Added Karatsuba Algo in Dart (#2616)

* Sqashing 6 commits

* deleting accidentally added file

* deleting accidentally added file

* deleting accidentally added file

* deleting accidentally added file

* deleting accidentally added file

* deleting accidentally added file

* Karatsuba_Algorithm.dart added (accidently deleted while squashing commits)

Karatsuba_Algorithm/Karatsuba_Algorithm.dart

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+import 'dart:io';
+import 'dart:math';
+
+// function to find minimun of two integers
+int minof(a, b){
+    if(a < b) 
+        return a;
+    else return b;
+}
+
+int karatSuba(num1, num2){
+
+    // for single digit number multiply directly
+    if (num1 < 10 || num2 < 10) {
+        return num1 * num2;
+    }
+
+    String num1Str = num1.toString();
+    String num2Str = num2.toString();
+    int n = minof(num1Str.length, num2Str.length);
+    int half = (n / 2).round();
+
+    // divide num1 into two halves
+    int num1_H = int.parse(num1Str.substring(0, num1Str.length - half));
+    int num1_L = int.parse(num1Str.substring(num1Str.length - half, num1Str.length));
+
+    // divide num2 into two halves
+    int num2_H = int.parse(num2Str.substring(0, num2Str.length - half));
+    int num2_L = int.parse(num2Str.substring(num2Str.length - half, num2Str.length));
+
+    // using the KaratSuba Definition
+    int s1 = karatSuba(num1_L, num2_L);
+    int s2 = karatSuba(num1_L + num1_H, num2_L + num2_H);
+    int s3 = karatSuba(num1_H, num2_H);
+    int s4 = s2 - s3 - s1;
+
+    // karatsuba formula for finding product
+    int result = s3 * pow(10, 2 * half) + s4 * pow(10, half) + s1;
+
+    return result;
+}
+
+void main(){
+    String a, b;
+    a = stdin.readLineSync(); 
+    b = stdin.readLineSync();
+    print(karatSuba(int.parse(a), int.parse(b)));
+}
+
+/*
+Sample input:
+12345
+6789
+
+Sample Output:
+83810205
+*/