Kurskal优化后的用法
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这是水题3
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.
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.
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
题意概括:
有n个村庄,输出将所有村庄联通最少需要多少花费。
解题分析:
这题最重要的是对数据的处理,要保证数据的输入正确,并将数据处理为1村庄到2村庄的dis这种形式,并存到结构体数组中以便套用Kurskal算法。但是用没有优化过的Kurskal的话很有可能会超时,所以要用优化后的Kurskal。
优化后的Kurskal算法讲解请访问:http://blog.csdn.net/k_young1997/article/details/76590545
代码:
#include<stdio.h>#include<algorithm>using namespace std;#define N 30struct edge{ int u, v, w;}stu[N*N];int parent[N*N];int cmp(edge a, edge b){ return a.w < b.w;}int Find(int x){ int s, tmp; for(s = x; parent[s] > 0; s = parent[s]); while(x != s){ tmp = parent[x]; parent[x] = s; x = tmp; } return s;}void Union(int R1, int R2){ int r1 = Find(R1), r2 = Find(R2); int tmp = parent[r1] + parent[r2]; if(parent[r1] > parent[r2]){ parent[r1] = r2; parent[r2] = tmp; } else{ parent[r2] = r1; parent[r1] = tmp; }}int Kruskal(int n, int m){ int i, sum, s; for(i = 0; i <= n; i++) parent[i] = -1; sort(stu, stu+m, cmp); for(i = sum = s = 0; i < m && s <= n-1; i++){ if(Find(stu[i].u) != Find(stu[i].v)){ sum += stu[i].w; s++; Union(stu[i].u, stu[i].v); } } return sum;}int main(){ int n, k, t, T, dis, num; char ch; while(scanf("%d", &n), n != 0){ t = 0; T = n-1; while(T--){ scanf(" %c%d ", &ch, &k);//数据的处理开始 num = ch-'A'+1; while(k--){ scanf(" %c%d", &ch, &dis); stu[t].u = num; stu[t].v = ch-'A'+1; stu[t].w = dis; t++; } } printf("%d\n",Kruskal(n, t)); } return 0;}
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