# 043-multiply-strings

## Question

https://leetcode.com/problems/multiply-strings/description/

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2.

Note:

1. The length of both num1 and num2 is < 110.
2. Both num1 and num2 contains only digits 0-9.
3. Both num1 and num2 does not contain any leading zero.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

Example:

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## Thought Process

1. Multiply from Back
1. Start the multiplication from the back, each time we will have at most 2 digits
2. We need

## Solution

``````class Solution {
public String multiply(String num1, String num2) {
if (num1.equals("0") || num2.equals("0")) return "0";
int m = num1.length(), n = num2.length();
int[] pos = new int[m + n];
char[] n1 = num1.toCharArray(), n2 = num2.toCharArray();
for (int i = m - 1; i >= 0; i--){
for (int j = n - 1; j >= 0; j--){
int mul = (n1[i] - '0') * (n2[j] - '0');
int p1 = i + j, p2 = i + j + 1;
int sum = mul + pos[p2];
pos[p1] += sum /10;
pos[p2] = sum % 10;
}
}
StringBuilder sb = new StringBuilder();
int i = 0;
while (pos[i] == 0) i++;
while (i < pos.length) sb.append(pos[i++]);
return sb.toString();
}
}
``````