## 21 May Aurora Saturday 14:30 Python Practice 22.05.14.

**Question 1: **

One day, Tom traveled to a country named AKLA. AKLA is a small country, but there are N (N <= 100) towns in it. Each town products one kind of food, the food will be transported to all the towns. In addition, the trucks will always take the shortest way. There are M (M <= 3000) two-way roads connecting the towns, and the length of the road is 1.

Let SUM be the total distance of the shortest paths between all pairs of the towns. Please write a program to calculate the new SUM after one of the M roads is destroyed.

**Input**

The input contains several test cases.

The first line contains two positive integers N, M. The following M lines each contains two integers u, v, meaning there is a two-way road between town u and v. The roads are numbered from 1 to M according to the order of the input.

The input will be terminated by EOF.

**Output**

Output M lines, the i-th line is the new SUM after the i-th road is destroyed. If the towns are not connected after the i-th road is destroyed, please output “INF” in the i-th line.

Sample Input

5 4

5 1

1 3

3 2

5 4

2 2

1 2

1 2Sample Output

INF

INF

INF

INF

2

2

**Question 2:**

Jack has been hired to build a cheap internet network among John’s N (2 <= N <= 1,000) barns that are conveniently numbered 1..N. John has already done some surveying, and found M (1 <= M <= 20,000) possible connection routes between pairs of barns. Each possible connection route has an associated cost C (1 <= C <= 100,000). John wants to spend the least amount on connecting the network; he doesn’t even want to pay Jack.

Realizing John will not pay him, Jack decides to do the worst job possible. He must decide on a set of connections to install so that:

(i) the total cost of these connections is as large as possible,

(ii) all the barns are connected together (so that it is possible to reach any barn from any other barn via a path of installed connections), and

(iii) so that there are no cycles among the connections (which Farmer John would easily be able to detect). Conditions (ii) and (iii) ensure that the final set of connections will look like a “tree”.

**Input**

* Line 1: Two space-separated integers: N and M

* Lines 2..M+1: Each line contains three space-separated integers A, B, and C that describe a connection route between barns A and B of cost C.

**Output**

* Line 1: A single integer, containing the price of the most expensive tree connecting all the barns. If it is not possible to connect all the barns, output -1.

Sample Input

5 8

1 2 3

1 3 7

2 3 10

2 4 4

2 5 8

3 4 6

3 5 2

4 5 17Sample Output

42Hint

OUTPUT DETAILS:

The most expensive tree has cost 17 + 8 + 10 + 7 = 42.

It uses the following connections:

4 to 5, 2 to 5, 2 to 3, and 1 to 3.

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