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

public class Solution {
    public String multiply(String num1, String num2) {
        if (num1 == null || num2 == null) {
            return null;
        }
        
        int len1 = num1.length();
        int len2 = num2.length();
        
        int[] product = new int[len1 + len2];
        
        // 计算相应位置的product.
        for (int i = 0; i < len1; i++) {
            for (int j = 0; j < len2; j++) {
                // 注意，这里要使用+=以不断累加乘积
                product[i + j] += (num1.charAt(len1 - 1 - i) - '0') * (num2.charAt(len2 - 1 - j) - '0');
            }
        }
        
        StringBuilder ret = new StringBuilder();
        
        int carry = 0;
        // 计算进位
        for (int i = 0; i < len1 + len2; i++) {
            product[i] = product[i] + carry;
            int digit = product[i] % 10;
            carry = product[i] / 10;
            ret.insert(0, digit);
        }
        
        // 去掉前导0
        while (ret.length() > 1 && ret.charAt(0) == '0') {
            ret.deleteCharAt(0);
        }
        
        return ret.toString();
    }
}

2015.1.20 redo 

public String multiply(String num1, String num2) {
        // 18:24
        if (num1 == null || num2 == null) {
            return null;
        }
        
        int len1 = num1.length();
        int len2 = num2.length();
        int[] sum = new int[len1 + len2];
        
        // sum all of the mutiply result.
        for (int i = 0; i < len1; i++) {
            for (int j = 0; j < len2; j++) {
                sum[i + j] += (num1.charAt(len1 - 1 - i) - '0') * (num2.charAt(len2 - 1 - j) - '0');
            }
        }
        
        int carry = 0;
        for (int i = 0; i < len1 + len2; i++) {
            sum[i] = sum[i] + carry;
            
            // Bug1: this line should be processed first.
            carry = sum[i] / 10;
            sum[i] %= 10;
        }
        
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < len1 + len2; i++) {
            sb.insert(0, sum[i] + "");
        }
        
        // delete the leading "0"
        while (sb.charAt(0) == '0' && sb.length() != 1) {
            sb.deleteCharAt(0);
        }
        
        return sb.toString();
    }

请至主页群GITHUB:

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