LeetCode: Multiply Strings 解题报告

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.

SOLUTION 1:

参考自http://blog.csdn.net/fightforyourdream/article/details/17370495

相当优雅的算法，主页君稍微改进，把翻转String这一步拿掉了。比起一般的做法，这个算法很容易就BUG FREE.

思路：
1 建立数组，双层循环遍历两个string，把单位的乘积累加到数组相应的位置
2 处理进位并输出
3 注意前导零的corner case

 1 public class Solution {

 2     public String multiply(String num1, String num2) {

 3         if (num1 == null || num2 == null) {

 4             return null;

 5         }

 6         

 7         int len1 = num1.length();

 8         int len2 = num2.length();

 9         

10         int[] product = new int[len1 + len2];

11         

12         // 计算相应位置的product.

13         for (int i = 0; i < len1; i++) {

14             for (int j = 0; j < len2; j++) {

15                 // 注意，这里要使用+=以不断累加乘积

16                 product[i + j] += (num1.charAt(len1 - 1 - i) - '0') * (num2.charAt(len2 - 1 - j) - '0');

17             }

18         }

19         

20         StringBuilder ret = new StringBuilder();

21         

22         int carry = 0;

23         // 计算进位

24         for (int i = 0; i < len1 + len2; i++) {

25             product[i] = product[i] + carry;

26             int digit = product[i] % 10;

27             carry = product[i] / 10;

28             ret.insert(0, digit);

29         }

30         

31         // 去掉前导0

32         while (ret.length() > 1 && ret.charAt(0) == '0') {

33             ret.deleteCharAt(0);

34         }

35         

36         return ret.toString();

37     }

38 }

View Code

2015.1.20 redo 

 1 public String multiply(String num1, String num2) {

 2         // 18:24

 3         if (num1 == null || num2 == null) {

 4             return null;

 5         }

 6         

 7         int len1 = num1.length();

 8         int len2 = num2.length();

 9         int[] sum = new int[len1 + len2];

10         

11         // sum all of the mutiply result.

12         for (int i = 0; i < len1; i++) {

13             for (int j = 0; j < len2; j++) {

14                 sum[i + j] += (num1.charAt(len1 - 1 - i) - '0') * (num2.charAt(len2 - 1 - j) - '0');

15             }

16         }

17         

18         int carry = 0;

19         for (int i = 0; i < len1 + len2; i++) {

20             sum[i] = sum[i] + carry;

21             

22             // Bug1: this line should be processed first.

23             carry = sum[i] / 10;

24             sum[i] %= 10;

25         }

26         

27         StringBuilder sb = new StringBuilder();

28         for (int i = 0; i < len1 + len2; i++) {

29             sb.insert(0, sum[i] + "");

30         }

31         

32         // delete the leading "0"

33         while (sb.charAt(0) == '0' && sb.length() != 1) {

34             sb.deleteCharAt(0);

35         }

36         

37         return sb.toString();

38     }

View Code

 

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https://github.com/yuzhangcmu/LeetCode_algorithm/blob/master/string/Multiply.java