43. Multiply Strings

题目

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.

解析

思路：按照乘法运算法则利用vector从右向左计算

代码

class Solution {public:    string multiply(string num1, string num2) {        unsigned int l1=num1.size(),l2=num2.size();        if (l1==0||l2==0) return "0";        vector<int> v(l1+l2,0);        for(unsigned int i=0;i<l1;i++){            int n1=(int)(num1[l1-i-1]-'0');            int carry=0;            for(unsigned int j=0;j<l2;j++){                int n2=(int)(num2[l2-j-1]-'0');                int sum=n1*n2+v[i+j]+carry;                carry=sum/10;                v[i+j]=sum%10;            }            if(carry>0)                v[l2+i]=carry;        }        int start=l1+l2-1;        while(v[start]==0&&start>=0) start--;        if(start==-1) return "0";        string s="";        for(int i=start;i>=0;i--)            s+=(char)(v[i]+'0');        return s;    }};