Math-43-Multiply Strings

Description:

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

Note:

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

Best Solution:

public class Solution {
public String multiply(String num1, String num2) {
int n1 = num1.length(), n2 = num2.length();
int[] products = new int[n1 + n2];
for (int i = n1 - 1; i >= 0; i--) {
for (int j = n2 - 1; j >= 0; j--) {
int d1 = num1.charAt(i) - '0';
int d2 = num2.charAt(j) - '0';
products[i + j + 1] += d1 * d2;
}
}
int carry = 0;
for (int i = products.length - 1; i >= 0; i--) {
int tmp = (products[i] + carry) % 10;
carry = (products[i] + carry) / 10;
products[i] = tmp;
}
StringBuilder sb = new StringBuilder();
for (int num : products) sb.append(num);
while (sb.length() != 0 && sb.charAt(0) == '0') sb.deleteCharAt(0);
return sb.length() == 0 ? "0" : sb.toString();
}
}

算法的形象表示如下:

123*12为

[1,2+2,3+4,6,0],得到该数组后我们只需从后往前遍历，对大于等于10的数%10，往前累加即可得到结果