POJ 2699 The Maximum Number of Strong Kings

网络流  模板题

参考

网络流汇总

http://blog.youkuaiyun.com/sdj222555/article/details/7797257

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <sstream>
using namespace std;
#define ll long long
const int MAXN = 105;
const int MAXM = 400010;
const int INF = 0x3f3f3f3f;
struct Edge{
    int st , to ,  next, cap , flow;
}edge[MAXN<<3];

int tol , head[MAXN<<1] , gap[MAXN<<1] , dep[MAXN<<1] , cur[MAXN<<1];
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<<1];
int isap(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 st, en, n;
int fg[MAXN][MAXN],g[MAXN],m[MAXN][MAXN];
void build(int k ){
    init();
    for(int i = 1; i <= n; i++){
        add_edge(i,en,g[i]);
        for(int j = i+1 ; j <= n; j++){
            add_edge(st,m[i][j],1);
        }
    }
    memset(fg,0,sizeof(fg));
    for(int i = n-k+1; i <= n; i++){
        for(int j = i+1; j <= n; j++){
            if(g[i] < g[j]){
                add_edge(m[i][j],i,1);
                fg[i][j] = 1;
            }
        }
    }
    for(int i = 1; i <= n; i++){
        for(int j = i+1; j <= n; j++){
            if(!fg[i][j]){
                add_edge(m[i][j],i,1);
                add_edge(m[i][j],j,1);
            }
        }
    }
}
void cut(char *s){
    int len = strlen(s);
    int t = 0;
    for(int i = 0; i < len; i++){
        if(s[i] >= '0' && s[i] <= '9')
        {
            t = t * 10 + s[i] - '0';
            if(i == len - 1 || s[i + 1] == ' ')
            {
                g[++n] = t;
                t = 0;
            }
        }
    }
}
int main(){
	char str[40];
	int i,j,t;
	scanf("%d",&t);
	getchar();
	while(t--){
		gets(str);
		n=0;
		cut(str);
		int tt = n;
		for(int i = 1; i <= n; i++){
			for(int j = i+1; j<= n ; j++){
				m[j][i] = m[i][j] = ++tt;
			}
		}
		st = 0, en = tt + 1;
		int ans = 1;
        for(int i = n; i >= 1; i--){
            build(i);
            int temp = isap(st,en,en);
            if(temp == n*(n-1)/2){
                ans = i;
                break;
            }
        }
        printf("%d\n",ans);
	}
	return 0;
}