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题目
设计电动汽车的电池容量,已知有n个城市,每个城市都有充电站,m条双向道路(可能两个城市间有多条道路),求最小的电池容量。
分析
最小生成树。利用kruskal算法,记录最后加入树的边长即可;如果并查集中的节点数量不是城市数量,则有的城市不连通,输出IMPOSIBALE。
说明
注意数据大小,防止RE。。。
#include <algorithm>
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int data_size = 1000001;
typedef struct _enode
{
int point1;
int point2;
int weight;
}enode;
enode edge[data_size];
//union_set
int union_sets[data_size];
int union_rank[data_size];
int union_size[data_size];
void union_initial(int a, int b)
{
for (int i = a; i <= b; ++ i) {
union_sets[i] = i;
union_rank[i] = 0;
union_size[i] = 1;
}
}
int union_find(int a)
{
if (a != union_sets[a]) {
union_sets[a] = union_find(union_sets[a]);
}
return union_sets[a];
}
void union_merge(int a, int b)
{
if (union_rank[a] < union_rank[b]) {
union_sets[a] = b;
union_size[b] += union_size[a];
} else {
if (union_rank[a] == union_rank[b]) {
union_rank[a] ++;
}
union_sets[b] = a;
union_size[a] += union_size[b];
}
}
//end_union_set
int cmp_e(enode a, enode b)
{
return a.weight < b.weight;
}
void kruskal(int n, int m)
{
if (m) {
sort(edge, edge+m, cmp_e);
}
union_initial(0, n-1);
int ans = 0;
for (int i = 0; i < m; ++ i) {
int A = union_find(edge[i].point1);
int B = union_find(edge[i].point2);
if (A != B) {
union_merge(A, B);
ans = edge[i].weight;
}
}
if (union_size[union_find(0)] != n) {
puts("IMPOSSIBLE");
} else {
printf("%d\n", ans);
}
}
int main()
{
int n, m, a, b, c;
while (scanf("%d%d", &n, &m) && n+m) {
for (int i = 0; i < m; ++ i) {
scanf("%d%d%d", &a, &b, &c);
edge[i].point1 = a;
edge[i].point2 = b;
edge[i].weight = c;
}
kruskal(n, m);
}
return 0;
}