From adc34fb2f50db35891460d482b260957b797a41c Mon Sep 17 00:00:00 2001
From: Leehouc <152672308+Leehouc@users.noreply.github.com>
Date: Wed, 4 Sep 2024 17:43:22 +0800
Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A00053.=E5=AF=BB=E5=AE=9D-Krusk?=
 =?UTF-8?q?al.mdC=E8=AF=AD=E8=A8=80=E6=96=B9=E6=B3=95=E4=BA=8C?=
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---
 problems/kamacoder/0053.寻宝-Kruskal.md | 63 +++++++++++++++++++++++
 1 file changed, 63 insertions(+)

diff --git a/problems/kamacoder/0053.寻宝-Kruskal.md b/problems/kamacoder/0053.寻宝-Kruskal.md
index 7a693882..52724956 100644
--- a/problems/kamacoder/0053.寻宝-Kruskal.md
+++ b/problems/kamacoder/0053.寻宝-Kruskal.md
@@ -634,3 +634,66 @@ int main()
 }
 
 ```
+并查集方法二
+```c
+// 定义边结构体，包含两个顶点vex1和vex2以及它们之间的权重val （略，同上）
+// 冒泡排序函数，用于按边的权重val不减序排序边数组（略，同上）
+
+// 并查集的查找操作
+int find(int m, int *father)
+{ // 如果当前节点是其自身的父节点，则直接返回该节点
+    // 否则递归查找其父节点的根，并将当前节点直接连接到根节点
+    return (m == father[m]) ? m : (father[m] = find(father[m], father)); // 路径压缩
+}
+
+// 并查集的加入集合
+void Union(int m, int n, int *father)
+{
+    int x = find(m, father);
+    int y = find(n, father);
+    if (x == y)
+        return; // 如果发现根相同，则说明在一个集合，不用两个节点相连直接返回
+    father[y] = x;
+}
+
+int main()
+{
+    int v, e;
+    int v1, v2, val;
+    int ret = 0;
+
+    scanf("%d%d", &v, &e);
+    struct Edge *edg = (struct Edge *)malloc(sizeof(struct Edge) * e);
+    int *conne_gra = (int *)malloc(sizeof(int) * (v + 1));
+    // 初始化连通图数组，每个顶点初始时只与自己相连通
+    for (int i = 0; i <= v; ++i)
+    {
+        conne_gra[i] = i;
+    }
+    // 读取所有边的信息并存储到edg（存储所有边）数组中
+    for (int i = 0; i < e; ++i)
+    {
+        scanf("%d%d%d", &v1, &v2, &val);
+        edg[i].vex1 = v1;
+        edg[i].vex2 = v2;
+        edg[i].val = val;
+    }
+    bubblesort(edg, e); // 调用冒泡排序函数对边进行排序
+
+    // Kruskal算法的实现，通过边数组构建最小生成树
+    int j = 0, count = 0;
+    while (v > 1)
+    {
+        if (find(edg[j].vex1, conne_gra) != find(edg[j].vex2, conne_gra))
+        {
+            ret += edg[j].val; // 将当前边的权重加到最小生成树的权重中
+            Union(edg[j].vex1, edg[j].vex2, conne_gra);
+            v--;
+        }
+        j++;
+    }
+    printf("%d", ret);
+    return 0;
+}
+
+```