题目链接
https://leetcode.cn/problems/multiply-strings/
解答过程
这个题目乍一看有点难度，我能想到的就是模拟竖式乘法，把字符串整数相乘拆解为字符串整数和数字相乘，然后进行字符串相加。在这个过程当中，要注意右侧补0等问题。
这个题目可以看作Problem415的升级版，Problem415是字符串整数相加，这里改为相乘。
简单看了下官方题解，官方题解给出的另外两种解法当然都更高级一些，尤其是卷积法。这些解法，如果没有相关经验或相关提示，并且用纸笔写写画画做推导，我觉得是不容易写出来的，有时间再研究下。
public String multiply(String num1, String num2) {
int len1 = num1.length();
int len2 = num2.length();
if (len1 == 0 || len2 == 0) {
throw new IllegalArgumentException();
}
String multiplicand, multiplier;
if (len1 < len2) {
multiplicand = num2;
multiplier = num1;
} else {
multiplicand = num1;
multiplier = num2;
}
if (multiplier.equals("0") || multiplicand.equals("0")) {
return "0";
}
String leftShift = "";
String result = "";
for (int i = multiplier.length()-1; i >= 0; i--) {
int ch = multiplier.charAt(i) - '0';
result = addTwoStrings(result, multiplyByDigit(multiplicand, ch) + leftShift);
leftShift += "0";
}
return result;
}
private String multiplyByDigit(String num, int digit) {
if (!(digit >= 1 && digit <= 9)) {
return "";
}
StringBuilder builder = new StringBuilder();
int carry = 0;
for (int i = num.length() - 1; i >= 0; i--) {
int ch = num.charAt(i) - '0';
int product = ch * digit + carry;
int remainder = product % 10;
carry = product / 10;
builder.append((char)(remainder + '0'));
}
if (carry != 0) {
builder.append((char)(carry + '0'));
}
return builder.reverse().toString();
}
private String addTwoStrings(String num1, String num2) {
StringBuilder builder = new StringBuilder();
String reversedNum1 = new StringBuilder(num1).reverse().toString();
String reversedNum2 = new StringBuilder(num2).reverse().toString();
int len1 = reversedNum1.length();
int len2 = reversedNum2.length();
int i, j;
int carry = 0;
for (i = 0, j = 0; i < len1 || j < len2; i++, j++) {
int ch1, ch2;
if (i < len1) {
ch1 = reversedNum1.charAt(i) - '0';
} else {
ch1 = 0;
}
if (j < len2) {
ch2 = reversedNum2.charAt(j) - '0';
} else {
ch2 = 0;
}
int sum = ch1 + ch2 + carry;
int remainder = sum % 10;
carry = sum / 10;
builder.append((char)(remainder + '0'));
}
if (carry != 0) {
builder.append((char)(carry + '0'));
}
return builder.reverse().toString();
}