Added the algorithms that I know of so far

Author: cooperblacks

Arithmetic/euclid-gcd-extended.c

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+// Algorithm: Extended Euclidean Algorithm
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(log(min(a, b)))
+
+#include <stdio.h>
+
+int extendedGCD(int a, int b, int* x, int* y) {
+    if (b == 0) {
+        *x = 1;
+        *y = 0;
+        return a;
+    }
+    int x1, y1;
+    int gcd = extendedGCD(b, a % b, &x1, &y1);
+    *x = y1;
+    *y = x1 - (a / b) * y1;
+    return gcd;
+}
+
+// Example:
+// int main() {
+//     int x, y;
+//     int g = extendedGCD(30, 20, &x, &y);
+//     printf("GCD: %d, x: %d, y: %d\n", g, x, y); // Output: GCD: 10, x: 1, y: -1
+//     return 0;
+// }

Arithmetic/euclid-gcd-extended.java

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+// Algorithm: Extended Euclidean Algorithm
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(log(min(a, b)))
+
+public class ExtendedGCD {
+    static class Result {
+        int gcd, x, y;
+        Result(int g, int x, int y) {
+            this.gcd = g; this.x = x; this.y = y;
+        }
+    }
+
+    static Result extendedGCD(int a, int b) {
+        if (b == 0)
+            return new Result(a, 1, 0);
+        Result r = extendedGCD(b, a % b);
+        int x = r.y;
+        int y = r.x - (a / b) * r.y;
+        return new Result(r.gcd, x, y);
+    }
+
+    public static void main(String[] args) {
+        Result r = extendedGCD(30, 20);
+        System.out.println("GCD: " + r.gcd + ", x: " + r.x + ", y: " + r.y);
+    }
+}

Arithmetic/euclid-gcd-extended.js

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+// Algorithm: Extended Euclidean Algorithm
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(log(min(a, b)))
+
+function extendedGCD(a, b) {
+    if (b === 0) return { gcd: a, x: 1, y: 0 };
+
+    const result = extendedGCD(b, a % b);
+    const x = result.y;
+    const y = result.x - Math.floor(a / b) * result.y;
+
+    return { gcd: result.gcd, x, y };
+}
+
+// Example:
+// const res = extendedGCD(30, 20);
+// console.log(res); // { gcd: 10, x: 1, y: -1 }

Arithmetic/euclid-gcd-extended.py

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+# Algorithm: Extended Euclidean Algorithm
+# Type: Number Theory
+# Time: O(log(min(a, b)))
+# Space: O(log(min(a, b)))
+
+def extended_gcd(a, b):
+    if b == 0:
+        return (a, 1, 0)
+    gcd, x1, y1 = extended_gcd(b, a % b)
+    x = y1
+    y = x1 - (a // b) * y1
+    return (gcd, x, y)
+
+# Example: print(extended_gcd(30, 20))  # Output: (10, 1, -1)

Arithmetic/euclid-gcd-extended.txt

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+// Algorithm: Extended Euclidean Algorithm
+// Type: Number Theory
+// Time Complexity: O(log(min(a, b)))
+// Space Complexity: O(1) iterative, O(log(min(a, b))) recursive
+
+function extendedGCD(a, b):
+    if b == 0:
+        return (a, 1, 0)
+    gcd, x1, y1 = extendedGCD(b, a % b)
+    x = y1
+    y = x1 - (a // b) * y1
+    return (gcd, x, y)
+

Arithmetic/euclid-gcd.c

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+// Algorithm: Euclidean Algorithm for GCD
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(1)
+
+#include <stdio.h>
+
+int gcd(int a, int b) {
+    while (b != 0) {
+        int temp = b;
+        b = a % b;
+        a = temp;
+    }
+    return a;
+}
+
+int main() {
+    printf("%d\n", gcd(48, 18)); // Output: 6
+    return 0;
+}

Arithmetic/euclid-gcd.java

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+// Algorithm: Euclidean Algorithm for GCD
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(1)
+
+public class GCD {
+    static int gcd(int a, int b) {
+        while (b != 0) {
+            int temp = b;
+            b = a % b;
+            a = temp;
+        }
+        return a;
+    }
+
+    public static void main(String[] args) {
+        System.out.println(gcd(48, 18)); // Output: 6
+    }
+}

Arithmetic/euclid-gcd.js

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+// Algorithm: Euclidean Algorithm for GCD
+// Type: Number Theory
+// Time: O(log(min(a, b)))
+// Space: O(1)
+
+function gcd(a, b) {
+    while (b !== 0) {
+        [a, b] = [b, a % b];
+    }
+    return a;
+}
+
+// Example: console.log(gcd(48, 18)); // Output: 6

Arithmetic/euclid-gcd.py

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+# Algorithm: Euclidean Algorithm for GCD
+# Type: Number Theory
+# Time: O(log(min(a, b)))
+# Space: O(1)
+
+def gcd(a, b):
+    while b != 0:
+        a, b = b, a % b
+    return a
+
+# Example: print(gcd(48, 18))  # Output: 6

Arithmetic/euclid-gcd.txt

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+// Algorithm: Euclidean Algorithm for GCD
+// Type: Number Theory, Recursive/Iterative
+// Time Complexity: O(log(min(a, b)))
+// Space Complexity: O(1) iterative, O(log(min(a, b))) recursive
+
+function gcd(a, b):
+    while b ≠ 0:
+        temp = b
+        b = a mod b
+        a = temp
+    return a