网络流24题--负载平衡问题【网络流】

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <iostream>
#include <vector>

using namespace std;
typedef long long LL;
const int maxn = 1e5 +7;
const int inf  = 0x3f3f3f3f;

int n, m, s, t;
int head[maxn],pre[maxn],inq[maxn],dis[maxn];
int a[maxn];
int cnt = 1;

struct edge {
    int u,to,nxt,w,c;
}e[maxn << 1];

template<class T>inline void read(T &res)
{
    char c;T flag=1;
    while((c=getchar())<‘0‘||c>‘9‘)if(c==‘-‘)flag=-1;res=c-‘0‘;
    while((c=getchar())>=‘0‘&&c<=‘9‘)res=res*10+c-‘0‘;res*=flag;
}

inline void BuildGraph(int u, int v, int w, int cost)
{
    e[++cnt] = (edge){u, v, head[u], w,  cost}, head[u] = cnt;
    e[++cnt] = (edge){v, u, head[v], 0, -cost}, head[v] = cnt;///反向边
}

queue < int > q;

bool SPFA(int x)
{
    memset(inq, 0, sizeof(inq));
    for(int i = s; i <= t; i++) {
        dis[i] = inf;
    }
    q.push(x);
    dis[x] = 0;
    inq[x] = 1;
    while(!q.empty()) {
        int u = q.front();
        q.pop();
        inq[u] = 0;
        for(int i = head[u]; i; i = e[i].nxt) {
            int v = e[i].to, w = e[i].c;
            if(e[i].w) {
                if(dis[u] + w < dis[v]) {
                    dis[v] = dis[u] + w;
                    pre[v] = i;
                    if(!inq[v]) {
                        q.push(v);
                        inq[v] = 1;
                    }
                }
            }
        }
    }
    if(dis[t] == inf)
        return 0;
    return 1;
}

int MCMF()
{
    int ans = 0;
    while(SPFA(s)) {
        int temp = inf;
        for(int i = pre[t]; i; i = pre[e[i].u]) {
            temp = min(temp, e[i].w);
        }
        for(int i = pre[t]; i; i = pre[e[i].u]) {
            e[i].w   -= temp;
            e[i^1].w += temp;
            ans += e[i].c * temp;
            //printf("ans:%d\n",ans);
        }
    }
    return ans;
}

int main()
{
    read(n);
    int sum = 0;
    for(int i = 1; i <= n; i++) {
        read(a[i]);
        sum += a[i];
    }
    sum /= n;
    s = 0; t = 2*n + 1;
    for(int i = 1; i <= n; i++) {
        if(sum > a[i]) {
            BuildGraph(s, i, sum - a[i], 0);
        }
        if(sum < a[i]) {
            BuildGraph(i, t, a[i] - sum, 0);
        }
    }
    for(int i = 1; i <= n; i++) {
        if(i == 1) {
            BuildGraph(i, n, inf, 1);
            BuildGraph(i, 2, inf, 1);
        }
        else if(i == n) {
            BuildGraph(n, 1, inf, 1);
            BuildGraph(n, n-1, inf, 1);
        }
        else {
            BuildGraph(i, i+1, inf, 1);
            BuildGraph(i, i-1, inf, 1);
        }
    }
    printf("%d\n",MCMF());
    return 0;
}