[leetcode] 43. Multiply Strings

Description

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

Example 1:

Input: num1 = "2", num2 = "3"
Output: "6"

Example 2:

Input: num1 = "123", num2 = "456"
Output: "56088"

Note:

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

分析

题目的意思是：求两个数字字符串的乘积。

• 把错位相加后的结果保存到一个一维数组中，然后分别在每位上算进位，最后每个数字都变成一位，然后要做的是去除掉首位0，最后把每位上的数字按顺序保存到结果中即可

代码

class Solution {
public:
    string multiply(string num1, string num2) {
        string res="";
        int m=num1.size();
        int n=num2.size();
        vector<int> v(m+n,0);
        int k=m+n-2;
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                v[k-i-j]+=(num1[i]-'0')*(num2[j]-'0');
            }
        }
        int carry=0;
        for(int i=0;i<m+n;i++){
            v[i]+=carry;
            carry=v[i]/10;
            v[i]=v[i]%10;
        }
        int i=m+n-1;
        while(v[i]==0){
            i--;
        }
        if(i<0){
            return "0";
        }
        while(i>=0) res.push_back(v[i--]+'0');
        return res;
    }
};

参考文献

​​[编程题]multiply-strings​​​​[LeetCode] Multiply Strings 字符串相乘​​