[LeetCode43] Multiply Strings

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本文详细阐述了如何通过字符串表示的数字进行乘法运算，并提供了C++和Java两种语言的实现代码，包括从末尾开始逐位相乘、考虑进位、以及最终将结果转换回字符串的过程。

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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.

Analysis:

Straight forward idea. Just like the way we multiply numbers. Don't forget considering the carry and be careful. e.g.

123*456,
what we usually do is:
123
* 456
-----------
738
615
+492
-----------
56088
thus, 123*456 = 56088.
In the same way, the algorithm is:

from end to start position, use a new array to store temproary digit.
A*B
(1)For each element B[i]
Compute tmp = B[i]*A
Add tmp to the previous result, note the start position. res = res"+"tmp
(2)Return result.

To be specific,
(1) char2int, int(char-'0');
(2) int2char, char(int+'0')
(3) Don't forget the carry in each add or multiply operation.
(4) Don't forget the carry after last operation. e.g. 82+33 = 115.
(5) Be careful with the string order and the number order.

c++

string multiply(string num1, string num2) {
       if(num1.size() ==0 || num2.size() == 0) return "0";
        string res(num1.size()+num2.size(),'0');
        std::reverse(num1.begin(),num1.end());
        std::reverse(num2.begin(),num2.end());
    for(int i=0;i<num1.size();i++){
        int digit1 = num1[i]-'0';
        int carry = 0;
        for(int j=0;j<num2.size();j++){
            int digit2 = num2[j]-'0';
            int exist = res[i+j]-'0';
            res[i+j] = (digit1*digit2+carry+exist)%10 + '0';
            carry = (digit1*digit2+carry+exist)/10;
        }
        if(carry>0){
            res[i+num2.size()] = carry +'0';
        }
    }
    std::reverse(res.begin(),res.end());
    int start = 0;
    while(res[start]=='0' && start<res.size()){
        start++;
    }
    if(start == res.size()) {return "0";}
    return res.substr(start,res.size()-start);
}

Java

public String multiply(String num1, String num2) {
        int len1 = num1.length();
		int len2 = num2.length();
        if(len1 == 0 || len2==0) return "0";
        int result[] = new int[len1+len2];
        for(int i=0;i<len1;i++){
        	int carry = 0;
        	int digit1 = num1.charAt(len1-1-i)-'0';
        	for(int j=0;j<len2;j++){
        		int digit2 = num2.charAt(len2-1-j)-'0';
        		result[i+j] += digit1*digit2+carry;
        		carry = result[i+j]/10;
        		result[i+j] %=10;
        	}
        	result[i+len2]+=carry;
        }
        
        int i = len1+len2-1;
        while(i>0 && result[i]==0) i--;
        StringBuilder temp = new StringBuilder("");
        while(i>=0)
        	temp.append((char)(result[i--]+'0'));
        return temp.toString();
    }