P5331 [SNOI2019]通信

https://www.luogu.com.cn/record/100755482

Luogu/P5331/P5331.cpp

@@ -0,0 +1,174 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+#include <iterator>
+#include <queue>
+#include <utility>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1005,
+          M = N * N;
+const int INF = 0x3f3f3f3f;
+
+int n, w, a[N], s, t, tot, pos1[N], pos2[N];
+long long cost;
+int idx, head[N << 4], ver[M << 5], next[M << 5];
+std::pair<int, int> edge[M << 5];
+int dist[N << 4];
+bool vis[N << 4];
+
+void add(int u, int v, int flow, int cost) {
+    next[idx] = head[u];
+    ver[idx] = v;
+    edge[idx] = std::make_pair(flow, cost);
+    head[u] = idx++;
+}
+
+bool spfa() {
+    std::fill(std::begin(vis), std::end(vis), false);
+    std::fill(std::begin(dist), std::end(dist), INF);
+
+    std::queue<int> q;
+
+    q.emplace(s);
+    dist[s] = 0;
+    vis[s] = true;
+
+    while (!q.empty()) {
+        int u = q.front();
+        q.pop();
+
+        vis[u] = false;
+
+        for (int i = head[u]; ~i; i = next[i]) {
+            int v = ver[i],
+                flow = edge[i].first,
+                cost = edge[i].second;
+
+            if (flow && dist[v] > dist[u] + cost) {
+                dist[v] = dist[u] + cost;
+
+                if (!vis[v]) {
+                    q.emplace(v);
+                    vis[v] = true;
+                }
+            }
+        }
+    }
+
+    return dist[t] != INF;
+}
+
+int dinic(int u, int limit) {
+    if (u == t) return limit;
+
+    int flow = 0;
+
+    vis[u] = true;
+
+    for (int i = head[u]; ~i && flow < limit; i = next[i]) {
+        int v = ver[i],
+            f = edge[i].first,
+            w = edge[i].second;
+
+        if (dist[v] == dist[u] + w && f && !vis[v]) {
+            int k = dinic(v, std::min(f, limit - flow));
+
+            if (!k) dist[v] = INF;
+
+            edge[i].first -= k;
+            edge[i ^ 1].first += k;
+            flow += k;
+            cost += k * w;
+        }
+    }
+
+    vis[u] = false;
+
+    return flow;
+}
+
+void solve(int l, int r) {
+    if (l == r) return;
+
+    int mid = (l + r) >> 1;
+
+    solve(l, mid);
+    solve(mid + 1, r);
+
+    std::vector<int> nums;
+
+    for (int i = l; i <= r; i++) {
+        nums.emplace_back(a[i]);
+    }
+
+    std::sort(nums.begin(), nums.end());
+    nums.erase(std::unique(nums.begin(), nums.end()), nums.end());
+
+    for (int i = 0; i < nums.size() - 1; i++) {
+        add(tot + 1 + i, tot + 1 + i + 1, INF, nums[i + 1] - nums[i]);
+        add(tot + 1 + i + 1, tot + 1 + i, 0, -(nums[i + 1] - nums[i]));
+
+        add(tot + 1 + i + 1, tot + 1 + i, INF, nums[i + 1] - nums[i]);
+        add(tot + 1 + i, tot + 1 + i + 1, 0, -(nums[i + 1] - nums[i]));
+    }
+
+    for (int i = l; i <= r; i++) {
+        int pos = std::lower_bound(nums.begin(), nums.end(), a[i]) - nums.begin();
+
+        if (i <= mid) {
+            add(tot + 1 + pos, pos2[i], 1, 0);
+            add(pos2[i], tot + 1 + pos, 0, 0);
+        } else {
+            add(pos1[i], tot + 1 + pos, 1, 0);
+            add(tot + 1 + pos, pos1[i], 0, 0);
+        }
+    }
+
+    tot += nums.size();
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    std::fill(std::begin(head), std::end(head), -1);
+
+    cin >> n >> w;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+
+    s = 0, t = ++tot;
+
+    for (int i = 1; i <= n; i++) {
+        pos1[i] = ++tot;
+        pos2[i] = ++tot;
+
+        // S -> i_1
+        add(s, pos1[i], 1, 0);
+        add(pos1[i], s, 0, 0);
+
+        // i_1 -> T
+        add(pos1[i], t, 1, w);
+        add(t, pos1[i], 0, -w);
+
+        // i_2 -> T
+        add(pos2[i], t, 1, 0);
+        add(t, pos2[i], 0, 0);
+    }
+
+    solve(1, n);
+
+    while (spfa()) {
+        while (dinic(s, INF)) {}
+    }
+
+    cout << cost << endl;
+
+    return 0;
+}