9th sduwhcpc

A-Don't Sit Next To Me

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
const int P = 1e9 + 7, N = 1e6 + 10;

int f[N], g[N];

int power(int a, int b) {
	int res = 1; 
	for(; b; b >>= 1, a = 1LL * a * a % P)
		if(b & 1) 
			res = 1LL * res * a % P;
	return res;
}

void init() {
	for(int i = 3; i < N; ++ i) 
		f[i] = (f[(i - 1) / 2] + f[i - 1 - (i - 1) / 2] + 1) % P;
	for(int i = 2; i < N; ++ i) 
		g[i] = (f[i - 1] + 1) % P;
	for(int i = 1; i < N; ++ i) 
		g[i] = (g[i] + g[i - 1]) % P;
}	

int main() {
	init();
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); 
	int T; 
	cin >> T;
	while(T -- ) {
		int n; 
		cin >> n;
		int up = (2LL * g[n - 1] + n) % P, down = power(n, P - 2);
		cout << 1LL * up * down % P << endl; 	
	}
	return 0;
} 

B-Counting The Stars

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
const int N = 100010;

int n, m, lenx, leny, a[N], ans[N];
int cnt[N], cnt_block[N];

int get_x(int x) { return x / lenx; }
int get_y(int x) { return x / leny; }
struct Query {
	int id, l, r, d, u;
	bool operator < (const Query& t) const {
		int i = get_x(l), j = get_x(t.l);
		if(i != j) return i < j;
		if(i & 1) return r < t.r;
		return r > t.r;
	}
}q[N];

void add(int x) { if(!cnt[a[x]]) cnt_block[get_y(a[x])] ++; cnt[a[x]] ++; }
void del(int x) { cnt[a[x]] --; if(!cnt[a[x]]) cnt_block[get_y(a[x])] --; }

int query(int l, int r) {
	int res = 0;
	if(get_y(l) == get_y(r)) {
		for(int i = l; i <= r; ++ i) 
			res += (cnt[i] ? 1 : 0);
	}
	else {
		int i = l, j = r;
		while(get_y(i) == get_y(l)) { res += (cnt[i] ? 1 : 0); ++ i; }
		while(get_y(j) == get_y(r)) { res += (cnt[j] ? 1 : 0); -- j; }
		for(int k = get_y(i); k <= get_y(j); ++ k) res += cnt_block[k]; 
	}
	return res;
}

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); 
	int T;
	cin >> T;
	while(T -- ) {
		for(int i = 0; i < N; ++ i) cnt[i] = cnt_block[i] = 0;
		cin >> n >> m;
		for(int i = 1; i <= n; ++ i) cin >> a[i];
		lenx = sqrt(n); 
		leny = sqrt(100000);
		for(int i = 1; i <= m; ++ i) {
			int x0, x1, y0, y1;
			cin >> x0 >> y0 >> x1 >> y1;
			q[i] = {i, x0, x1, y0, y1};
		}
		sort(q + 1, q + m + 1);
		for(int k = 1, r = 0, l = 1; k <= m; ++ k) {
			while(r < q[k].r) add(++ r); 
			while(r > q[k].r) del(r --);
			while(l < q[k].l) del(l ++);
			while(l > q[k].l) add(-- l);
			ans[q[k].id] = query(q[k].d, q[k].u);
		}
		for(int i = 1; i <= m; ++ i) cout << ans[i] << "\n";
	}
	return 0;
} 

C-Building Roads

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using PII = pair<int, int>;
using PLI = pair<LL, int>;
const LL INF = 1e18;

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int n, m, s1, s2, t;
	cin >> n >> m >> s1 >> s2 >> t;
	vector<vector<PII>> G(n), rG(n);
	for(int i = 0; i < m; ++ i) {
		int u, v, w;
		cin >> u >> v >> w;
		G[u].push_back({v, w});
		rG[v].push_back({u, w});
	}
	auto dijkstra = [&](int s, vector<vector<PII>> &g) -> vector<LL> {
		vector<bool> vis(n, 0);
        vector<LL> d(n, INF);
        priority_queue<PLI, vector<PLI>, greater<PLI>> Q; 
        d[s] = 0;
        Q.push({0, s});
        while(!Q.empty()) {
            auto u = Q.top().second; Q.pop();            
            if(vis[u]) continue;
            vis[u] = 1;
            for(auto &[v, w] : g[u]) {
                if(d[v] > d[u] + w) {
                    d[v] = d[u] + w;
                    Q.push({d[v], v});
                }
            }
    	}
    	return d;
	};
	auto d1 = dijkstra(s1, G);
	auto d2 = dijkstra(s2, G);
	auto d3 = dijkstra(t, rG);
	LL ans = INF;
    for(int i = 0; i < n; ++ i) 
    	ans = min(ans, d1[i] + d2[i] + d3[i]);
    cout << (ans >= INF ? -1 : ans) << "\n";
	return 0;
}

