feat: add kruskals algorithm for minimum spanning tree

Author: Rishabh672003

Data-Structures/Graphs/017.minium-spanning-tree-kruskal.py

@@ -0,0 +1,41 @@
+class Solution:
+    class DSU:
+        def __init__(self, n: int):
+            self.parents = list(range(n))
+            self.ranks = [0] * n
+
+        def find(self, u: int) -> int:
+            if u == self.parents[u]:
+                return u
+
+            self.parents[u] = self.find(self.parents[u])
+            return self.parents[u]
+
+        def union(self, u: int, v: int):
+            pU, pV = self.find(u), self.find(v)
+
+            if pU == pV:
+                return
+
+            if self.ranks[pU] < self.ranks[pV]:
+                self.parents[pU] = pV
+            elif self.ranks[pV] < self.ranks[pU]:
+                self.parents[pV] = pU
+            else:
+                self.parents[pU] = pV
+                self.ranks[pV] += 1
+
+    def spanningTree(self, V: int, edges: list[list[int]]) -> int:
+        dsu = self.DSU(V)
+
+        # sort by weights in ascending order
+        edges.sort(key=lambda x: x[2])
+        mst = 0
+
+        for u, v, weight in edges:
+            # if both are in different components union them
+            if dsu.find(u) != dsu.find(v):
+                dsu.union(u, v)
+                mst += weight
+
+        return mst