Multiply Large Numbers represented as Strings
Given two positive numbers as strings. The numbers may be very large (may not fit in long long int), the task is to find product of these two numbers.
Input : num1 = 4154 num2 = 51454 Output : 213739916 Input : num1 = 654154154151454545415415454 num2 = 63516561563156316545145146514654 Output : 41549622603955309777243716069997997007620439937711509062916
The idea is based on school mathematics.
We start from last digit of second number multiply it with first number. Then we multiply second digit of second number with first number, and so on. We add all these multiplications. While adding, we put i-th multiplication shifted.
The approach used in below solution is to keep only one array for result. We traverse all digits first and second numbers in a loop and add the result at appropriate position.
The above code is adapted from the code provided by Gaurav.
Time Complexity: O(m*n), where m and n are length of two number that need to be multiplied.
Related Article :
Karatsuba algorithm for fast multiplication
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