Hdu5385 The path

The path

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 995    Accepted Submission(s): 419
Special Judge

Problem Description

You have a connected directed graph.Let d(x) be the length of the shortest path from 1 to x.Specially d(1)=0.A graph is good if there exist x satisfy d(1)<d(2)<....d(x)>d(x+1)>...d(n).Now you need to set the length of every edge satisfy that the graph is good.Specially,if d(1)<d(2)<..d(n),the graph is good too.
The length of one edge must ∈ [1,n]
It's guaranteed that there exists solution.

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:
The first line contains two integers n and m,the number of vertexs and the number of edges.Next m lines contain two integers each, ui and vi (1≤ui,vi≤n), indicating there is a link between nodes ui and vi and the direction is from ui to vi.
∑n≤3∗105,∑m≤6∗105
1≤n,m≤105

Output

For each test case,print m lines.The i-th line includes one integer:the length of edge from ui to vi

Sample Input

2 4 6 1 2 2 4 1 3 1 2 2 2 2 3 4 6 1 2 2 3 1 4 2 1 2 1 2 1

Sample Output

1 2 2 1 4 4 1 1 3 4 4 4

Author

SXYZ

Source

2015 Multi-University Training Contest 8

题目大意：给定一张n个点m条有向边的图，构造每条边的边权（边权为正整数），令d(x)表示1到x的最短路，使得存在点i(1<=i<=n)满足d(1)<d(2)<…<d(i)>d(i+1)>…>d(n)。

分析：有关最短路的构造题，和hdu4903有点类似，都是事先确定最短路再来构造边权.

　　　首先，令每个点的最短路都在[0,n-1]区间内，并且每个点的最短路都不一样.如果能够能够使所有点的最短路都合理，那么对于一条边所连的点u,v，只需要这条边的权值等于abs(d(v) - d(u))即可.这就能满足最短路的要求.

　　　接下来是要使得最短路合理.从两边向中间构造,维护两个指针l,r和一个计数器cnt,一开始l = 2,r = n.先设d[1] = 0,将1号点连边指向的点都打上标记.接着从l,r指针指向的点中选一个打上标记的点，那么这个点的d值就是++cnt.然后把这个点连边所指向的点都打上标记，并且向中间移动指针.因为题目保证有解，所以每次必然有一个指针能够移动.

　　　这样做是使得这些点到1的最短路合理，如果直接胡乱分配d,设定边权，那么可能只是这条边是最短路上的边，但实际上这些点到1的最短路并不一定是分配好的d.

#include <cstdio>
#include <cstring>
#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

const int maxn = 600010;

int T,n,m,head[maxn],nextt[maxn],to[maxn],tot = 1,d[maxn],cnt;
bool vis[maxn];

struct node
{
    int x,y,w;
}e[600010];

void add(int x,int y)
{
    to[tot] = y;
    nextt[tot] = head[x];
    head[x] = tot++;
}

int main()
{
    scanf("%d",&T);
    while (T--)
    {
        memset(head,0,sizeof(head));
        memset(vis,false,sizeof(vis));
        memset(d,0,sizeof(d));
        cnt = 1;
        tot = 1;
        scanf("%d%d",&n,&m);
        for (int i = 1; i <= m; i++)
        {
            scanf("%d%d",&e[i].x,&e[i].y);
            add(e[i].x,e[i].y);
        }
        d[1] = 0;
        for (int i = head[1];i;i = nextt[i])
        {
            int v = to[i];
            vis[v] = 1;
        }
        int l = 2,r = n;
        while (cnt < n)
        {
            int u;
            if (vis[l])
                u = l++;
            else
                u = r--;
            d[u] = cnt++;
            for (int i = head[u];i;i = nextt[i])
            {
                int v = to[i];
                vis[v] = 1;
            }
        }
        for (int i = 1; i <= m; i++)
        {
            if(e[i].x == e[i].y)
                printf("%d\n",n);
            else
                printf("%d\n",abs(d[e[i].x] - d[e[i].y]));
        }
    }

    return 0;
}