Codeforces Gym 100610 Problem E. Explicit Formula 水题

[b]Problem E. Explicit Formula[/b]

Time Limit: 1 Sec

Memory Limit: 256 MB

题目连接

http://codeforces.com/gym/100610

Description

Consider 10 Boolean variables x1, x2, x3, x4, x5, x6, x7, x8, x9, and x10. Consider all pairs and triplets of distinct variables among these ten. (There are 45 pairs and 120 triplets.) Count the number of pairs and triplets that contain at least one variable equal to 1. Set f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = 1 if this number is odd and f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = 0 if this number is even. Here’s an explicit formula that represents the function f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) correctly: f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = (x1 ∨ x2)⊕(x1 ∨ x3)⊕(x1 ∨ x4)⊕(x1 ∨ x5)⊕(x1 ∨ x6)⊕(x1 ∨ x7)⊕ (x1 ∨ x8) ⊕ (x1 ∨ x9) ⊕ (x1 ∨ x10) ⊕ (x2 ∨ x3) ⊕ (x2 ∨ x4) ⊕ (x2 ∨ x5) ⊕ (x2 ∨ x6) ⊕ (x2 ∨ x7) ⊕ (x2 ∨ x8) ⊕ (x2 ∨ x9)⊕(x2 ∨ x10)⊕(x3 ∨ x4)⊕(x3 ∨ x5)⊕(x3 ∨ x6)⊕(x3 ∨ x7)⊕(x3 ∨ x8)⊕(x3 ∨ x9)⊕(x3 ∨ x10)⊕ (x4 ∨ x5) ⊕ (x4 ∨ x6) ⊕ (x4 ∨ x7) ⊕ (x4 ∨ x8) ⊕ (x4 ∨ x9) ⊕ (x4 ∨ x10) ⊕ (x5 ∨ x6) ⊕ (x5 ∨ x7) ⊕ (x5 ∨ x8) ⊕ (x5 ∨ x9)⊕(x5 ∨ x10)⊕(x6 ∨ x7)⊕(x6 ∨ x8)⊕(x6 ∨ x9)⊕(x6 ∨ x10)⊕(x7 ∨ x8)⊕(x7 ∨ x9)⊕(x7 ∨ x10)⊕ (x8 ∨ x9) ⊕ (x8 ∨ x10) ⊕ (x9 ∨ x10) ⊕ (x1 ∨ x2 ∨ x3) ⊕ (x1 ∨ x2 ∨ x4) ⊕ (x1 ∨ x2 ∨ x5) ⊕ (x1 ∨ x2 ∨ x6) ⊕ (x1 ∨ x2 ∨ x7) ⊕ (x1 ∨ x2 ∨ x8) ⊕ (x1 ∨ x2 ∨ x9) ⊕ (x1 ∨ x2 ∨ x10) ⊕ (x1 ∨ x3 ∨ x4) ⊕ (x1 ∨ x3 ∨ x5) ⊕ (x1 ∨ x3 ∨ x6) ⊕ (x1 ∨ x3 ∨ x7) ⊕ (x1 ∨ x3 ∨ x8) ⊕ (x1 ∨ x3 ∨ x9) ⊕ (x1 ∨ x3 ∨ x10) ⊕ (x1 ∨ x4 ∨ x5) ⊕ (x1 ∨ x4 ∨ x6) ⊕ (x1 ∨ x4 ∨ x7) ⊕ (x1 ∨ x4 ∨ x8) ⊕ (x1 ∨ x4 ∨ x9) ⊕ (x1 ∨ x4 ∨ x10) ⊕ (x1 ∨ x5 ∨ x6) ⊕ (x1 ∨ x5 ∨ x7) ⊕ (x1 ∨ x5 ∨ x8) ⊕ (x1 ∨ x5 ∨ x9) ⊕ (x1 ∨ x5 ∨ x10) ⊕ (x1 ∨ x6 ∨ x7) ⊕ (x1 ∨ x6 ∨ x8) ⊕ (x1 ∨ x6 ∨ x9) ⊕ (x1 ∨ x6 ∨ x10) ⊕ (x1 ∨ x7 ∨ x8) ⊕ (x1 ∨ x7 ∨ x9) ⊕ (x1 ∨ x7 ∨ x10) ⊕ (x1 ∨ x8 ∨ x9) ⊕ (x1 ∨ x8 ∨ x10) ⊕ (x1 ∨ x9 ∨ x10) ⊕ (x2 ∨ x3 ∨ x4) ⊕ (x2 ∨ x3 ∨ x5) ⊕ (x2 ∨ x3 ∨ x6) ⊕ (x2 ∨ x3 ∨ x7) ⊕ (x2 ∨ x3 ∨ x8) ⊕ (x2 ∨ x3 ∨ x9) ⊕ (x2 ∨ x3 ∨ x10) ⊕ (x2 ∨ x4 ∨ x5) ⊕ (x2 ∨ x4 ∨ x6) ⊕ (x2 ∨ x4 ∨ x7) ⊕ (x2 ∨ x4 ∨ x8) ⊕ (x2 ∨ x4 ∨ x9) ⊕ (x2 ∨ x4 ∨ x10) ⊕ (x2 ∨ x5 ∨ x6) ⊕ (x2 ∨ x5 ∨ x7) ⊕ (x2 ∨ x5 ∨ x8) ⊕ (x2 ∨ x5 ∨ x9) ⊕ (x2 ∨ x5 ∨ x10) ⊕ (x2 ∨ x6 ∨ x7) ⊕ (x2 ∨ x6 ∨ x8) ⊕ (x2 ∨ x6 ∨ x9) ⊕ (x2 ∨ x6 ∨ x10) ⊕ (x2 ∨ x7 ∨ x8) ⊕ (x2 ∨ x7 ∨ x9) ⊕ (x2 ∨ x7 ∨ x10) ⊕ (x2 ∨ x8 ∨ x9) ⊕ (x2 ∨ x8 ∨ x10) ⊕ (x2 ∨ x9 ∨ x10) ⊕ (x3 ∨ x4 ∨ x5) ⊕ (x3 ∨ x4 ∨ x6) ⊕ (x3 ∨ x4 ∨ x7) ⊕ (x3 ∨ x4 ∨ x8) ⊕ (x3 ∨ x4 ∨ x9) ⊕ (x3 ∨ x4 ∨ x10) ⊕ (x3 ∨ x5 ∨ x6) ⊕ (x3 ∨ x5 ∨ x7) ⊕ (x3 ∨ x5 ∨ x8) ⊕ (x3 ∨ x5 ∨ x9) ⊕ (x3 ∨ x5 ∨ x10) ⊕ (x3 ∨ x6 ∨ x7) ⊕ (x3 ∨ x6 ∨ x8) ⊕ (x3 ∨ x6 ∨ x9) ⊕ (x3 ∨ x6 ∨ x10) ⊕ (x3 ∨ x7 ∨ x8) ⊕ (x3 ∨ x7 ∨ x9) ⊕ (x3 ∨ x7 ∨ x10) ⊕ (x3 ∨ x8 ∨ x9) ⊕ (x3 ∨ x8 ∨ x10) ⊕ (x3 ∨ x9 ∨ x10) ⊕ (x4 ∨ x5 ∨ x6) ⊕ (x4 ∨ x5 ∨ x7) ⊕ (x4 ∨ x5 ∨ x8) ⊕ (x4 ∨ x5 ∨ x9) ⊕ (x4 ∨ x5 ∨ x10) ⊕ (x4 ∨ x6 ∨ x7) ⊕ (x4 ∨ x6 ∨ x8) ⊕ (x4 ∨ x6 ∨ x9) ⊕ (x4 ∨ x6 ∨ x10) ⊕ (x4 ∨ x7 ∨ x8) ⊕ (x4 ∨ x7 ∨ x9) ⊕ (x4 ∨ x7 ∨ x10) ⊕ (x4 ∨ x8 ∨ x9) ⊕ (x4 ∨ x8 ∨ x10) ⊕ (x4 ∨ x9 ∨ x10) ⊕ (x5 ∨ x6 ∨ x7) ⊕ (x5 ∨ x6 ∨ x8) ⊕ (x5 ∨ x6 ∨ x9) ⊕ (x5 ∨ x6 ∨ x10) ⊕ (x5 ∨ x7 ∨ x8) ⊕ (x5 ∨ x7 ∨ x9) ⊕ (x5 ∨ x7 ∨ x10) ⊕ (x5 ∨ x8 ∨ x9) ⊕ (x5 ∨ x8 ∨ x10) ⊕ (x5 ∨ x9 ∨ x10) ⊕ (x6 ∨ x7 ∨ x8) ⊕ (x6 ∨ x7 ∨ x9) ⊕ (x6 ∨ x7 ∨ x10) ⊕ (x6 ∨ x8 ∨ x9) ⊕ (x6 ∨ x8 ∨ x10) ⊕ (x6 ∨ x9 ∨ x10) ⊕ (x7 ∨ x8 ∨ x9) ⊕ (x7 ∨ x8 ∨ x10) ⊕ (x7 ∨ x9 ∨ x10) ⊕ (x8 ∨ x9 ∨ x10) In this formula ∨ stands for logical or, and ⊕ stands for exclusive or (xor). Remember that in C++ and Java these two binary operators are denoted as “||” and “^”. Given the values of x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, calculate the value of f(x1, x2, . . . , x10).

