LeetCode #415: Add Strings

最新推荐文章于 2019-10-14 12:10:17 发布

原创最新推荐文章于 2019-10-14 12:10:17 发布 · 339 阅读

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本文介绍了一种解决两个大数相加问题的算法实现，输入为两个非负整数字符串形式，输出也为字符串形式。该算法通过从后往前逐位相加的方式，实现了不使用内置大数库或直接转换为整数的解决方案。

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Problem Statement

(Source)Given two non-negative numbers num1 and num2 represented as string, return the sum of num1 and num2.

Note:

The length of both num1 and num2 is < 5100.
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.

Solution

第一遍从后往前扫描的时候先把中间结果（按位求和）存到较长的“数字”里，此时不考虑进位。第二遍从后往前扫描的时候处理进位。时间复杂度与空间复杂度均为： $O(max(len(num1), len(num2)))$ .

class Solution(object):
    def addStrings(self, num1, num2):
        """
        :type num1: str
        :type num2: str
        :rtype: str
        """
        x = map(int, list(num1))
        y = map(int, list(num2))
        if len(x) > len(y):
            x, y = y, x
        n1, n2 = len(x), len(y)
        i, j = n1 - 1, n2 - 1
        while i >= 0:
            y[j] += x[i]
            i -= 1
            j -= 1
        j = n2 - 1
        while j >= 1:
            if y[j] >= 10:
                y[j - 1] += 1
                y[j] -= 10
            j -= 1

        return ''.join(map(str, y))