• 离线的并查集


    http://acm.hdu.edu.cn/showproblem.php?pid=3938

    Portal

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
    Total Submission(s): 820    Accepted Submission(s): 425


    Problem Description
    ZLGG found a magic theory that the bigger banana the bigger banana peel .This important theory can help him make a portal in our universal. Unfortunately, making a pair of portals will cost min{T} energies. T in a path between point V and point U is the length of the longest edge in the path. There may be lots of paths between two points. Now ZLGG owned L energies and he want to know how many kind of path he could make.
     

    Input
    There are multiple test cases. The first line of input contains three integer N, M and Q (1 < N ≤ 10,000, 0 < M ≤ 50,000, 0 < Q ≤ 10,000). N is the number of points, M is the number of edges and Q is the number of queries. Each of the next M lines contains three integers a, b, and c (1 ≤ a, b ≤ N, 0 ≤ c ≤ 10^8) describing an edge connecting the point a and b with cost c. Each of the following Q lines contain a single integer L (0 ≤ L ≤ 10^8).
     

    Output
    Output the answer to each query on a separate line.
     

    Sample Input
    10 10 10 7 2 1 6 8 3 4 5 8 5 8 2 2 8 9 6 4 5 2 1 5 8 10 5 7 3 7 7 8 8 10 6 1 5 9 1 8 2 7 6
     

    Sample Output
    36 13 1 13 36 1 36 2 16 13

    题意:给出一个连通图,以及每条路径的长度,定义从u走到v的所有边的最长边作为消耗的能量,q次询问,每次给出一个L能量,问存在多少这样的<u,v>路径对;

    分析:很明显是并查集,但是每询问一次就做一次并查集肯定会超时,所以应采用离线算法,先把所有答案全求出来,然后一块输出;首先把边权从小到大排序,然后把询问也从小到大排序,对于每次询问,只加入小于询问的边到一个集合中,用h数组记录每个集合中的元素,sum记录当加完这条边后此时的u,v点对数目;

    程序:

    #pragma comment(linker, "/STACK:1024000000,1024000000")
    #include"stdio.h"
    #include"string.h"
    #include"iostream"
    #include"map"
    #include"string"
    #include"queue"
    #include"stdlib.h"
    #include"math.h"
    #include"algorithm"
    #include"vector"
    #define M 100009
    #define eps 1e-10
    #define inf 1000000000
    #define mod 1000000000
    #define INF 1000000000
    using namespace std;
    struct node
    {
        int u,v,w;
    }e[M*5],q[M];
    int f[M],h[M];
    __int64 sum,ans[M];
    int cmp(node a,node b)
    {
        return a.w<b.w;
    }
    int finde(int x)
    {
        if(x!=f[x])
            f[x]=finde(f[x]);
        return f[x];
    }
    void make(int a,int b)
    {
        int x=finde(a);
        int y=finde(b);
        if(x==y)return;
        else if(x>y)
        {
            f[x]=y;
            int tt=h[y];
            h[y]+=h[x];
            sum+=h[y]*(h[y]-1)/2-h[x]*(h[x]-1)/2-tt*(tt-1)/2;
        }
        else
        {
            f[y]=x;
            int tt=h[x];
            h[x]+=h[y];
            sum+=h[x]*(h[x]-1)/2-h[y]*(h[y]-1)/2-tt*(tt-1)/2;
        }
    }
    int main()
    {
        int n,m,k,i;
        while(scanf("%d%d%d",&n,&m,&k)!=-1)
        {
            for(i=0;i<m;i++)
                scanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);
            sort(e,e+m,cmp);
            for(i=0;i<k;i++)
            {
                scanf("%d",&q[i].w);
                q[i].u=i;
            }
            sort(q,q+k,cmp);
            for(i=1;i<=n;i++)
            {
                f[i]=i;h[i]=1;
            }
            sum=0;
            int j=0;
            for(i=0;i<k;i++)
            {
                while(j<m&&e[j].w<=q[i].w)
                {
                    make(e[j].u,e[j].v);
                    j++;
                }
                ans[q[i].u]=sum;
            }
            for(i=0;i<k;i++)
                printf("%I64d
    ",ans[i]);
        }
        return 0;
    }
    


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  • 原文地址:https://www.cnblogs.com/mypsq/p/4348189.html
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