第一次尝试视频题解的方式，已将视频发在b站上面，详细可戳我。
如果有什么不足之处还请大家指出。
这里说一下(C)题较为详细的证明，题目就等价为经过操作过后，不存在一个位置上面有超过(2)个点，如果有空缺那么有个位置点数必然大于(1)。
如果两个点可以到达同一个位置，那么就有(displaystyle i+a_{i\% n}equiv j+a_{j\% n}(mod n))，所以我们可以将(i,j)都转化为(\% n)意义下，最后再将变化结果(\%n)看看是否重复就行。
代码：
A. Puzzle Pieces
/*
* Author: heyuhhh
* Created Time: 2020/5/6 22:37:55
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
void run() {
int n, m; cin >> n >> m;
if (n == 1 || m == 1) {
cout << "YES" << '
';
} else if (n <= 2 && m <= 2) {
cout << "YES" << '
';
} else cout << "NO" << '
';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
int T; cin >> T; while(T--)
run();
return 0;
}
B. Card Constructions
/*
* Author: heyuhhh
* Created Time: 2020/5/6 22:41:30
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 100000 + 5;
ll f[N], k;
void init() {
for (int i = 1;; i++) {
f[i] = f[i - 1] + 2 + 3 * (i - 1);
if (f[i] >= (ll)1e9) {
k = i; break;
}
}
}
void run() {
int n; cin >> n;
int ans = 0;
while(1) {
int t = upper_bound(f + 1, f + k + 1, n) - f - 1;
if (f[t] == n) {
++ans; break;
}
if (t <= 0) break;
n -= f[t];
++ans;
}
cout << ans << '
';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
init();
int T; cin >> T; while(T--)
run();
return 0;
}
C. Hilbert's Hotel
/*
* Author: heyuhhh
* Created Time: 2020/5/6 22:57:54
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 2e5 + 5;
int n;
int a[N];
bool vis[N];
void run() {
cin >> n;
for (int i = 0; i < n; i++) {
cin >> a[i];
}
for (int i = 0; i < n; i++) vis[i] = false;
for (int i = 0; i < n; i++) {
int x = ((i + a[i]) % n + n) % n;
if (vis[x]) {
cout << "NO" << '
';
return;
}
vis[x] = true;
}
cout << "YES" << '
';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
int T; cin >> T; while(T--)
run();
return 0;
}
D. Monopole Magnets
/*
* Author: heyuhhh
* Created Time: 2020/5/6 23:21:04
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e3 + 5;
int n, m;
char s[N][N];
const int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};
bool vis[N][N];
int cols[N], rows[N];
void dfs(int x, int y) {
if (vis[x][y]) return ;
vis[x][y] = 1;
for (int i = 0; i < 4; i++) {
int nx = x + dx[i], ny = y + dy[i];
if (s[nx][ny] == '#') dfs(nx, ny);
}
}
void run() {
cin >> n >> m;
for (int i = 1; i <= n; i++) {
cin >> (s[i] + 1);
for (int j = 1; j <= m; j++) {
if (s[i][j] == '#') {
++cols[j], ++rows[i];
}
}
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
if (cols[j] == 0 && rows[i] == 0) {
vis[i][j] = true;
}
}
}
for (int i = 1; i <= n; i++) {
int cnt = 0;
for (int j = 1; j <= m; j++) {
if (vis[i][j]) ++cnt;
}
cnt += rows[i];
if (cnt == 0) {
cout << "-1" << '
';
return;
}
int all = rows[i];
for (int j = 1; j <= m; j++) {
if (s[i][j] == '.' && all && all != rows[i]) {
cout << "-1" << '
';
return;
}
if (s[i][j] == '#') --all;
}
}
for (int j = 1; j <= m; j++) {
int cnt = 0;
for (int i = 1; i <= n; i++) {
if (vis[i][j]) ++cnt;
}
cnt += cols[j];
if (cnt == 0) {
cout << "-1" << '
';
return;
}
int all = cols[j];
for (int i = 1; i <= n; i++) {
if (s[i][j] == '.' && all && all != cols[j]) {
cout << "-1" << '
';
return;
}
if (s[i][j] == '#') --all;
}
}
memset(vis, 0, sizeof(vis));
int ans = 0;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
if (!vis[i][j] && s[i][j] == '#') {
++ans;
dfs(i, j);
}
}
}
cout << ans << '
';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}
E. Quantifier Question
/*
* Author: heyuhhh
* Created Time: 2020/5/7 0:31:29
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 2e5 + 5;
int n, m, f;
int ans[N], vis[N], vis2[N];
vector <int> G[N], rG[N];
void dfs(int u) {
vis[u] = 1;
for (auto v : G[u]) {
if (vis[v] == 1) f = 1;
else if(!vis[v]) dfs(v);
}
vis[u] = 2;
}
void dfs2(int u) {
vis2[u] = 1;
for (auto v : rG[u]) {
if (!vis2[v]) dfs2(v);
}
}
void run() {
cin >> n >> m;
for (int i = 1; i <= m; i++) {
int u, v; cin >> u >> v;
G[u].push_back(v);
rG[v].push_back(u);
}
for (int i = 1; i <= n; i++) {
if (!vis[i]) dfs(i);
}
if (f) {
cout << -1 << '
';
return;
}
memset(ans, -1, sizeof(ans));
memset(vis, 0, sizeof(vis));
int res = 0;
for (int i = 1; i <= n; i++) {
if (!vis[i] && !vis2[i]) {
ans[i] = 1;
++res;
} else {
ans[i] = 0;
}
if (!vis[i]) dfs(i);
if (!vis2[i]) dfs2(i);
}
cout << res << '
';
for (int i = 1; i <= n; i++) {
if (ans[i]) cout << "A";
else cout << "E";
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}
F - Résumé Review
/*
* Author: heyuhhh
* Created Time: 2020/5/7 21:30:21
*/
#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <vector>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <iomanip>
#include <assert.h>
#define MP make_pair
#define fi first
#define se second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define INF 0x3f3f3f3f
#define Local
#ifdef Local
#define dbg(args...) do { cout << #args << " -> "; err(args); } while (0)
void err() { std::cout << std::endl; }
template<typename T, typename...Args>
void err(T a, Args...args) { std::cout << a << ' '; err(args...); }
template <template<typename...> class T, typename t, typename... A>
void err(const T <t> &arg, const A&... args) {
for (auto &v : arg) std::cout << v << ' '; err(args...); }
#else
#define dbg(...)
#endif
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
//head
const int N = 1e5 + 5;
ll n, k;
int a[N], b[N];
bool chk(ll A) {
ll s = 0;
for (int i = 1; i <= n; i++) {
int l = 0, r = a[i] + 1, mid;
while (l < r) {
mid = (l + r) >> 1;
if (a[i] - 3ll * mid * (mid - 1) - 1 >= A) l = mid + 1;
else r = mid;
}
b[i] = l - 1;
s += b[i];
}
return s >= k;
}
void run() {
cin >> n >> k;
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
ll l = -8e18, r = 8e18, mid;
while (l < r) {
mid = (l + r) >> 1;
if (chk(mid)) {
l = mid + 1;
} else {
r = mid;
}
}
ll A = l - 1, R = 0;
chk(A);
for (int i = 1; i <= n; i++) R += b[i];
R -= k;
for (int i = 1; i <= n && R; i++) {
if (b[i] && a[i] - 3ll * b[i] * (b[i] - 1) - 1 == A) {
--b[i], --R;
}
}
for (int i = 1; i <= n; i++) {
cout << b[i] << "
"[i == n];
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cout << fixed << setprecision(20);
run();
return 0;
}