D-Money Tree

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
const int N = 510;

int n, m, w[N];
LL dp[N][N];
vector<int> G[N];

int DFS(int u, int f) {
    int p = 1;
    dp[u][1] = w[u];
    for(auto v : G[u]) {
    	if(v == f) continue;
        int siz = DFS(v, u);
        for(int i = min(m, p); i; -- i)
            for(int j = 1; j <= siz && i + j <= m; ++ j)
                dp[u][i + j] = min(dp[u][i + j], dp[u][i] + dp[v][j]);
        p += siz;
    }
    return p;
}

int main() {
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> n >> m;
 	LL sum = 0;
    m = n - m;
    for(int i = 1; i < n; ++ i) {
        int x, y;
        cin >> x >> y;
        G[x].push_back(y);
        G[y].push_back(x);
    }
    for(int i = 1; i <= n; ++ i) cin >> w[i], sum += w[i];
    memset(dp, 0x3f, sizeof dp);
    DFS(1, 1);
    cout << sum - dp[1][m] << "\n";
    return 0;
}

E-Max Min Count

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
const int N = 200010;
 
LL n, a[N];
LL ans;
 
void solve(LL x, LL y, LL t) {
	int lst = 1;
	for(int i = 1; i <= n; ++ i) {
    	if(a[i] > x or a[i] < y) {
    		lst = i + 1;
    	}
    	ans += (i - lst + 1) * t;
    }
}
 
int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
    LL x, y;
    cin >> n >> x >> y;
    for(int i = 1; i <= n; ++ i) cin >> a[i];
    solve(x, y, 1);
    solve(x - 1, y, -1);
    solve(x, y + 1, -1);
    solve(x - 1, y + 1, 1);
    cout << ans << "\n";
    return 0;
}

F-Shoot Balloon

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;

template <typename T>void read(T &x) {
    x = 0; register int f = 1;
    register 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();}
    x *= f;
}
namespace Polynomial {
using Poly = std::vector<int>;
constexpr int P(998244353), G(3), L(1 << 18); // L : max length of dft
inline void inc(int &x, int y) { (x += y) >= P ? x -= P : 0; }
inline int mod(int64_t x) { return x % P; }
inline int fpow(int x, int k = P - 2) {
  int r = 1;
  for (; k; k >>= 1, x = 1LL * x * x % P)
    if (k & 1) r = 1LL * r * x % P;
  return r;
}
 
int w[L], _ = [] {
  w[L / 2] = 1;
  for (int i = L / 2 + 1, x = fpow(G, (P - 1) / L); i < L; i++) w[i] = 1LL * w[i - 1] * x % P;
  for (int i = L / 2 - 1; i >= 0; i--) w[i] = w[i << 1];
  return 0;
}();
void dft(int *a, int n) {
  assert((n & n - 1) == 0);
  for (int k = n >> 1; k; k >>= 1) {
    for (int i = 0; i < n; i += k << 1) {
      for (int j = 0; j < k; j++) {
        int y = a[i + j + k];
        a[i + j + k] = 1LL * (a[i + j] - y + P) * w[k + j] % P;
        inc(a[i + j], y);
      }
    }
  }
}
void idft(int *a, int n) {
  assert((n & n - 1) == 0);
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += k << 1) {
      for (int j = 0; j < k; j++) {
        int x = a[i + j], y = 1LL * a[i + j + k] * w[k + j] % P;
        a[i + j + k] = x - y < 0 ? x - y + P : x - y;
        inc(a[i + j], y);
      }
    }
  }
  for (int i = 0, inv = P - (P - 1) / n; i < n; i++)
    a[i] = 1LL * a[i] * inv % P;
  std::reverse(a + 1, a + n);
}
// expand dft of length n to 2n
void dftDoubling(int *a, int n) {
  std::copy_n(a, n, a + n);
  idft(a + n, n);
  for (int i = 0; i < n; i++) a[n + i] = 1LL * w[n + i] * a[n + i] % P;
  dft(a + n, n);
}
int norm(int n) { return 1 << std::__lg(n * 2 - 1); }
void norm(Poly &a) {
  if (!a.empty()) a.resize(norm(a.size()));
}
void dft(Poly &a) { dft(a.data(), a.size()); }
void idft(Poly &a) { idft(a.data(), a.size()); }
inline Poly &dotEq(Poly &a, Poly b) {
  assert(a.size() == b.size());
  for (int i = 0; i < a.size(); i++) a[i] = 1LL * a[i] * b[i] % P;
  return a;
}
inline Poly dot(Poly a, Poly b) { return dotEq(a, b); }
Poly operator*(const Poly &a, const Poly &b) {
  int len = a.size() + b.size() - 1;
  if (a.size() <= 16 || b.size() <= 16) {
    Poly c(len);
    for (size_t i = 0; i < a.size(); i++)
      for (size_t j = 0; j < b.size(); j++)
        c[i + j] = (c[i + j] + 1LL * a[i] * b[j]) % P;
    return c;
  }
  int n = norm(len);
  Poly foo = a;
  foo.resize(n);
  dft(foo);
  if (&a == &b) {
    dotEq(foo, foo);
  } else {
    Poly bar = b;
    bar.resize(n);
    dft(bar);
    dotEq(foo, bar);
  }
  idft(foo);
  foo.resize(len);
  return foo;
}
}  // namespace Polynomial

