119 lines
2.3 KiB
C
119 lines
2.3 KiB
C
#include <stdio.h>
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#include <stdlib.h>
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#ifdef _WIN32
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#include <windows.h>
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#endif
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// 图的边的表示
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typedef struct
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{
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int u, v;
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int w;
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} Edge;
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// 边的比较函数，用于排序
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static int cmp_edge(const void *a, const void *b)
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{
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int wa = ((const Edge *)a)->w;
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int wb = ((const Edge *)b)->w;
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return (wa > wb) - (wa < wb);
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}
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// 并查集的查找函数
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static int find(int *parent, int x)
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{
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if (parent[x] == x)
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{
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return x;
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}
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return parent[x] = find(parent, parent[x]);
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}
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// 并查集的合并函数
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static void unite(int *parent, int *sz, int a, int b)
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{
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if (sz[a] < sz[b])
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{
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int t = a;
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a = b;
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b = t;
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}
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parent[b] = a;
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sz[a] += sz[b];
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}
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int main(void)
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{
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#ifdef _WIN32
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system("chcp 65001 > nul");
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SetConsoleOutputCP(65001);
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SetConsoleCP(65001);
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#endif
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// 读取图的边数和节点数
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int n, m;
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if (scanf("%d %d", &n, &m) != 2)
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{
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printf("输入错误\n");
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return 0;
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}
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// 读取图的边
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Edge *e = (Edge *)malloc((size_t)m * sizeof(Edge));
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for (int i = 0; i < m; ++i)
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{
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int u, v, w;
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scanf("%d %d %d", &u, &v, &w);
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e[i].u = u;
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e[i].v = v;
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e[i].w = w;
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}
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// 初始化并查集
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int *parent = (int *)malloc((size_t)(n + 1) * sizeof(int));
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int *sz = (int *)malloc((size_t)(n + 1) * sizeof(int));
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for (int i = 1; i <= n; ++i)
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{
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parent[i] = i;
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sz[i] = 1;
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}
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// 对边按权重排序
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qsort(e, (size_t)m, sizeof(Edge), cmp_edge);
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// 最小生成树的计算
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long long ans = 0;
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int cnt = 0;
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for (int i = 0; i < m && cnt < n - 1; ++i)
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{
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// 跳过无效的边
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int u = e[i].u, v = e[i].v;
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if (u < 1 || u > n || v < 1 || v > n)
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{
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continue;
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}
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// 检查是否形成环
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int ru = find(parent, u), rv = find(parent, v);
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if (ru != rv)
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{
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ans += e[i].w;
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unite(parent, sz, ru, rv);
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++cnt;
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}
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}
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// 检查是否所有节点都在最小生成树中
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if (cnt == n - 1)
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{
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printf("%lld\n", ans);
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}
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else
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{
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printf("impossible\n");
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}
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free(sz);
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free(parent);
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free(e);
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return 0;
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} |