Input

The input file contains 10 numbers x1, x2, x3, x4, x5, x6, x7, x8, x9, and x10. Each of them is either 0 or 1.

Output

Output a single value — f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10).

Sample Input

1 0 0 1 0 0 1 0 0 1

Sample Output

0

HINT

题意

就求题目给的那个式子的答案是多少

题解：


ctrl+f 把符号替换一下就好了……

代码：

//qscqesze
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <bitset>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define maxn 110000
#define mod 10007
#define eps 1e-9
#define pi 3.1415926
int Num;
//const int inf=0x7fffffff;   //§ß§é§à§é¨f§³
const ll Inf=0x3f3f3f3f3f3f3f3fll;
inline ll read()
{
ll x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
return x*f;
}
//*************************************************************************************

ll x1,x2,x3,x4,x5,x6,x7,x8,x9,x10;
int main()
{
freopen("explicit.in","r",stdin);
freopen("explicit.out","w",stdout);
cin>>x1>>x2>>x3>>x4>>x5>>x6>>x7>>x8>>x9>>x10;

cout<<((x1 || x2)^(x1 || x3)^(x1 || x4)^(x1 || x5)^(x1 || x6)^(x1 || x7)^
(x1 || x8) ^ (x1 || x9) ^ (x1 || x10) ^ (x2 || x3) ^ (x2 || x4) ^ (x2 || x5) ^ (x2 || x6) ^ (x2 || x7) ^ (x2 || x8) ^
(x2 || x9)^(x2 || x10)^(x3 || x4)^(x3 || x5)^(x3 || x6)^(x3 || x7)^(x3 || x8)^(x3 || x9)^(x3 || x10)^
(x4 || x5) ^(x4 || x6) ^ (x4 || x7) ^ (x4 || x8) ^ (x4 || x9) ^ (x4 || x10) ^ (x5 || x6) ^ (x5 || x7) ^ (x5 || x8) ^
(x5 || x9)^(x5 || x10)^(x6 || x7)^(x6 || x8)^(x6 || x9)^(x6 || x10)^(x7 || x8)^(x7 || x9)^(x7 || x10)^
(x8 || x9) ^ (x8 || x10) ^(x9 || x10) ^ (x1 || x2 || x3) ^ (x1 || x2 || x4) ^ (x1 || x2 || x5) ^ (x1 || x2 || x6) ^
(x1 || x2 || x7) ^ (x1 || x2 || x8) ^ (x1 || x2 || x9) ^ (x1 || x2 || x10) ^ (x1 || x3 || x4) ^ (x1 || x3 || x5) ^
(x1 || x3 || x6) ^ (x1 || x3 || x7) ^ (x1 || x3 || x8) ^ (x1 || x3 || x9) ^ (x1 || x3 || x10) ^ (x1 || x4 || x5) ^
(x1 || x4 || x6) ^ (x1 || x4 || x7) ^ (x1 || x4 || x8) ^ (x1 || x4 || x9) ^ (x1 || x4 || x10) ^ (x1 || x5 || x6) ^
