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Codeforces Round #804 (Div. 2) Editorial(A-B)
2022-07-06 05:14:00 【. Ashy.】
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C I really don't understand the solution of the question , Write first A,B
A — The Third Three Number Problem
The question
Give a number n , Find any three numbers a b c Satisfy
( a ⊕ b ) + ( b ⊕ c ) + ( a ⊕ c ) = n (a⊕b)+(b⊕c)+(a⊕c)=n (a⊕b)+(b⊕c)+(a⊕c)=n
Ideas
First of all, according to the
a + b = a ⊕ b + 2 ∗ ( a & b ) a+b=a⊕b+2*(a\&b) a+b=a⊕b+2∗(a&b)
This formula shows that
a ⊕ b a⊕b a⊕b The parity of is with a + b a+b a+b same
so ( a ⊕ b ) + ( b ⊕ c ) + ( a ⊕ c ) (a⊕b)+(b⊕c)+(a⊕c) (a⊕b)+(b⊕c)+(a⊕c) The parity of is with ( a + b ) + ( b + c ) + ( a + c ) (a+b)+(b+c)+(a+c) (a+b)+(b+c)+(a+c) same , Is with the 2 ∗ ( a + b + c ) 2*(a+b+c) 2∗(a+b+c) The parity of is the same , so It can be proved that n It must be an even number , Therefore, there is no solution in the case of odd numbers ;
And then the structure , According to the nature a ⊕ 0 = a a⊕0=a a⊕0=a We Can construct 0 0 n 2 n\over2 2n Three numbers
#include<bits/stdc++.h>
using namespace std;
int n,t;
int main()
{
cin>>t;
while(t--)
{
cin>>n;
if(n%2!=0) puts("-1");
else cout<<"0 0 "<<n/2<<endl;
}
}
B — Almost Ternary Matrix
The question
Matrix construction , There are exactly two different blocks that make each block connected
Ideas :
hold n And m Get a little bigger and draw a picture to see the law
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int a,b;
int t;
int s[51][51];
int main()
{
cin>>t;
while(t--)
{
cin>>a>>b;
s[1][1]=1;
s[1][2]=0;
s[2][1]=0;
s[2][2]=1;// First construct 2*2 The smallest unit block of
for(int i=3;i<=b;i++)
if(i%2==0) s[1][i]=s[1][i-3];
else s[1][i]=s[1][i-1];
for(int i=3;i<=b;i++)
if(i%2==0) s[2][i]=s[2][i-3];
else s[2][i]=s[2][i-1];// Construct the first two lines
for(int i=3;i<=a;i++)
{
if(i%2==0)
{
for(int j=1;j<=b;j++)
{
s[i][j]=s[i-3][j];
}
}
else
{
for(int j=1;j<=b;j++)
{
s[i][j]=s[i-1][j];
}
}
}// Construct the following line
for(int i=1;i<=a;i++)
{
for(int j=1;j<=b;j++)
{
cout<<s[i][j]<<" ";
}
puts("");
}
}// Output
return 0;
}
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