POJ1275　差分约束系统

最新推荐文章于 2019-08-04 23:03:05 发布

原创最新推荐文章于 2019-08-04 23:03:05 发布 · 162 阅读

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#差分约束

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本文深入探讨了SPFA（Shortest Path Faster Algorithm）算法的原理及其在解决最短路径问题中的应用。通过实例讲解了如何使用SPFA算法进行网络流优化，并提供了详细的代码实现，适合对图论和算法感兴趣的读者。

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#include<iostream>
#include<algorithm>
#include<cstdio>
#include<stdio.h>
#include<string.h>
#include<queue>
#include<cmath>
#include<map>
#include<set>
#include<vector> 
using namespace std;
#define inf 0x3f3f3f3f
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define mem(a,b) memset(a,b,sizeof(a));
#define lowbit(x)  x&-x;  
#define debugint(name,x) printf("%s: %d\n",name,x);
#define debugstring(name,x) printf("%s: %s\n",name,x);
typedef long long ll;
typedef unsigned long long ull;
const double eps = 1e-6;
const int maxn = 105;
const int mod = 1e9+7;
inline int read()
{
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int head[maxn],vis[maxn],cnt[maxn],dis[maxn],tol;
struct node{
    int u,v,w,nxt;
}E[maxn<<1];

void init(){
    mem(vis,0);
    mem(cnt,0);
    mem(head,-1);
    mem(dis,-inf);
    tol = 0;
}
void addedge(int u,int v,int w){
    E[tol].u = u;
    E[tol].v = v;
    E[tol].w = w;
    E[tol].nxt = head[u];
    head[u] = tol++;
}

int spfa(int st,int ed,int mid){
	
    int all = ed;
    queue<int>q;
	while(!q.empty()) q.pop();
    vis[st] = true;
    dis[st] = 0;
    q.push(st);
    while(!q.empty()){
        int u = q.front();
        q.pop();
        vis[u] = false;
        //if(u == ed) continue;
        for(int i = head[u]; ~i; i = E[i].nxt){
            int v = E[i].v;
            int w = E[i].w;
            if(dis[v] < dis[u]+w){
                dis[v] = dis[u]+w;
                if(!vis[v]){
                    vis[v] = true;
                    cnt[v]++;
                    if(cnt[v] > all) return 0;
                    q.push(v);
                }
            }
        }
    }
    return 1;
}
int sum[55], R[55], t[1005];
int n;

int main(){
	//freopen("in.txt","r",stdin);
	int _;
	for(scanf("%d",&_);_;_--){
		mem(sum,0);
		for(int i = 1; i <= 24; i++){
			scanf("%d",	&R[i]);
		}
		scanf("%d",&n);
		for(int i = 1; i <= n; i++){
			scanf("%d",&t[i]);
			sum[t[i]+1]++;
		}
		int l = 0, r = n,ans = -1;
		while(l <= r){
			int s24 = (l+r)>>1;
			init();
			addedge(0,24,s24);
			for(int i = 1; i <= 24; i++) 
				addedge(i-1,i,0),addedge(i,i-1,-sum[i]);
			for(int i = 8; i <= 24; i++)
				addedge(i-8,i,R[i]);
			for(int i = 1; i <= 7; i++)
				addedge(i+16,i,R[i]-s24);
			if(spfa(0,24,s24)){
				ans = s24;
				r = s24-1;
			}else
				l = s24+1;
		}
		if(ans == -1) puts("No Solution");
		else printf("%d\n",ans);
	}
}