43. Multiply Strings

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.

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来源： https://leetcode.com/problems/multiply-strings/

分析

与大数相加类似下面的算法是按照正常的算数过程，计算出num1和num2每个位数字的乘积，然后再相加28ms进一步改进因为add函数每一次都要reverse两个string，最后算数结束还需要再次reverse结果，导致效率很低
其实可以将乘法和最后相加的过程整合在一起。这里用到一个条件，两个数（一个n位，一个m位）相乘，则乘积最大长度，不超过n+m位这样的话，建立一个n+m位的string，作为存储乘积结果的字符串result，每次每个数字相乘后，就和result相加
num1: "11223" n = 5num2: "123456" m = 6index: 0 1 2 3 4 5 6 7 8 9 10result: 0 0 0 0 0 0 0 0 0 0 0 当 i = 2; j = 3时，指向的result位置是i+j+1 *null