1 #include <bits/stdc++.h>
2 using namespace std;
3 const int maxn = 1005, inf = 0x3f3f3f3f;
4 struct Edge {
5 int from, to, cap, flow, cost;
6 };
7
8 struct MCMF {
9 int n, m, s, t;
10 vector<Edge> edges;
11 vector<int> G[maxn];
12 int inq[maxn];
13 int d[maxn];
14 int p[maxn];
15 int a[maxn];
16
17 void init(int n) {
18 this->n = n;
19 for (int i = 1; i <= n; ++i) G[i].clear();
20 edges.clear();
21 }
22
23 void AddEdge(int from, int to, int cap, int cost) {
24 edges.push_back((Edge){from, to, cap, 0, cost});
25 edges.push_back((Edge){to, from, 0, 0, -cost});
26 m = edges.size();
27 G[from].push_back(m-2);
28 G[to].push_back(m-1);
29 }
30 bool BellmanFord(int s, int t, int& flow, int& cost) {
31 for (int i = 1; i <= n; ++i) d[i] = inf;
32 memset(inq, 0, sizeof(inq));
33 d[s] = 0; inq[s] = 1; p[s] = 0; a[s] = inf;
34
35 queue<int> que;
36 que.push(s);
37 while (!que.empty()) {
38 int u = que.front(); que.pop();
39 inq[u] = 0;
40 for (int i = 0; i < G[u].size(); ++i) {
41 Edge& e = edges[G[u][i]];
42 if (e.cap > e.flow && d[e.to] > d[u] + e.cost) {
43 d[e.to] = d[u] + e.cost;
44 p[e.to] = G[u][i];
45 a[e.to] = min(a[u], e.cap-e.flow);
46 if (!inq[e.to]) { que.push(e.to); inq[e.to] = 1; }
47 }
48 }
49 }
50 if (d[t] == inf) return false;
51 flow += a[t];
52 cost += d[t] * a[t];
53 int u = t;
54 while (u != s) {
55 edges[p[u]].flow += a[t];
56 edges[p[u]^1].flow -= a[t];
57 u = edges[p[u]].from;
58 }
59 return true;
60 }
61 int mincost(int s, int t) {
62 int flow = 0, cost = 0;
63 while (BellmanFord(s, t, flow, cost));
64 return cost;
65 }
66 }mcmf;
67 int a[maxn];
68 int main() {
69 int n; scanf("%d",&n);
70 int s = n+1, t = n+2, ave = 0;
71 mcmf.init(n+2);
72 for (int i = 1; i <= n; ++i) {
73 scanf("%d",&a[i]);
74 ave += a[i];
75 }
76 ave /= n;
77 for (int i = 1; i <= n; ++i) {
78 /// 如果仓库量小于平均值，则说明要从源点流入到该仓库
79 if (a[i] < ave) mcmf.AddEdge(s,i,ave-a[i],0);
80 /// 如果仓库量大于平均值，则说明要从该仓库流出到汇点
81 if (a[i] > ave) mcmf.AddEdge(i,t,a[i]-ave,0);
82 }
83 /// 相邻点之间建立关系
84 for (int i = 1; i <= n; ++i) {
85 if (i == 1) {
86 mcmf.AddEdge(i,i+1,inf,1);
87 mcmf.AddEdge(i,n,inf,1);
88 continue;
89 }
90 if (i == n) {
91 mcmf.AddEdge(i,1,inf,1);
92 mcmf.AddEdge(i,i-1,inf,1);
93 }
94 mcmf.AddEdge(i,i+1,inf,1);
95 mcmf.AddEdge(i,i-1,inf,1);
96 }
97 int ans = mcmf.mincost(s,t);
98 printf("%d\n",ans);
99 return 0;
100 }
