hihocoder 1138 Islands Travel dijkstra+heap 难度:2

http://hihocoder.com/problemset/problem/1138

 

很久不用最短路,几乎连基本性质也忘了,结果这道题就是某些最短路算法空间复杂度是o(n)

这里总结四种算法

 

算法名称           时间复杂度       空间复杂度

dijkstra+heap  O(elog(e+n))   O(n)

bellman-ford    O(ne)             O(n)

spfa                O(ke)             O(n)

floyd-warshall   O(n^3)          O(n^2)

#include<cstdio>

#include<cstring>

#include<cstdlib>

#include<algorithm>

#include<queue>



using namespace std;

const int maxn = 1e5 + 5;

const int maxm = 1e6 + 6;



int first[maxn],n;

struct edge

{

    int t,c,nxt;

} e[maxm];



void addedge(int f,int t,int c,int ind)

{

    e[ind].nxt = first[f];

    e[ind].t = t;

    e[ind].c = c;

    first[f] = ind;

}



struct pnt

{

    int x,y,id;

    pnt()

    {

        x = y = id = 0;

    }

    pnt(int _x,int _y,int _id)

    {

        x = _x;

        y = _y;

        id = _id;

    }

};

bool cmpx(pnt p1,pnt p2)

{

    if(p1.x!= p2.x)return p1.x < p2.x;

    return p1.y < p2.y;

}

bool cmpy(pnt p1,pnt p2)

{

    if(p1.y!= p2.y)return p1.y < p2.y;

    return p1.x < p2.x;

}

pnt a[maxn];

long long dis[maxn];

bool vis[maxn];

typedef pair<long long ,int> P;

priority_queue<P, vector <P>, greater<P> > que;

long long dijkstra()

{

    for(int i = 0; i < n; i++)dis[i] = 2e18;

    memset(vis,false,sizeof vis);

    while(!que.empty())que.pop();





    dis[0] = 0;

    vis[0] = true;

    for(int p = first[0]; p != -1; p = e[p].nxt)

    {

        int t = e[p].t;

        dis[t] = e[p].c;

        que.push(P(dis[t],t));

    }



    while(!que.empty())

    {

        int f = que.top().second;

        que.pop();

        if(f == n-1)break;

        if(vis[f])continue;

        vis[f] = true;



        for(int p = first[f]; p != -1; p = e[p].nxt)

        {

            int t = e[p].t;

            if(dis[t] > dis[f] + e[p].c){

                dis[t] = dis[f] + e[p].c;

                que.push(P(dis[t],t));

            }

        }

    }



    return dis[n - 1];

}

int main()

{

    while(scanf("%d",&n)==1)

    {

        memset(first, -1, sizeof first);

        for(int i = 0; i < n; i++)

        {

            scanf("%d%d",&a[i].x,&a[i].y);

            a[i].id = i;

        }



        sort(a,a + n,cmpx);

        for(int i = 0; i < n - 1; i++)

        {

            addedge(a[i].id,a[i + 1].id,

                    min(abs(a[i].x - a[i + 1].x),abs(a[i].y - a[i + 1].y)),2 * i);

            addedge(a[i + 1].id,a[i].id,

                    min(abs(a[i].x - a[i + 1].x),abs(a[i].y - a[i + 1].y)),2 * i + 1);

        }

        sort(a,a + n,cmpy);

        for(int i = 0; i < n - 1; i++)

        {

            addedge(a[i].id,a[i + 1].id,

                    min(abs(a[i].x - a[i + 1].x),abs(a[i].y - a[i + 1].y)),2 * i + 2 * n);

            addedge(a[i + 1].id,a[i].id,

                    min(abs(a[i].x - a[i + 1].x),abs(a[i].y - a[i + 1].y)),2 * i + 1 + 2 * n);

        }



        long long ans = dijkstra();

        printf("%lld\n",ans);

    }

    return 0;

}