Added mst : kruskal, prim #1

Author: subinium

README.md

@@ -13,6 +13,8 @@
 
 ## Graph
 
+### ETC
+
 ### Shotest Path
 
 - [Floyd-Warshall](/graph/shortest_path/floyd_warshall.py)
@@ -22,6 +24,12 @@
 - [Bellman-Ford](/graph/shortest_path/bellman_ford.py)
   - [BOJ 11657 : 타임머신](https://www.acmicpc.net/problem/11657)
 
+### MST
+
+- [Kruskal](/graph/mst/kruskal.py)
+- [Prim](/graph/mst/prim.py)
+  - [BOJ 1197 : 최소 스패닝 트리](https://www.acmicpc.net/problem/1197)
+
 ## String
 
 - [KMP](/string/kmp.py)

graph/mst/kruskal.py

@@ -0,0 +1,36 @@
+# [BOJ 1197] 최소 스패닝 트리
+# link : https://www.acmicpc.net/problem/1197
+# tag : graph, mininum spanning tree, MST, kruskal, union find
+# @subinium
+
+import sys
+
+# Kruskal Algorithm
+def kruskal(v, edge):
+    edge = sorted(edge, key=lambda x: x[2])
+    parent = [i for i in range(v+1)]
+    result = 0
+
+    def find_(num):
+        if num == parent[num] : return num
+        parent[num] = find_(parent[num])
+        return parent[num]
+
+    def union_(a, b):
+        if a < b : parent[a] = b
+        else : parent[b] = a
+
+    for st, ed, val in edge:
+        v, w = find_(st), find_(ed)
+        if v == w : continue
+        union_(v, w)
+        result += val
+    
+    return result
+
+if __name__ == '__main__':
+    input = sys.stdin.readline 
+    V, E = map(int, input().split())
+    edge = [tuple(map(int, input().split())) for _ in range(E)]
+    result = kruskal(V, edge)
+    print(result)

graph/mst/prim.py

@@ -0,0 +1,36 @@
+# [BOJ 1197] 최소 스패닝 트리
+# link : https://www.acmicpc.net/problem/1197
+# tag : graph, mininum spanning tree, MST, prim, priority queue
+# @subinium
+
+import sys
+from heapq import heappush, heappop
+
+# Prim
+def prim(v, edge_raw):
+    checked = [False for _ in range(v+1)] 
+    edge = [[] for _ in range(v+1)]
+    for st, ed, val in edge_raw: 
+        edge[st].append((val, ed))
+        edge[ed].append((val, st))
+
+    pq = [(0, 1)]
+    result = 0
+    while pq:
+        val, node = heappop(pq)
+        if checked[node]: continue 
+        checked[node] = True
+        result += val
+        for val, ed in edge[node]:
+            if checked[ed] : continue
+            heappush(pq, (val, ed))
+
+    return result
+
+# Main
+if __name__ == '__main__':
+    input = sys.stdin.readline 
+    V, E = map(int, input().split())
+    edge = [tuple(map(int, input().split())) for _ in range(E)]
+    result = prim(V, edge)
+    print(result)