HDU 5353

 题目大意：

相邻的朋友可以给出自己手上最多一颗糖，n个朋友形成一个环，问给的方式能否最后使所有朋友都糖的数量相同

 

这里我用的是网络流来做的，这里n=100000，用sap的模板可以跑过

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
#define ll long long
const int MAXN = 100010;
const int MAXM = 400010;
const int INF = 0x3f3f3f3f;
struct Edge{
    int st , to ,  next, cap , flow;
}edge[MAXM];

int tol , head[MAXN] , gap[MAXN] , dep[MAXN] , cur[MAXN];

void init(){
    tol = 0;
    memset(head , -1  , sizeof(head));
}

void add_edge(int u , int v , int w , int rw=0)
{
    edge[tol].st = u , edge[tol].to=v , edge[tol].cap = w , edge[tol].flow=0;
    edge[tol].next = head[u] , head[u] = tol++;

    edge[tol].st = v , edge[tol].to = u , edge[tol].cap = rw , edge[tol].flow=0;
    edge[tol].next = head[v] , head[v] = tol++;
}

int Q[MAXN];

void BFS(int start , int end)
{
    memset(dep , -1 , sizeof(dep));
    memset(gap , 0 , sizeof(gap));
    gap[0] = 1;
    int front = 0 , rear = 0;
    dep[end] = 0;
    Q[rear++] = end;
    while(front != rear){
        int u  = Q[front++];
        for(int i=head[u] ; i!=-1 ; i=edge[i].next){
            int v = edge[i].to ;
            if(dep[v]!=-1) continue;
            Q[rear++] = v;
            dep[v] = dep[u] + 1;
            gap[dep[v]]++;
        }
    }
}

int S[MAXN];
int sap(int start , int end , int N)
{
    BFS(start , end);
    memcpy(cur , head , sizeof(head));
    int top=0;
    int u=start;
    int ans = 0;
    while(dep[start]<N)
    {
        if(u == end){
            int Min = INF;
            int inser;
            for(int i=0 ; i<top ; i++)
                if(Min>edge[S[i]].cap-edge[S[i]].flow){
                    Min = edge[S[i]].cap-edge[S[i]].flow;
                    inser = i;
                }
            for(int i=0 ; i<top ; i++){
                edge[S[i]].flow+=Min;
                edge[S[i]^1].flow-=Min;
            }
            ans+=Min;
            top = inser;
            u = edge[S[top]^1].to;
            continue;
        }
        bool flag = false;
        int v ;
        for(int i=cur[u] ; i!=-1 ; i=edge[i].next){
            v = edge[i].to;
            if(edge[i].cap-edge[i].flow && dep[v]+1==dep[u]){
                flag = true;
                cur[u] = i;
                break;
            }
        }
        if(flag){
            S[top++] = cur[u];
            u = v;
            continue;
        }
        int Min = N;
        for(int i=head[u] ; i!=-1 ; i=edge[i].next){
            if(edge[i].cap-edge[i].flow && dep[edge[i].to]<Min){
                Min = dep[edge[i].to];
                cur[u] = i;
            }
        }
        gap[dep[u]]--;
        if(!gap[dep[u]]) return ans;
        dep[u] = Min+1;
        gap[dep[u]]++;
        if(u != start) u = edge[S[--top]^1].to;
    }
    return ans;
}
int n , m , val[MAXN] , id[MAXN] , in[MAXN] , out[MAXN] , x,  y , fl;
ll sum , ave;
int main()
{
  // freopen("in.txt" , "r" , stdin);
    int cas;
    scanf("%d",&cas);
    while(cas--){
        init();
        scanf("%d" , &n);
        sum = 0;
        for(int i=1 ; i<=n ; i++){
            scanf("%d" , val+i);
            sum+=val[i];
        }
        bool ok = true;
        if(sum%n != 0){
            ok = false;
        }
        if(!ok){
            puts("NO");
            continue;
        }
        ave = sum/n;
        for(int i=1 ; i<=n ; i++){
            if(abs(val[i]-ave)>2) ok = false;
        }
        if(!ok){
            puts("NO");
            continue;
        }
        add_edge(n , 1 , 1 , 1);
        for(int i=2 ; i<=n ; i++){
            add_edge(i , i-1 , 1 , 1);
        }
        int min_flow = 0;
        for(int i=1 ; i<=n ; i++){
            if(val[i]>ave){
                add_edge(0 , i , val[i]-ave);
            }
            else if(val[i]<ave){
                add_edge(i , n+1 , ave-val[i]);
                min_flow+=ave-val[i];
            }
        }
        int flow = sap(0 ,n+1 , n+2);
      //  cout<<flow<<" "<<min_flow<<endl;
        if(flow!=min_flow) ok = false;
        if(!ok){
            puts("NO");
            continue;
        }
        int rec[MAXN][2] , tot=0;
        for(int i=0 ; i<tol ; i+=2){
            if(edge[i].st>=1 && edge[i].to<=n){
                /*if(edge[i].flow + edge[i^1].flow == 0){
                    cout<<edge[i].st<<" "<<edge[i].to<<endl;
                    cout<<edge[i^1].st<<" "<<edge[i^1].to<<endl;
                    continue;
                }*/
                if(edge[i].flow>0) rec[tot][0] = edge[i].st , rec[tot++][1] = edge[i].to;
                else if(edge[i^1].flow>0) rec[tot][0] = edge[i^1].st , rec[tot++][1] = edge[i^1].to;
            }
        }
        printf("YES\n%d\n" , tot);
        for(int i=0 ; i<tot ; i++) printf("%d %d\n" , rec[i][0] , rec[i][1]);
    }
    return 0;
}