
+showoff("Combinations", C_big, "C", 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000)