P3812 【模板】线性基

https://www.luogu.com.cn/record/103041260

Luogu/P3386/P3386.cpp

@@ -1,5 +1,6 @@
 #include <iostream>
 #include <algorithm>
+#include <iterator>
 #include <queue>
 
 using std::cin;
@@ -10,19 +11,19 @@ const int N = 505,
           M = 5e4 + 5;
 const int INF = 0x3f3f3f3f;
 
-int n, m, e, s, t, flow, ans;
+int n, m, e, s, t;
 int idx, head[N << 1], ver[M << 2], edge[M << 2], next[M << 2];
 int d[N << 1], cur[N << 1];
 
 void add(int u, int v, int w) {
-    next[idx] = head[u];
     ver[idx] = v;
     edge[idx] = w;
+    next[idx] = head[u];
     head[u] = idx++;
 }
 
 bool bfs() {
-    std::fill_n(d, N << 1, 0);
+    std::fill(std::begin(d), std::end(d), 0);
 
     std::queue<int> q;
 
@@ -38,7 +39,7 @@ bool bfs() {
             int v = ver[i],
                 w = edge[i];
 
-            if (w && !d[v]) {
+            if (!d[v] && w) {
                 d[v] = d[u] + 1;
                 cur[v] = head[v];
                 if (v == t) return true;
@@ -54,20 +55,21 @@ int dinic(int u, int limit) {
     if (u == t) return limit;
 
     int flow = 0;
+
     for (int i = cur[u]; ~i && flow < limit; i = next[i]) {
         cur[u] = i;
 
         int v = ver[i],
             w = edge[i];
 
-        if (w && d[v] == d[u] + 1) {
+        if (d[v] == d[u] + 1 && w) {
             int k = dinic(v, std::min(limit - flow, w));
 
             if (!k) d[v] = 0;
 
+            flow += k;
             edge[i] -= k;
             edge[i ^ 1] += k;
-            flow += k;
         }
     }
 
@@ -78,7 +80,7 @@ int main() {
     std::ios::sync_with_stdio(false);
     cin.tie(nullptr);
 
-    std::fill_n(head, N << 1, -1);
+    std::fill(std::begin(head), std::end(head), -1);
 
     cin >> n >> m >> e;
 
@@ -97,15 +99,17 @@ int main() {
     for (int i = 1, u, v; i <= e; i++) {
         cin >> u >> v;
 
-        add(u, n + v, 1);
-        add(n + v, u, 0);
+        add(u, v + n, 1);
+        add(v + n, u, 0);
     }
 
+    int res = 0;
+
     while (bfs()) {
-        while (flow = dinic(s, INF)) ans += flow;
+        while (int flow = dinic(s, INF)) res += flow;
     }
 
-    cout << ans << endl;
+    cout << res << endl;
 
     return 0;
 }

Luogu/P3805/P3805.cpp

@@ -1,46 +1,57 @@
 #include <iostream>
+#include <algorithm>
 #include <string>
+#include <vector>
 
 using std::cin;
 using std::cout;
 const char endl = '\n';
 
-const int N = 1.1e7 + 5;
+std::vector<int> manacher(std::string _s) {
+    // s = "abba" -> "^#a#b#b#a#$"
+    int n = _s.size();
+    std::string s(n * 2 + 3, '#');
 
-int p[N << 1], mid, r, ans;
-std::string s1, s2;
+    for (int i = 0; i < n; i++) {
+        s[i * 2 + 2] = _s[i];
+    }
+
+    s[0] = '^';
+    s[n * 2 + 2] = '$';
+
+    std::vector<int> p(s.size(), 1);
+
+    for (int i = 1, mid = 0, r = 0; i <= n * 2 + 1; i++) {
+        p[i] = i < r ? std::min(p[mid * 2 - i], r - i) : 1;
+
+        while (s[i - p[i]] == s[i + p[i]]) p[i]++;
+
+        if (i + p[i] - 1 > r) {
+            r = i + p[i] - 1;
+            mid = i;
+        }
+    }
+
+    // for (int i = 0; i < n; i++) {
+    //     p[i] = p[i * 2 + 2] / 2;
+    // }
+
+    // p.resize(n);
+
+    return p;
+}
 
 int main() {
     std::ios::sync_with_stdio(false);
     cin.tie(nullptr);
 
-    cin >> s1;
+    std::string s;
 
-    // Init
+    cin >> s;
 
-    s2.push_back('^');
-    for (const char &c : s1) {
-        s2.push_back('#');
-        s2.push_back(c);
-    }
-    s2 += "#$";
+    auto p = manacher(s);
 
