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Codeforces Round #804 (Div. 2)
2022-07-07 23:18:00 【AC自动寄】
目录
A. The Third Three Number Problem
官方题解
点击跳转:官方题解
A. The Third Three Number Problem
A. The Third Three Number Problem
思路:
首先,⊕(异或) 又称不进位加法,所以:对于 (a⊕b)+(b⊕c)+(a⊕c) 的最后的一位而言
(a⊕b)+(b⊕c)+(a⊕c) = a + b + b + c + a + c = 2*(a + b + c) 必为偶数
故:当 n 为奇数时,无解
当 n 为偶数时:
知:a⊕0 = a ,所以,令 a = 0, b = n / 2, c = n / 2;
此时:a⊕b = n/2,a⊕c = n/2,b⊕c = 0,结果为 n 成立
代码如下:
#include <bits/stdc++.h>
#define fast ios::sync_with_stdio(false),cin.tie(0), cout.tie(0)
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int N = 2e5 + 10, mod = 1e9 + 7;
int T;
int lowbit(int x)
{
return x & -x;
}
void solve()
{
int n, c;
scanf("%d", &n);
if(n%2)
{
puts("-1");
return ;
}
printf("%d %d %d\n", 0, n/2, n/2);
//printf("%d\n", res);
}
int main()
{
//fast;
//cin >> T;
scanf("%d", &T);
while(T -- )
solve();
return 0;
}
B. Almost Ternary Matrix
思路:
类似:
10011001
01100110
01100110
10011001
模拟构造即可
代码如下:
#include <bits/stdc++.h>
#define fast ios::sync_with_stdio(false),cin.tie(0), cout.tie(0)
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int N = 110, mod = 1e9 + 7;
int T;
int lowbit(int x)
{
return x & -x;
}
void solve()
{
int n, m;
scanf("%d %d", &n, &m);
string r1, r2;
while(true)
{
if(r1.size() < 2 * m) r1 += "1 0 ";
else break;
if(r1.size() < 2 * m) r1 += "0 1 ";
else break;
}
while(true)
{
if(r2.size() < 2 * m) r2 += "0 1 ";
else break;
if(r2.size() < 2 * m) r2 += "1 0 ";
else break;
}
int a[N][N];
for(int i = 1; i <= n; i ++ )
{
if(i % 4 == 1 || i % 4 == 0) cout << r1 << endl;
else cout << r2 << endl;
}
//printf("%d\n", res);
}
int main()
{
//fast;
//cin >> T;
scanf("%d", &T);
while(T -- )
solve();
return 0;
}
此段代码也有类似效果:
void solve()
{
int n, m;
scanf("%d %d", &n, &m);
for(int i = 1; i <= n; i ++ )
{
for(int j = 1; j <= m; j ++ )
cout << ((i % 4 <= 1)==(j % 4 <= 1)) << " ";
puts("");
}
//printf("%d\n", res);
}
C. The Third Problem
思路:
res = 每个数能变换的范围
分析:
01的位置不能变;
对于其余的数,小于本数的数在本数的一侧,则本数也不能动;
其余的数能动,能动的范围为比本数小的数组成的区间;
代码如下:
#include <bits/stdc++.h>
#define fast ios::sync_with_stdio(false),cin.tie(0), cout.tie(0)
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int N = 1e5 + 10, mod = 1e9 + 7;
int T;
void solve()
{
int n, m;
scanf("%d", &n);
int a[N] = {0}, p[N] = {0};
for(int i = 0; i < n; i ++ )
{
scanf("%d", &a[i]);
p[a[i]] = i;
}
int res = 1;
int l = p[0], r = p[0];
for(int i = 1; i < n; i ++ )
{
if(p[i] < l) l = p[i];
else if(p[i] > r) r = p[i];
else res = (LL)res*(r - l + 1 - i) % mod;
//cout << res << endl;
}
printf("%d\n", res);
//printf("%d\n", res);
}
int main()
{
//fast;
//cin >> T;
scanf("%d", &T);
while(T -- )
solve();
return 0;
}
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