Codeforces Gym: 105053

The 2024 ICPC Latin America Championship

Codeforces Gym/105053D.cpp

@@ -0,0 +1,53 @@
+/**
+ * @file 105053D.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-03
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+typedef pair<int, int> pii;
+
+vector<pii> split;
+
+void solve(void) {
+    int64_t n;
+    cin >> n;
+    for (int64_t v = 2; v * v <= n; v++) {
+        int cnt = 0;
+        while (n % v == 0) cnt++, n /= v;
+        if (cnt) split.emplace_back(cnt, v);
+    }
+    if (n > 1) split.emplace_back(1, n);
+    if (split.size() == 1) return cout << "NY"[split[0].first % 2] << endl, void();
+    if (split.size() == 2 && split[0].first == 1 && split[1].first == 1) return cout << 'Y' << endl, void();
+    cout << 'N' << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}

Codeforces Gym/105053E.cpp

@@ -0,0 +1,78 @@
+/**
+ * @file 105053E.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-03
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 1005
+
+typedef pair<int, int> pii;
+
+vector<int> graph[maxn * 2];
+pii a[maxn];
+bool vis[maxn * 2];
+
+bool cross(pii a, pii b) {
+    if (a.first > b.first) swap(a, b);
+    return b.first < a.second && a.second < b.second;
+}
+void dfs(int p) {
+    vis[p] = true;
+    for (auto i : graph[p])
+        if (!vis[i]) dfs(i);
+    return;
+}
+
+void solve(void) {
+    int n;
+    cin >> n;
+    for (int i = 1; i <= 2 * n; i++) {
+        char c;
+        int x;
+        cin >> c >> x;
+        if (c == '+')
+            a[x].first = i;
+        else
+            a[x].second = i;
+    }
+    for (int i = 1; i <= n; i++)
+        for (int j = 1; j <= n; j++)
+            if (cross(a[i], a[j]))
+                graph[i].push_back(j + n), graph[j + n].push_back(i), graph[i + n].push_back(j), graph[j].push_back(i + n);
+    for (int i = 1; i <= n; i++)
+        if (!vis[i] && !vis[i + n]) dfs(i);
+    for (int i = 1; i <= n; i++)
+        if (vis[i] && vis[i + n]) return cout << '*' << endl, void();
+    for (int i = 1; i <= n; i++) cout << "GS"[vis[i]];
+    cout << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}

Codeforces Gym/105053F.cpp

@@ -0,0 +1,65 @@
+/**
+ * @file 105053F.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-03
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 200005
+
+int a[maxn], b[maxn], cnt[maxn], g[maxn];
+bool f[maxn];
+
+void solve(void) {
+    int n, sum = 0;
+    cin >> n;
+    int delt = 0;
+    bool zero = false;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i] >> b[i], sum += a[i], zero |= !a[i], delt = gcd(delt, b[i]);
+        if (i > 1) cnt[a[i]]++;
+    }
+    f[0] = true;
+    for (int t = 1; t < maxn; t++) {
+        if (!cnt[t]) continue;
+        for (int i = 0; i <= sum; i++) g[i] = 0;
+        for (int i = 0; i <= sum; i++) {
+            if (f[i]) g[i] = cnt[t] + 1;
+            if (i >= t) g[i] = max(g[i], g[i - t] - 1);
+            f[i] |= g[i];
+        }
+    }
+    f[0] = zero;
+    for (int i = 0; i <= sum; i++)
+        if (f[i] && i % delt == (sum - i) % delt) return cout << 'Y' << endl, void();
+    cout << 'N' << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}

Codeforces Gym/105053G.cpp

@@ -0,0 +1,98 @@
+/**
+ * @file 105053G.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-03
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 100005
+
+typedef pair<int, int> pii;
+
+double p[maxn], f[maxn];
+bool notPrime[maxn];
+vector<int> num[maxn], prime;
+vector<pii> primeNum[maxn];
+
+void solve(void) {
+    int n;
+    cin >> n;
+    double psum = 0;
+    for (int i = 1; i <= n; i++) cin >> p[i], psum += p[i];
+    for (int i = 1; i <= n; i++) p[i] /= psum;
+
+    for (int i = 1; i <= n; i++)
+        for (int j = i; j <= n; j += i) num[j].push_back(i);
+    for (int i = 1; i <= n; i++) {
+        int x = i;
+        for (auto j = prime.begin(); *j * *j <= x; j++) {
+            int cnt = 1;
+            while (x % *j == 0) cnt *= *j, x /= *j;
+            if (cnt) primeNum[i].emplace_back(*j, cnt);
+        }
+        if (x > 1) primeNum[i].emplace_back(x, x);
+    }
+
+    for (int x = n; x; x--) {
+        double own = 0;
+        for (int lcm = x; lcm <= n; lcm += x) {
+            int base = 1, extra = 1;
+            for (auto i = primeNum[x].begin(), j = primeNum[lcm].begin(); j != primeNum[lcm].end(); j++)
+                if (i != primeNum[x].end() && i->first == j->first) {
+                    if (i->second < j->second)
+                        base *= j->second;
+                    else
+                        extra *= i->second;
+                    i++;
+                } else
+                    base *= j->second;
+            for (auto y : num[extra]) {
+                if (base * y > n) break;
+                if (lcm == x)
+                    own += p[base * y];
+                else
+                    f[x] += p[base * y] * (f[lcm] + 1);
+            }
+        }
+        f[x] = (own + f[x]) / (1 - own);
+    }
+    cout << setprecision(10) << fixed << f[1] << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    freopen("G.in", "r", stdin);
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    for (int i = 2; i < maxn; i++) {
+        if (!notPrime[i]) prime.push_back(i);
+        for (auto j = prime.begin(); j != prime.end() && i * *j < maxn; j++) {
+            notPrime[i * *j] = true;
+            if (i % *j == 0) break;
+        }
+    }
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}

Codeforces Gym/105053K.cpp

@@ -0,0 +1,71 @@
+/**
+ * @file 105053K.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-03
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 1000005
+
+int f[maxn][3];
+
+bool isVowel(char c) { return c == 'A' || c == 'E' || c == 'I' || c == 'O' || c == 'U' || c == 'Y'; }
+
+void solve(void) {
+    int n;
+    cin >> n;
+    memset(f, 0x3f, sizeof(f));
+    f[0][0] = 0;
+    for (int i = 1; i <= n; i++) {
+        string s;
+        cin >> s;
+        int l = 0, r = 0;
+        bool pre = true;
+        for (int j = 0; j < min(3, (int)s.size()); j++) {
+            if (isVowel(s[j]))
+                pre = false, r = 0;
+            else {
+                if (pre) l++;
+                r++;
+            }
+            if (pre)
+                for (int x = 0; x + j + 1 < 3; x++) f[i][x + j + 1] = min(f[i][x + j + 1], f[i - 1][x] + j + 1);
+            else
+                for (int x = 0; x + l < 3; x++) f[i][r] = min(f[i][r], f[i - 1][x] + j + 1);
+        }
+    }
+    int64_t v = min({f[n][0], f[n][1], f[n][2]});
+    if (v == 0x3f3f3f3f)
+        cout << '*' << endl;
+    else
+        cout << v << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}