feat: improved nth roots

.vscode/settings.json

@@ -23,6 +23,16 @@
         "tuple": "cpp",
         "type_traits": "cpp",
         "string_view": "cpp",
-        "vector": "cpp"
+        "vector": "cpp",
+        "algorithm": "cpp",
+        "memory": "cpp",
+        "random": "cpp",
+        "iosfwd": "cpp",
+        "iostream": "cpp",
+        "istream": "cpp",
+        "numeric": "cpp",
+        "ostream": "cpp",
+        "ratio": "cpp",
+        "streambuf": "cpp"
     }
 }

languages/c++/code/nthRoot.cc

@@ -2,39 +2,104 @@
 #include <cmath>
 #include <limits>
 
-double nthRoot(double n, double x) {
-	double lastX;
-	double y = 1; // initial guess
+std::string superscript[10] = { "⁰", "¹", "²", "³", "⁴", "⁵", "⁶", "⁷", "⁸", "⁹" };
 
-	while (y != lastX) {
-		// f(y) = yⁿ - x
-		// f'(y) = nyⁿ⁻¹
-		double f = std::pow(y, n) - x;
-		double fprime = n * std::pow(y, n - 1);
+struct Result {
+	double result;
+	int maxIterations;
+	int iterationsUsed;
+};
 
-		lastX = y;
-		y -= f / fprime;
+// See https://github.com/newtykins/the-honk/tree/main/maths/nth%20root.png
+Result nthRoot(double n, double x, int maxIterations = 200) {
+	Result output;
+	output.result = 1;
+	output.maxIterations = maxIterations;
+	output.iterationsUsed = 0;
+
+	double lastIteration = 0;
+
+	for (int i = 0; i < maxIterations; i++) {
+		if (lastIteration == output.result) {
+			break;
+		}
+		
+		output.iterationsUsed += 1;
+		lastIteration = output.result;
+		output.result = ((lastIteration * (n - 1)) + (x * std::pow(lastIteration, 1 - n))) / n;
 	}
 
-	return y;
+	return output;
 }
 
-int promptForInteger(std::string letter) {
+int fetchInput(std::string letter) {
     std::cout << "Please input a value for " + letter + ": ";
     
-    int input;
+    double input;
     std::cin >> input;
 
     return input;
 }
 
+bool isInt(double n) {
+	return (int) n == n;
+}
+
+std::string formatDouble(double input) {
+    std::string str = std::to_string(input);
+	str.erase(str.find_last_not_of('0') + 1, std::string::npos);
+	return str;
+}
+
+std::string formatRadical(double n, double x) {
+	std::string formattedN = "";
+	std::string formattedX = "";
+
+	if (isInt(n)) {
+		std::string nString = std::to_string((int) n);
+
+		for (int i = 0; i < nString.length(); i++) {
+			int digit = (int) nString[i] - 48;
+			formattedN += superscript[digit];
+		}
+	} else {
+		std::string nString = formatDouble(n);
+
+		for (int i = 0; i < nString.length(); i++) {
+			try {
+				int digit = (int) nString[i] - 48;
+				formattedN += superscript[digit];
+			} catch (const std::exception) {
+				formattedN += "˙";
+			}
+		}
+	}
+
+	if (isInt(x)) {
+		formattedX = std::to_string((int) x);
+	} else {
+		formattedX = formatDouble(x);
+	}
+
+	return formattedN + "√" + formattedX;
+}
 
 int main() {
 	std::cout << "ⁿ√x\n";
-	int n = promptForInteger("n");
-	int x = promptForInteger("x");
+
+	double n = fetchInput("n");
+	double x = fetchInput("x");
+
+	std::cout << "Please enter an amount of iterations to perform: ";
+
+	int iterations;
+	std::cin >> iterations;
 
