uva1349 - Optimal Bus Route Design
出處 ： https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4095
A big city wants to improve its bus transportation system. One of the improvement is to add scenic routes which go es through attractive places. Your task is to construct a bus-route-plan for sight-seeing buses in a city.
You are given a set of scenic lo cations. For each of these given lo cations, there should be only one bus route that passes this lo cation, and that bus route should pass this lo cation exactly once. The number of bus routes is unlimited. However, each route should contain at least two scenic lo cations.
From location i to location j , there may or may not be a connecting street. If there is a street from location i to location j , then we sayj is an out-neighbor of i . The length of the street from i to j is d (i, j) . The streets might be one way. So it may happen that there is a street from i to j , but no street from j to i . In case there is a street from i to j and also a street from j to i , the lengths d (i, j) and d (j, i)might be different. The route of each bus must follow the connecting streets and must be a cycle. For example, the route of Bus A might be from location 1 to location 2, from location 2 to location 3, and then from location 3 to location 1. The route of Bus B might be from location 4 to location 5, then from location 5 to location 4. The length of a bus route is the sum of the lengths of the streets in this bus route. The total length of the bus-route-plan is the sum of the lengths of all the bus routes used in the plan. A bus-route-plan is optimal if it has the minimum total length. You are required to compute the total length of an optimal bus-route-plan.
Input
The input file consists of a number of test cases. The first line of each test case is a positive integer n , which is the number of locations. These n locations are denoted by positive integers 1, 2,..., n . The next n lines are information about connecting streets between these lo cations. The i -th line of these n lines consists of an even number of positive integers and a 0 at the end. The first integer is a lo cation j which is an out-neighbor of location i , and the second integer is d (i, j) . The third integer is another location j'which is an out-neighbor of i , and the fourth integer is d (i, j') , and so on. In general, the (2k - 1) th integer is a location t which is an out-neighbor of location i , and the 2k th integer is d (i, t) .
The next case starts immediately after these n lines. A line consisting of a single `0' indicates the end of the input file.
Each test case has at most 99 locations. The length of each street is a positive integer less than 100.
Output
The output contains one line for each test case. If the required bus-route-plan exists, then the output is a positive number, which is the total length of an optimal bus-route-plan. Otherwise, the output is a letter `N'.
Sample Input
3
2 2 3 1 0
1 1 3 2 0
1 3 2 7 0
8
2 3 3 1 0
3 3 1 1 4 4 0
1 2 2 7 0
5 4 6 7 0
4 4 3 9 0
7 4 8 5 0
6 2 5 8 8 1 0
6 6 7 2 0
3
2 1 0
3 1 0
2 1 0
0
Sample Output
7
25
N
解題策略
最小權重的二分圖完美匹配，來源點在2*n+1，目標點在T=2*n+2，n為點的個數，根據題目敘述，點j到點a，流量為1，花費為c，j等於1~n；點S到點j，流量為1，花費為0，點S為出發點，j等於1~n；點n+j到點T，流量為1，花費為0，點T為目標點，j等於1~n。
不斷找出最小花費的最大流量，maxF回傳true就繼續找下一條路徑的花費。