feat: implement multiplication of strings using Karatsuba algorithm

43_multiply_strings/Cargo.lock

@@ -0,0 +1,7 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
+[[package]]
+name = "multiply_strings"
+version = "0.1.0"

43_multiply_strings/Cargo.toml

@@ -0,0 +1,6 @@
+[package]
+name = "multiply_strings"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]

43_multiply_strings/src/main.rs

@@ -0,0 +1,90 @@
+use std::cmp;
+
+fn main() {
+    let x = "000".to_string();
+    let y = "0".to_string();
+    println!("{}", Solution::plus(x, y));
+}
+
+struct Solution;
+
+impl Solution {
+    pub fn multiply(x: String, y: String) -> String {
+        Solution::karatsuba(&x, &y)
+    }
+
+    fn karatsuba(x: &str, y: &str) -> String {
+        if x.len() <= 9 && y.len() <= 9 {
+            return (x.parse::<i64>().unwrap() * y.parse::<i64>().unwrap()).to_string();
+        }
+
+        let len = cmp::max(x.len(), y.len());
+        let len_half = len / 2;
+
+        let mut x_string = x.to_string();
+        if x.len() < len {
+            let zeros = "0".repeat(len - x.len());
+            x_string = zeros + &x;
+        }
+        let mut y_string = y.to_string();
+        if y.len() < len {
+            let zeros = "0".repeat(len - y.len());
+            y_string = zeros + &y;
+        }
+
+        let x1 = &x_string[..len_half];
+        let x2 = &x_string[len_half..];
+        let y1 = &y_string[..len_half];
+        let y2 = &y_string[len_half..];
+
+        let a = Solution::karatsuba(x1, y1);
+        let b = Solution::karatsuba(x2, y2);
+        let c = Solution::karatsuba(x1, y2);
+        let d = Solution::karatsuba(x2, y1);
+
+        let result = Solution::plus(a + &"0".repeat((len - len_half) * 2), b);
+        let result = Solution::plus(result, c + &"0".repeat(len - len_half));
+        let result = Solution::plus(result, d + &"0".repeat(len - len_half));
+
+        result
+    }
+
+    fn plus(x: String, y: String) -> String {
+        let len = cmp::max(x.len(), y.len());
+
+        let x_chars_rev = x.chars().rev().collect::<Vec<char>>();
+        let y_chars_rev = y.chars().rev().collect::<Vec<char>>();
+
+        let mut carry = 0;
+        let mut result = String::new();
+
+        for i in 0..len {
+            let xn = if i < x.len() { x_chars_rev[i] } else { '0' } as i32 - 48;
+            let yn = if i < y.len() { y_chars_rev[i] } else { '0' } as i32 - 48;
+
+            let sum = xn + yn + carry;
+            carry = sum / 10;
+            result.push_str(&(sum % 10).to_string());
+        }
+
+        if carry > 0 {
+            result.push_str(&carry.to_string());
+        }
+
+        let mut start_index = -1;
+        for (i, c) in result.chars().rev().enumerate() {
+            if c != '0' {
+                start_index = i as i32;
+                break;
+            }
+        }
+
+        if start_index < 0 {
+            "0".to_string()
+        } else {
+            result.chars().rev().collect::<Vec<char>>()[start_index as usize..]
+                .iter()
+                .collect()
+        }
+    }
+}