Jungle Roads

Description

The Head Elder of the tropical island of Lagrishan has a problem. A burst of foreign aid money was spent on extra roads between villages some years ago. But the jungle overtakes roads relentlessly, so the large road network is too expensive to maintain. The Council of Elders must choose to stop maintaining some roads. The map above on the left shows all the roads in use now and the cost in aacms per month to maintain them. Of course there needs to be some way to get between all the villages on maintained roads, even if the route is not as short as before. The Chief Elder would like to tell the Council of Elders what would be the smallest amount they could spend in aacms per month to maintain roads that would connect all the villages. The villages are labeled A through I in the maps above. The map on the right shows the roads that could be maintained most cheaply, for 216 aacms per month. Your task is to write a program that will solve such problems.

Input

The input consists of one to 100 data sets, followed by a final line containing only 0. Each data set starts with a line containing only a number n, which is the number of villages, 1 < n < 27, and the villages are labeled with the first n letters of the alphabet, capitalized. Each data set is completed with n-1 lines that start with village labels in alphabetical order. There is no line for the last village. Each line for a village starts with the village label followed by a number, k, of roads from this village to villages with labels later in the alphabet. If k is greater than 0, the line continues with data for each of the k roads. The data for each road is the village label for the other end of the road followed by the monthly maintenance cost in aacms for the road. Maintenance costs will be positive integers less than 100. All data fields in the row are separated by single blanks. The road network will always allow travel between all the villages. The network will never have more than 75 roads. No village will have more than 15 roads going to other villages (before or after in the alphabet). In the sample input below, the first data set goes with the map above.

Output

The output is one integer per line for each data set: the minimum cost in aacms per month to maintain a road system that connect all the villages. Caution: A brute force solution that examines every possible set of roads will not finish within the one minute time limit.

Sample Input

9
A 2 B 12 I 25
B 3 C 10 H 40 I 8
C 2 D 18 G 55
D 1 E 44
E 2 F 60 G 38
F 0
G 1 H 35
H 1 I 35
3
A 2 B 10 C 40
B 1 C 20
0
 

Sample Output

216
30

叢林中的道路

題目描述

熱帶島嶼Lagrishan的長老們遇到了一個問題。在幾年前，有一大筆外援資金被用在了連接各個村莊之間道路上，可是有些道路是多余的，這就意味著島上要用一大筆資金來維護這些累贅的道路。更糟的是，這些道路還穿越了從林，長老會顯然承擔不起這麽大的財政開支，所以長老們開會決定，停止維護一些道路。左邊的地圖展示了現在所有道路以及每個月維護他們所需的費用。當然了，雖然道路沒有像以前那麽短，但是村莊與村莊之間肯定是連通的。長老會想知道連通所有村莊所需的最少費用。在上圖中，每個村莊被從A到I被編號，右圖展示了用在道路維護上的最少開支，只要217的花費。你的任務就是編寫一個程序來解決這個問題。

Input

輸入有多組，至多有100組輸入，輸入的最後一行只包含一個數字0。每組數據首先輸入一個整數n(1 $<$ n $<$ 26)，表示有n個村莊，用字母表的前n個大寫字母來為每個村莊標號。接下來的n-1行輸入，首先輸入村莊的編號，表示路的一端，然後輸入一個整數k，如果k大於0，那麽緊接著的是k條路的數據。每組路的數據首先是道路另一端村莊的編號，然後是路的維護成本，維護成本是一個小於100的正整數。輸入保證每個村莊都能到達其他村莊，道路數不超過75條，且沒有一個村莊有超過15條與其他村莊連接的道路。在輸入樣例中，第一組數據即為上圖所示的地圖。

Output

每組輸入對應一行輸出，每行輸出一個表示最小花費的整數。註意:若檢查每種可能的修建方案，程序可能無法在時間限制內結束運行。

Sample Input

9
A 2 B 12 I 25
B 3 C 10 H 40 I 8
C 2 D 18 G 55
D 1 E 44
E 2 F 60 G 38
F 0
G 1 H 35
H 1 I 35
3
A 2 B 10 C 40
B 1 C 20
0

Sample Output

216
30

POJ1251 Jungle Roads(翻譯)