hdu2363Cycling 二分+最短路

//一个无向图 ，每个点都有高度，
//问从起点1到终点n的最高点减最低点的差值最小的前提下的最短路和这个差值
//由于n<100所以可以先将这n个点按升序排，枚举这个最短路的左边最小mi，二分找最小的右边ma
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std ;
const int maxn = 110 ;
const int maxm = 5010 ;
const int inf = 0x3f3f3f3f ;
struct Edge
{
    int v  ,w ;
    int next ;
}edge[maxm<<1] ;
int n , m ;
int head[maxn] , vis[maxn] , dis[maxn] , h[maxn] , a[maxn];
int nedge ;
void addedge(int u , int v , int w)
{
    edge[nedge].v = v ;
    edge[nedge].w = w ;
    edge[nedge].next = head[u] ;
    head[u] = nedge++ ;
}
bool dijkstra(int mi , int ma)
{
     if(h[1] < mi || h[1] > ma) return false ;
    for(int i = 2;i <= n;i++)
    dis[i] = inf ;
    dis[1] = 0 ;
    memset(vis , 0 , sizeof(vis)) ;
    while(1)
    {
        int mi_1  = inf, pos ;
        for(int i = 1; i <= n ;i++)
        if(!vis[i] && dis[i] < mi_1)
        mi_1 = dis[pos = i] ;
        if(mi_1 == inf)break;
        vis[pos] = 1 ;
        for(int i = head[pos] ; i != -1 ;i = edge[i].next)
        {
            int v = edge[i].v ;
            if(h[v] < mi || h[v] > ma)continue ;
            if(dis[v] > dis[pos] + edge[i].w)
            dis[v] = dis[pos] + edge[i].w ;
        }
    }
    if(dis[n] == inf)return false  ;
    else return true ;
}
int find(int l , int r)
{
    int pos = l ;
    while(l <= r)
    {
        int mid = (l + r) >> 1 ;
        if(!dijkstra(a[pos] , a[mid]))
        l = mid + 1 ;
        else r = mid - 1;
    }
    return l ;
}
int main()
{
    //freopen("in.txt" ,"r" , stdin) ;
   // freopen("out.txt" ,"w" ,stdout) ;
    int t ;
    scanf("%d" , &t) ;
    while(t--)
    {
        scanf("%d%d" , &n , &m) ;
        memset(head , -1 , sizeof(head)) ;
        nedge = 0 ;
        for(int i = 1;i <= n;i++)
        {
            scanf("%d" , &h[i]) ;
            a[i] = h[i] ;
        }
        sort(a + 1 , a + 1 + n);
        int len_a = unique(a + 1 , a + 1 + n) - a ;
        while(m--)
        {
            int u , v , w ;
            scanf("%d%d%d" , &u  ,&v , &w) ;
            addedge(u , v , w) ;
            addedge(v , u , w) ;
        }
        int mi = 0  , ma = inf  , len = inf ;
        for(int i = 1;i <= len_a;i++)
        {
           if(a[i] > h[1])break;
           int r = find(i , len_a) ;
           if(r <= len_a)
           {
               if(a[r] - a[i] < ma - mi)
               {
                   dijkstra(a[i] , a[r]) ;
                   mi = a[i] , ma = a[r] , len = dis[n] ;
               }
               if(a[r] - a[i] == ma - mi)
               {
                   dijkstra(a[i] , a[r]) ;
                   if(dis[n] < len)
                   mi = a[i] , ma = a[r] , len = dis[n] ;
               }
           }
        }
        printf("%d %d\n" , ma - mi , len) ;
    }
    return 0 ;
}

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