Sum Equals Xor

最新推荐文章于 2022-10-27 17:29:32 发布

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最新推荐文章于 2022-10-27 17:29:32 发布 · 288 阅读

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给定一个正整数L的二进制表示，求所有非负整数对(a, b)，使得a + b ≤ L且a + b = a ^ b，输出满足条件的数对数量模10^9 + 7。文章包含样例输入输出及解题思路。" 123683379,13011111,Java基础知识精讲：标识符与数据类型,"['JavaSE', '程序设计', '数据类型', '类型转换', '基础概念']

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Sum Equals Xor

题目描述

You are given a positive integer L in base two. How many pairs of non-negative integers (a,b) satisfy the following conditions?
·a+b≤L
·a+b=a XOR b
Since there can be extremely many such pairs, print the count modulo 109+7.
→What is XOR?
The XOR of integers A and B, A XOR B, is defined as follows:
·When A XOR B is written in base two, the digit in the 2k’s place (k≥0) is 1 if either A or B, but not both, has 1 in the 2k’s place, and 0 otherwise.
For example, 3 XOR 5=6. (In base two: 011 XOR 101=110.)

Constraints
·L is given in base two, without leading zeros.
·1≤L<2100001

输入
Input is given from Standard Input in the following format:

输出
Print the number of pairs (a,b) that satisfy the conditions, modulo 109+7.

样例输入
【样例1】
10
【样例2】
1111111111111111111
样例输出
【样例1】
5
【样例2】
162261460

思路：见代码注释