P1565 牛宫

https://www.luogu.com.cn/record/84050544

Luogu/CF444C/CF444C.cpp

@@ -0,0 +1,151 @@
+#include <iostream>
+#include <cmath>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+struct node {
+    int l, r;
+    int color, new_color;
+    long long sum, sum_delta;
+    node *lchild, *rchild;
+
+    node()
+        : l(0), r(0), color(-1), new_color(-1), sum(0), sum_delta(0), lchild(nullptr), rchild(nullptr) {}
+
+    node(int _l, int _r)
+        : l(_l), r(_r), color(-1), new_color(-1), sum(0), sum_delta(0), lchild(nullptr), rchild(nullptr) {}
+
+    ~node() {
+        delete lchild;
+        delete rchild;
+    }
+
+    void pushup() {
+        sum = 0;
+        color = -1;
+
+        if (lchild != nullptr) {
+            sum += lchild->sum;
+            color = lchild->color;
+        }
+
+        if (rchild != nullptr) {
+            sum += rchild->sum;
+            color = color == rchild->color ? color : -1;
+        }
+    }
+
+    void pushdown() {
+        if (new_color == -1 || sum_delta == 0) return;
+
+        if (lchild != nullptr) {
+            if (sum_delta) {
+                lchild->sum_delta += sum_delta;
+                lchild->sum += sum_delta * (lchild->r - lchild->l + 1);
+            }
+
+            if (new_color != -1) {
+                lchild->color = lchild->new_color = new_color;
+            }
+        }
+
+        if (rchild != nullptr) {
+            if (sum_delta) {
+                rchild->sum_delta += sum_delta;
+                rchild->sum += sum_delta * (rchild->r - rchild->l + 1);
+            }
+
+            if (new_color != -1) {
+                rchild->color = rchild->new_color = new_color;
+            }
+        }
+
+        new_color = -1;
+        sum_delta = 0;
+    }
+};
+
+void build(node *&u, int l, int r) {
+    u = new node(l, r);
+
+    if (l == r) {
+        u->color = l;
+
+        return;
+    }
+
+    int mid = (l + r) >> 1;
+
+    if (l <= mid) build(u->lchild, l, mid);
+    if (r > mid) build(u->rchild, mid + 1, r);
+
+    u->pushup();
+}
+
+void modify(node *u, int l, int r, int new_color) {
+    if (l <= u->l && u->r <= r && ~u->color) {
+        u->sum += static_cast<long long>(std::abs(u->color - new_color)) * (u->r - u->l + 1);
+        u->sum_delta += std::abs(u->color - new_color);
+        u->color = u->new_color = new_color;
+
+        return;
+    }
+
+    int mid = (u->l + u->r) >> 1;
+    u->pushdown();
+
+    if (l <= mid) modify(u->lchild, l, r, new_color);
+    if (r > mid) modify(u->rchild, l, r, new_color);
+
+    u->pushup();
+}
+
+long long query(node *u, int l, int r) {
+    if (l <= u->l && u->r <= r) {
+        return u->sum;
+    }
+
+    int mid = (u->l + u->r) >> 1;
+    long long res = 0;
+
+    u->pushdown();
+
+    if (l <= mid) res += query(u->lchild, l, r);
+    if (r > mid) res += query(u->rchild, l, r);
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, m;
+    node *root;
+
+    cin >> n >> m;
+
+    build(root, 1, n);
+
+    while (m--) {
+        int op, l, r;
+
+        cin >> op >> l >> r;
+
+        if (op == 1) {
+            int x;
+
+            cin >> x;
+
+            modify(root, l, r, x);
+        } else {
+            cout << query(root, l, r) << endl;
+        }
+    }
+
+    delete root;
+
+    return 0;
+}

Luogu/P1565/P1565.cpp

@@ -8,7 +8,36 @@ const char endl = '\n';
 const int N = 205;
 
 int n, m;
-long long g[N][N], ans;
+long long g[N][N], s[N][N], c[N], ans;
+
+bool check(int x) {
+    long long t = 0;
+
+    for (int i = x; i <= m; i++) {
+        t = std::min(t, c[i - x]);
+
+        if (c[i] > t) return true;
+    }
+
+    return false;
+}
+
+int calc() {
+    int l = 1, r = n, res = 0;
+
+    while (l <= r) {
+        int mid = (l + r) >> 1;
+
+        if (check(mid)) {
+            res = mid;
+            l = mid + 1;
+        } else {
+            r = mid - 1;
+        }
+    }
+
+    return res;
+}
 
 int main() {
     std::ios::sync_with_stdio(false);
@@ -20,19 +49,17 @@ int main() {
         for (int j = 1; j <= m; j++) {
             cin >> g[i][j];
 
-            g[i][j] += g[i - 1][j] + g[i][j - 1] - g[i - 1][j - 1];
+            s[i][j] = s[i - 1][j] + g[i][j];
         }
     }
 
     for (int i = 1; i <= n; i++) {
-        for (int j = 1; j <= m; j++) {
-            for (int k = i; k <= n; k++) {
-                for (int l = j; l <= m; l++) {
-                    if (g[k][l] - g[k][j - 1] - g[i - 1][l] + g[i - 1][j - 1] >= 0) {
-                        ans = std::max(ans, static_cast<long long>(k - i + 1) * (l - j + 1));
-                    }
-                }
+        for (int j = i; j <= n; j++) {
+            for (int k = 1; k <= m; k++) {
+                c[k] = c[k - 1] + s[j][k] - s[i - 1][k];
             }
+
+            ans = std::max(ans, static_cast<long long>(j - i + 1) * calc());
         }
     }