 	// Make sure that cout prints to the highest precision possible
 	std::cout.precision(std::numeric_limits<double>::max_digits10);
-	std::cout << nthRoot(n, x);
+
+	Result root = nthRoot(n, x, iterations);
+
+	std::cout << "\n" << formatRadical(n, x) << " = " << root.result << "\n";
+	std::cout << "Used " << root.iterationsUsed << " out of " << root.maxIterations << " iterations (:";
 }

languages/c++/code/squareForm.cc

@@ -44,17 +44,9 @@ std::string formatFraction(int numerator, int denominator) {
 
 // Format a double by cutting off as many trailing zeros as possible
 std::string formatDouble(double input) {
-    std::string output = std::to_string(abs(input));
-    int pointIndex = output.find_last_of('.');
-    int firstZeroIndex = output.find_last_not_of('0') + 1;
-
-    if (firstZeroIndex - 1 == pointIndex) {
-        output.erase(firstZeroIndex - 1, std::string::npos);
-    } else {
-        output.erase(firstZeroIndex, std::string::npos);
-    }
-
-    return output;
+    std::string str = std::to_string(input);
+	str.erase(str.find_last_not_of('0') + 1, std::string::npos);
+	return str;
 }
 
 // ax² + b^x + c^x -> a(x + p) + q

languages/python/calculators/_helpers/floatInput.py

@@ -2,7 +2,7 @@
 def floatInput(text):
 	while True:
 		try:
-			x = float(input(text + '\n'))
+			x = float(input(text))
 			return x
 		except ValueError:
 			print('You must input a float integer!\n')

languages/python/calculators/_helpers/intInput.py

@@ -2,7 +2,7 @@
 def intInput(text):
 	while True:
 		try:
-			x = int(input(text + '\n'))
+			x = int(input(text))
 			return x
 		except ValueError:
 			print('You must input an integer!\n')

languages/python/calculators/nth root.py

@@ -1,16 +1,63 @@
-def nthRoot(n: int, x: int):
-	lastX = None
-	y = 1 # initial guess
+from typing import Union
+from _helpers import floatInput, intInput
+from dataclasses import dataclass
 
-	while y != lastX:
-		# f(y) = yⁿ - x
-		# f'(y) = nyⁿ⁻¹
-		f = (y ** n) - x
-		fprime = n * (y ** (n - 1))
+@dataclass
+class Result:
+	result: Union[float, int]
+	maxIterations: int
+	iterationsUsed: int
 
-		lastX = y
-		y -= f / fprime
+superscript = [ '⁰', '¹', '²', '³', '⁴', '⁵', '⁶', '⁷', '⁸', '⁹' ]
 
-	return y
+def formatRadical(n: float, x: float):
+	formattedN, formattedX = '', ''
 
-print(nthRoot(5, 6 ** 6))
+	if int(n) == n:
+		nString = str(int(n))
+
+		for i in range(len(nString)):
+			digit = int(nString[i])
+			formattedN += superscript[digit]
+
+	else:
+		nString = str(n)
+
+		for i in range(len(nString)):
+			try:
+				digit = int(nString[i])
+				formattedN += superscript[digit]
+			except:
+				formattedN += '˙'
+
+	if int(x) == x:
+		formattedX = str(int(x))
+	else:
+		formattedX = str(x)
+	
+	return f"{formattedN}√{formattedX}"
+
+def nthRoot(n: float, x: float, maxIterations: int = 200) -> Result:
+	lastIteration, iteration, iterationsUsed = 0, 1, 0
+	
+	for _ in range(maxIterations):
+		if lastIteration == iteration:
+			break
+
+		iterationsUsed += 1
+		lastIteration = iteration
+		iteration = ((iteration * (n - 1)) + (x * (iteration ** (1 - n)))) / n
+
+	if int(iteration) == iteration:
+		iteration = int(iteration)
+
+	return Result(iteration, maxIterations, iterationsUsed)
+
+print('ⁿ√x')
+n = floatInput('Please input a value for n: ')
+x = floatInput('Please input a value for x: ')
+iterations = intInput('Please enter an amount of iterations to perform: ')
+root = nthRoot(n, x, iterations)
+
+print(f'\n{formatRadical(n, x)} = {root.result}')
+print(f'Used {root.iterationsUsed} out of {root.maxIterations} iterations (:')