using namespace Polynomial;
using LL = long long;
const int dlt = 30000;

int main() {
	int nu, nm, nl;
	read(nu);
	int N = 60000;
	Poly A(N + 1), C(N + 1); 
	for(int i = 0, x; i < nu; ++ i) {
		read(x);
		A[x + dlt] += 1;
	}
	read(nm);
	vector<int> B;
	for(int i = 0, x; i < nm; ++ i) {
		read(x);
		B.push_back(x + dlt);
	}
	read(nl);
	for(int i = 0, x; i < nl; ++ i) {
		read(x);
		C[x + dlt] += 1;
	}
	A = A * C;
	LL ans = 0;
	for(int &x : B) ans += A[x * 2];
	cout << ans << "\n";
	return 0;
}

G-String Value

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int n;
	cin >> n;
	string s;
	cin >> s;
	vector<int> pos(26, -1);
    long long ans = 0;
    for(int i = 0; i < n; ++ i) {
        ans += 1LL * (i - pos[s[i] - 'a']) * (n - i);
        pos[s[i] - 'a'] = i;
    }
    cout << ans << "\n";
	return 0;
}

H-Flip Matrix

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int T;
	cin >> T;
	while(T -- ) {
		int n;
		cin >> n;
		vector<vector<int>> A(n, vector<int> (n));
		for(int i = 0; i < n; ++ i) 
			for(int j = 0; j < n; ++ j)
				cin >> A[i][j];
		vector<int> row, col;
		auto solve = [&]() -> bool {
			row.clear(); 
			col.clear();
			for(int i = 1; i < n; ++ i) {
				int c = 0;
				for(int j = 0; j < n; ++ j)
					c += (A[i][j] ^ A[0][j]);
				if(c > 0 and c < n) return 0;
				if(c == n) row.push_back(i);
			}
			for(int i = 0; i < n; ++ i)
				if(A[0][i]) col.push_back(i);
			return 1;
		};
		if(solve()) {
			cout << "YES\n";
			cout << row.size() + col.size() << "\n";
			for(int &i : row) cout << "row " << i + 1 << "\n";
			for(int &i : col) cout << "col " << i + 1 << "\n";
			continue;
		};
		for(int i = 0; i < n; ++ i) A[i][i] ^= 1;
		if(solve()) {
			cout << "YES\n";
			cout << row.size() + col.size() + 1 << "\n";
			cout << "diagonal\n";
			for(int &i : row) cout << "row " << i + 1 << "\n";
			for(int &i : col) cout << "col " << i + 1 << "\n";
			continue;
		};
		cout << "NO\n";
	}
	return 0;
} 

I-Exam Week

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;

int f[55][510];
int g[55][510][5];

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int T;
	cin >> T;
	while(T -- ) {
		map<string, int> mp;
		memset(g, -0x3f, sizeof g); 
		memset(f, 0, sizeof f);
		int n, m; cin >> n;
		string str;
		int idx = 0;
		for(int i = 1; i <= n; ++ i) cin >> str, mp[str] = ++ idx;
		cin >> m; 
		int w, c;
		for(int i = 1; i <= m; ++ i) {
			cin >> str >> w >> c;
			int id = mp[str];
			for(int j = 500; j >= c; -- j) {
				f[id][j] = max(f[id][j - c] + w, f[id][j]);
				f[id][j] = min(f[id][j], 100);
			}
		}
		int t, p; 
		cin >> t >> p;
		g[0][0][0] = 0;
		for(int i = 1; i <= n; ++ i) 
			for(int j = t; j >= 0; -- j)
				for(int k = 0; k <= t; ++ k) {
					if(k > j) break;
					for(int q = 0; q <= p; ++ q) {
						if(f[i][k] >= 60) g[i][j][q] = max(g[i - 1][j - k][q] + f[i][k], g[i][j][q]);
						else g[i][j][q + 1] = max(g[i - 1][j - k][q] + f[i][k], g[i][j][q + 1]);
					}
				}
		int res = -1;
		for(int i = 0; i <= p; ++ i) res = max(res, g[n][t][i]);
		cout << res << "\n";
	}
	return 0;
} 