-    for (int i = 1; i < s2.size(); i++) {
-        p[i] = i < r ? std::min(p[mid * 2 - i], r - i) : 1;
-
-        while (s2[i - p[i]] == s2[i + p[i]]) p[i]++;
-
-        if (i + p[i] > r) {
-            r = i + p[i];
-            mid = i;
-        }
-    }
-
-    for (int i = 0; i < s2.size(); i++) {
-        ans = std::max(ans, p[i]);
-    }
-
-    cout << ans - 1 << endl;
+    cout << *std::max_element(p.begin(), p.end()) - 1 << endl;
 
     return 0;
 }

Luogu/P3812/P3812.cpp

@@ -1,50 +1,67 @@
 #include <iostream>
+#include <algorithm>
+#include <iterator>
+#include <limits>
+#include <type_traits>
 
 using std::cin;
 using std::cout;
 const char endl = '\n';
 
-const int N = 55;
+const int N = 1e5 + 5;
 
-int n;
-long long x, a[N], ans;
+template <typename T>
+struct LinearBasis
+    : std::enable_if<std::is_unsigned<T>::value, T> {
+    T a[std::numeric_limits<T>::digits];
 
-void insert(long long x) {
-    for (int i = 50; ~i; i--) {
-        if (!(x & (1ll << i))) continue;
+    LinearBasis() {
+        std::fill(std::begin(a), std::end(a), 0);
+    }
 
-        if (a[i]) {
-            x ^= a[i];
-        } else {
-            for (int k = 0; k < i; k++) {
-                if (x & (1ll << k)) x ^= a[k];
+    void insert(unsigned long long x) {
+        for (int i = std::numeric_limits<T>::digits - 1; ~i; i--) {
+            if ((x >> i) & 1) {
+                if (a[i]) {
+                    x ^= a[i];
+                } else {
+                    a[i] = x;
+
+                    return;
+                }
             }
-
-            for (int k = i + 1; k <= 50; k++) {
-                if (a[k] & (1ll << i)) a[k] ^= x;
-            }
-
-            a[i] = x;
-            return;
         }
     }
-}
+
+    T query() {
+        T res(0);
+
+        for (int i = std::numeric_limits<T>::digits - 1; ~i; i--) {
+            if ((res ^ a[i]) > res) res ^= a[i];
+        }
+
+        return res;
+    }
+};
 
 int main() {
     std::ios::sync_with_stdio(false);
     cin.tie(nullptr);
 
+    int n;
+    LinearBasis<unsigned long long> lb;
+
     cin >> n;
 
     for (int i = 1; i <= n; i++) {
+        unsigned long long x;
+
         cin >> x;
 
-        insert(x);
+        lb.insert(x);
     }
 
-    for (int i = 0; i <= 50; i++) ans ^= a[i];
-
-    cout << ans << endl;
+    cout << lb.query() << endl;
 
     return 0;
 }

S2OJ/1970/1970.cpp

@@ -0,0 +1,56 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+const int mod = 1e9 + 7;
+
+int n, m, a[N], b[N];
+long long ans1, ans2, ans3;
+
+long long binpow(long long a, long long b, long long mod = ::mod) {
+    a %= mod;
+
+    long long res = 1;
+
+    while (b) {
+        if (b & 1) res = res * a % mod;
+        a = a * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+
+        b[n - i + 1] = a[i];
+    }
+
+    long long x = binpow(2, m - 1);
+
+    for (int i = 1; i <= n; i++) {
+        ans1 = (((ans1 + static_cast<long long>(a[i]) * ((static_cast<long long>(x + 1) * n - i + 1) % mod + mod % mod) % mod * x) % mod) + mod) % mod;
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans2 = (((ans2 + static_cast<long long>(b[i]) * ((static_cast<long long>(x + 1) * n - i + 1) % mod + mod % mod) % mod * x) % mod) + mod) % mod;
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans3 = (((ans3 + static_cast<long long>(a[i]) * ((static_cast<long long>(x) * n - i + 1) % mod + mod % mod) % mod * x) % mod) + mod) % mod;
+    }
+
+    cout << std::max(((ans1 + ans3) % mod + mod) % mod, ((ans2 + ans3) % mod + mod) % mod) << endl;
+
+    return 0;
+}

S2OJ/1971/1971.cpp

@@ -0,0 +1,54 @@
+#include <iostream>
+#include <iomanip>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1005;
+const double eps = 1e-6;
+
+int n, m, c;
+double p, f[N][N];
+
+bool check(double x) {
+    for (int i = 0; i <= m; i++) {
+        f[0][i] = x;
+    }
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= m; j++) {
+            f[i][j] = std::min(x, f[i - 1][j] * (1.0 - p) + f[i][j - 1] * p + 1);
+        }
+    }
+
+    return f[n][m] < x;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m >> c;
+
+    p = c / 100.0;
+
+    double l = 0,
+           r = 1e9,
+           res = 1e9;
+
+    while (r - l > eps) {
+        double mid = (l + r) / 2;
+
+        if (check(mid)) {
+            r = mid;
+            res = mid;
+        } else {
+            l = mid;
+        }
+    }
+
+    cout << std::fixed << std::setprecision(12) << res << endl;
+
+    return 0;
+}