[LeetCode43] 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.

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();    }