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OI-codes/LibreOJ/6013/6013.cpp

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#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;
}