P4016 负载平衡问题

R72104716

Luogu/P4016/P4016.cpp

@@ -0,0 +1,131 @@
+#include <cstring>
+#include <iostream>
+#include <queue>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 105,
+          M = 2005,
+          INF = 0x3f3f3f3f;
+
+int n, s, t, a[N], sum, avg, cost;
+
+// Graph
+int idx, head[N], ver[M << 1], next[M << 1];
+std::pair<int, int> edge[M << 1];
+//      <flow, cost>
+
+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++;
+}
+
+// Dinic
+int dist[N];
+bool vis[N];
+
+bool spfa() {
+    std::memset(vis, 0x00, sizeof(vis));
+    std::memset(dist, 0x3f, sizeof(dist));
+
+    std::queue<int> q;
+    q.push(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],
+                c = edge[i].first,
+                w = edge[i].second;
+
+            if (dist[v] > dist[u] + w && c > 0) {
+                dist[v] = dist[u] + w;
+                if (!vis[v]) {
+                    q.push(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],
+            c = edge[i].first,
+            w = edge[i].second;
+
+        if (dist[v] == dist[u] + w && c && !vis[v]) {
+            int k = dinic(v, std::min(c, 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;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+
+    memset(head, 0xff, sizeof(head));
+
+    cin >> n;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+        sum += a[i];
+    }
+    avg = sum / n;
+
+    s = 0, t = n + 1;
+    for (int i = 1; i <= n; i++) {
+        if (a[i] - avg > 0) {
+            add(s, i, a[i] - avg, 0);
+            add(i, s, 0, 0);
+        } else if (a[i] - avg < 0) {
+            add(i, t, avg - a[i], 0);
+            add(t, i, 0, 0);
+        }
+    }
+
+    for (int i = 1; i <= n; i++) {
+        if (i > 1) {
+            add(i, i - 1, INF, 1);
+            add(i - 1, i, 0, -1);
+        }
+        if (i < n) {
+            add(i, i + 1, INF, 1);
+            add(i + 1, i, 0, -1);
+        }
+    }
+
+    add(1, n, INF, 1);
+    add(n, 1, 0, -1);
+    add(n, 1, INF, 1);
+    add(1, n, 0, -1);
+
+    while (spfa()) dinic(s, INF);
+
+    cout << cost << endl;
+
+    return 0;
+}