Multiply Strings

Given two numbers represented as strings, return multiplication of the numbers as a string.

Note:

• The numbers can be arbitrarily large and are non-negative.
• Converting the input string to integer is NOT allowed.
• You should NOT use internal library such as BigInteger.

分析：

把结果放在一个数组里，用offset来移动起始位置。

public class Solution {
    public String multiply(String num1, String num2) {
        if (num1 == null || num1.length() == 0 || num2 == null || num2.length() == 0) return "";
        int[] result = new int[num1.length() + num2.length()];  // maximum length
        
        int offset = 0;
        for (int i = num1.length() - 1; i >= 0; i--) {
            int number1 = num1.charAt(i) - '0';
            int carry = 0;
            for (int j = num2.length() - 1; j >= 0; j--) {
                int number2 = num2.charAt(j) - '0';
                int value = number1 * number2 + result[(result.length - 1) - offset + j - (num2.length() - 1)] + carry;  
                carry = value / 10;  
                value = value % 10;  
                result[(result.length - 1) - offset + j - (num2.length() - 1)] = value;                  
            }  
            result[(result.length - 1) - offset - 1 - (num2.length() - 1)] = carry;  
            offset++;  
        }  
        String str = "";  
        boolean isBeginningZero = true;  
        for (int i = 0; i < result.length; i++) {  
            if (!(result[i] == 0 && isBeginningZero == true)) {
                isBeginningZero = false;  
                str += result[i];  
            }  
        }  
        return str == "" ? "0" : str;  
    }
}

 方法二：

https://leetcode.com/problems/multiply-strings/discuss/17605/Easiest-JAVA-Solution-with-Graph-Explanation

Start from right to left, perform multiplication on every pair of digits, and add them together. Let's draw the process! From the following draft, we can immediately conclude:

 `num1[i] * num2[j]` will be placed at indices `[i + j`, `i + j + 1]` 

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public class Solution {
    public String multiply(String num1, String num2) {
        int m = num1.length(), n = num2.length();
        int[] pos = new int[m + n];

        for (int i = m - 1; i >= 0; i--) {
            for (int j = n - 1; j >= 0; j--) {
                int mul = (num1.charAt(i) - '0') * (num2.charAt(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();
        for (int p : pos) {
            if (!(sb.length() == 0 && p == 0)) {
                sb.append(p);
            }
        }
        return sb.length() == 0 ? "0" : sb.toString();
    }
}