From 6744fa059e285c45049e089f143b262331579280 Mon Sep 17 00:00:00 2001
From: newt <hi@newty.dev>
Date: Wed, 9 Oct 2024 18:02:43 +0100
Subject: [PATCH] C++ Square Form!

---
 languages/c++/CMakeLists.txt     |  1 +
 languages/c++/code/squareForm.cc | 92 ++++++++++++++++++++++++++++++++
 2 files changed, 93 insertions(+)
 create mode 100644 languages/c++/code/squareForm.cc

diff --git a/languages/c++/CMakeLists.txt b/languages/c++/CMakeLists.txt
index c33e248..2cd6726 100644
--- a/languages/c++/CMakeLists.txt
+++ b/languages/c++/CMakeLists.txt
@@ -11,3 +11,4 @@ add_executable(babylonian code/babylonian.cc)
 add_executable(karatsuba code/karatsuba.cc)
 add_executable(dice code/dice.cc)
 add_executable(binomialExpansion code/binomialExpansion.cc)
+add_executable(squareForm code/squareForm.cc)
diff --git a/languages/c++/code/squareForm.cc b/languages/c++/code/squareForm.cc
new file mode 100644
index 0000000..5df9893
--- /dev/null
+++ b/languages/c++/code/squareForm.cc
@@ -0,0 +1,92 @@
+#include <iostream>
+
+double power(double base, double exponent) {
+    double out = base;
+
+    for (int i = 1; i < exponent; i++) {
+        out *= base;
+    }
+
+    return out;
+}
+
+// Euclid algorithm
+int greatestCommonDivisor(int a, int b) {
+    int currentA = a;
+    int currentB = b;
+    bool divisorFound = false;
+
+    while (currentA != currentB) {
+        if (currentA > currentB) {
+            currentA -= currentB;
+        }
+
+        if (currentB > currentA) {
+            currentB -= currentA;
+        }
+    }
+
+    return currentA;
+}
+
+// Simplify and then format a fraction
+std::string formatFraction(int numerator, int denominator) {
+    int gcd = greatestCommonDivisor(numerator, denominator);
+    int n = numerator / gcd;
+    int d = denominator / gcd;
+
+    if (d == 1) {
+        return std::to_string(n);
+    } else {
+        // Fraction unicode
+        return std::to_string(n) + "\u2044" + std::to_string(d);
+    }
+}
+
+// Format a double by cutting off as many trailing zeros as possible
+std::string formatDouble(double input) {
+    std::string output = std::to_string(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;
+}
+
+// ax² + b^x + c^x -> a(x + p) + q
+std::string completeTheSquare(double a, double b, double c) {
+    // Calculate relevant values
+    double p = b / (2 * a);
+    double q = c - (power(b, 2) / 4 * a);
+    std::string output = "(x";
+
+    // Add the p value
+    if (p != 0) {
+        std::string sign = p > 0 ? "+" : "-";
+        output += " " + sign + " " + formatFraction(b, 2 * a) + ")²";
+    } else {
+        output += ")²";
+    }
+
+    // Add the q value
+    if (q != 0) {
+        std::string sign = q > 0 ? "+" : "-";
+        output += " " + sign + " " + formatDouble(q);
+    }
+
+    // Add the coefficient if relevant
+    if (a > 1) {
+        output.insert(0, formatDouble(a));
+    }
+
+    return output;
+}
+
+int main() {
+    std::cout << completeTheSquare(1, 2, 5);
+}
\ No newline at end of file