(x1 || x5 || x7) ^ (x1 || x5 || x8) ^ (x1 || x5 || x9) ^ (x1 || x5 || x10) ^ (x1 || x6 || x7) ^ (x1 || x6 || x8) ^
(x1 || x6 || x9) ^ (x1 || x6 || x10) ^ (x1 || x7 || x8) ^ (x1 || x7 || x9) ^ (x1 || x7 || x10) ^ (x1 || x8 || x9) ^
(x1 || x8 || x10) ^ (x1 || x9 || x10) ^ (x2 || x3 || x4) ^ (x2 || x3 || x5) ^ (x2 || x3 || x6) ^ (x2 || x3 || x7) ^
(x2 || x3 || x8) ^ (x2 || x3 || x9) ^ (x2 || x3 || x10) ^ (x2 || x4 || x5) ^ (x2 || x4 || x6) ^ (x2 || x4 || x7) ^
(x2 || x4 || x8) ^ (x2 || x4 || x9) ^ (x2 || x4 || x10) ^ (x2 || x5 || x6) ^ (x2 || x5 || x7) ^ (x2 || x5 || x8) ^
(x2 || x5 || x9) ^ (x2 || x5 || x10) ^ (x2 || x6 || x7) ^ (x2 || x6 || x8) ^ (x2 || x6 || x9) ^ (x2 || x6 || x10) ^
(x2 || x7 || x8) ^ (x2 || x7 || x9) ^ (x2 || x7 || x10) ^ (x2 || x8 || x9) ^ (x2 || x8 || x10) ^ (x2 || x9 || x10) ^
(x3 || x4 || x5) ^ (x3 || x4 || x6) ^ (x3 || x4 || x7) ^ (x3 || x4 || x8) ^ (x3 || x4 || x9) ^ (x3 || x4 || x10) ^
(x3 || x5 || x6) ^ (x3 || x5 || x7) ^ (x3 || x5 || x8) ^ (x3 || x5 || x9) ^ (x3 || x5 || x10) ^ (x3 || x6 || x7) ^
(x3 || x6 || x8) ^ (x3 || x6 || x9) ^ (x3 || x6 || x10) ^ (x3 || x7 || x8) ^ (x3 || x7 || x9) ^ (x3 || x7 || x10) ^
(x3 || x8 || x9) ^ (x3 || x8 || x10) ^ (x3 || x9 || x10) ^ (x4 || x5 || x6) ^ (x4 || x5 || x7) ^ (x4 || x5 || x8) ^
(x4 || x5 || x9) ^ (x4 || x5 || x10) ^ (x4 || x6 || x7) ^ (x4 || x6 || x8) ^ (x4 || x6 || x9) ^ (x4 || x6 || x10) ^
(x4 || x7 || x8) ^ (x4 || x7 || x9) ^ (x4 || x7 || x10) ^ (x4 || x8 || x9) ^ (x4 || x8 || x10) ^ (x4 || x9 || x10) ^
(x5 || x6 || x7) ^ (x5 || x6 || x8) ^ (x5 || x6 || x9) ^ (x5 || x6 || x10) ^ (x5 || x7 || x8) ^ (x5 || x7 || x9) ^
(x5 || x7 || x10) ^ (x5 || x8 || x9) ^ (x5 || x8 || x10) ^ (x5 || x9 || x10) ^ (x6 || x7 || x8) ^ (x6 || x7 || x9) ^
(x6 || x7 || x10) ^ (x6 || x8 || x9) ^ (x6 || x8 || x10) ^ (x6 || x9 || x10) ^ (x7 || x8 || x9) ^ (x7 || x8 || x10) ^
(x7 || x9 || x10) ^ (x8 || x9 || x10)) <<endl;

}