8VC Venture Cup 2016 - Final Round (Div. 2 Edition) C. XOR Equation 数学

2024-06-04 17:24:56

C. XOR Equation

题目连接：

http://www.codeforces.com/contest/635/problem/C

Description

Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?

Input

The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and bitwise xor of the pair of positive integers, respectively.

Output

Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.

Sample Input

9 5

Sample Output

4

Hint

题意

给你两个数的和，以及两个数的异或结果，问你有多少个数对a,b满足要求

题解：

首先你要知道 a+b = a&b*2 + a^b,这个东西是递归加法的定义

所以你就知道了a&b和a^b，然后根据这两个东西对于数字的每一位进行讨论就好了

如果a^b = 1,那么a&b必须等于0，否则肯定不对嘛，这时候，ai=1 bi=0,ai=0 bi=1有两种选择

如果a^b = 0,那么a&b = ai = bi，只有一种选择

所以答案就是2的a^b中1的个数次方。当然，最后还得判一判s==x的情况，这种情况得把0的情况给剖去。

代码

#include<bits/stdc++.h>
using namespace std;long long s,x;
int flag = 0;
int main()
{cin>>s>>x;if(s==x)flag = 1;s-=x;if(s%2==1)return puts("0");s/=2;long long ans = 1;for(int i=0;i<60;i++){int p1 = (s>>i)&1;int p2 = (x>>i)&1;if(p2==1&&p1==1)return puts("0");if(p2==1)ans*=2;}if(flag)ans-=2;cout<<ans<<endl;
}

转载于:https://www.cnblogs.com/qscqesze/p/5230561.html

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