J-Dangerous Maze

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int n, m, x, y;
	cin >> n >> m >> x >> y;
	if((n * m - x - y) % 2 == 0) {
		cout << "-1\n";
		return 0;
	}
	int a = 1, b = 1, ok = 0;
	if(n % 2 == 0) {
		while(b < y) {
			for(int i = 1; i < n; ++ i) cout << (ok ? 'L' : 'R');
			cout << 'U';
			ok ^= 1;
			b ++; 
			a = n + 1 - a;
		}
		ok = 0;
		for(int i = 1; i <= n; ++ i) {
			if((a == 1 and i == x) or (a == n and i == n - x + 1)) m --;
			for(int j = b; j < m; ++ j) cout << (ok ? 'D' : 'U');
			ok ^= 1;
			if(i == n) break;
			else cout << (a == 1 ? 'R' : 'L');
		}
		a = n + 1 - a;
		cout << 'D';
		if(a == 1) for(int i = 1; i < x; ++ i) cout << 'R';
		else for(int i = n; i > x; -- i) cout << 'L';
	}
	else if(m % 2 == 0) {
		swap(m, n);
		swap(x, y);
		while(b < y) {
			for(int i = 1; i < n; ++ i) cout << (ok ? 'D' : 'U');
			cout << 'R';
			ok ^= 1;
			b ++; 
			a = n + 1 - a;
		}
		ok = 0;
		for(int i = 1; i <= n; ++ i) {
			if((a == 1 and i == x) or (a == n and i == n - x + 1)) m --;
			for(int j = b; j < m; ++ j) cout << (ok ? 'L' : 'R');
			ok ^= 1;
			if(i == n) break;
			else cout << (a == 1 ? 'U' : 'D');
		}
		a = n + 1 - a;
		cout << 'L';
		if(a == 1) for(int i = 1; i < x; ++ i) cout << 'U';
		else for(int i = n; i > x; -- i) cout << 'D';
	}
	else {
		while(b < y) {
			for(int i = 1; i < n; ++ i) cout << (ok ? 'L' : 'R');
			cout << 'U';
			ok ^= 1;
			b ++; 
			a = n + 1 - a;
		}
		if(a == 1) {
			while(b <= m) {
				for(int i = 1; i < (b == m ? x : x - 1); ++ i) cout << (ok ? 'L' : 'R');
				if(b == m) break;
				cout << 'U';
				ok ^= 1;
				b ++;
			}
			ok = 0;
			for(int i = x; i < n; ++ i) {
				for(int j = m; j > y + 1; -- j) cout << (ok ? 'U' : 'D');
				ok ^= 1;
				cout << 'R';	
			}
			for(int i = m; i > y; -- i) cout << 'D';
			for(int i = n; i > x; -- i) cout << 'L';
		}
		else {
			ok = 0;
			for(int i = n; i > x; -- i) {
				for(int j = y; j < m; ++ j) cout << (ok ? 'D' : 'U');
				cout << 'L';
				ok ^= 1;
			}
			ok = 0;
			for(int i = m; i >= y; -- i) {
				for(int j = 1; j < x; ++ j) cout << (ok ? 'R' : 'L');
				if(i != y) cout << 'D';
				ok ^= 1;
			}   
		}
	}
	return 0;
} 

K-A Simple Question

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;

int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	int T; 
	cin >> T;
	while(T -- ) {
		LL n;
		cin >> n; 
		n --;
		LL t = log2(n);
		cout << (1ll << t) - 1 << "\n";
	}
	return 0;
} 

L-Polynomial Division

Sample Code (C++)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;
 
int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
 	int n, m;
 	cin >> n >> m;
 	vector<int> a(n + 1), b(m + 1, 0), c(n + m + 1);
 	for(int i = 0; i < n + 1; ++ i) cin >> a[i];
 	for(int i = 0; i < n + m + 1; ++ i) cin >> c[i];
 	for(int x = 0; x < n + 1; ++ x) {
	 	if(a[x] == 0) continue;
	 	for(int i = x; i - x < m + 1; ++ i) {
	 		int t = c[i];
	 		for(int j = x + 1; j <= i and j < n + 1; ++ j)
	 			t -= a[j] * b[i - j];
	 		b[i - x] = t / a[x];
	 	}
	 	break;
 	}
 	for(int i = 0; i < m + 1; ++ i) cout << b[i] << " \n"[i == m];
    return 0;
}