diff --git a/apps/docs/content/union-find/323-number-of-connected-components-in-an-undirected-graph.mdx b/apps/docs/content/union-find/323-number-of-connected-components-in-an-undirected-graph.mdx new file mode 100644 index 0000000..909ecc9 --- /dev/null +++ b/apps/docs/content/union-find/323-number-of-connected-components-in-an-undirected-graph.mdx @@ -0,0 +1,58 @@ +--- +title: '323. Number of Connected Components in an Undirected Graph' +description: You have a graph of n nodes. You are given an integer n and an array edges where edges[i] = [ai, bi] indicates that there is an edge between ai and bi in the graph +sidebar: + label: 'Number of Connected Components in an Undirected Graph' + badge: 'Medium' +--- + +Depth-First Search + +### Example 1: +- Input: `n = 5, edges = [[0,1],[1,2],[3,4]]` +- Output: `2` + +### Example 2: +- Input: `n = 5, edges = [[0,1],[1,2],[2,3],[3,4]]` +- Output: `1` + +### Constraints: + +- `1 <= n <= 2000` +- `1 <= edges.length <= 5000` +- `edges[i]` = [ai, bi] +- `ai != bi` +- There are no repeated edges. + +## Solution + +```py +class Solution: + def countComponents(self, n: int, edges: list[list[int]]) -> int: + par = [i for i in range(n + 1)] + rank = [1] * (n + 1) + + def find(n): + res = n + while res != par[res]: + par[res] = par[par[res]] + res = par[res] + return res + + def union(n1, n2): + p1, p2 = find(n1), find(n2) + if p1 == p2: + return 0 + if rank[p1] > rank[p2]: + par[p2] = p1 + rank[p1] += rank[p2] + else: + par[p1] = p2 + rank[p2] += rank[p1] + return 1 + + res = n + for n1, n2 in edges: + res -= union(n1, n2) + return res +``` diff --git a/work/1/Medium/Depth-First Search/323.number-of-connected-components-in-an-undirected-graph.py b/work/1/Medium/Depth-First Search/323.number-of-connected-components-in-an-undirected-graph.py new file mode 100644 index 0000000..04ae21f --- /dev/null +++ b/work/1/Medium/Depth-First Search/323.number-of-connected-components-in-an-undirected-graph.py @@ -0,0 +1,69 @@ +""" +323. Number of Connected Components in an Undirected Graph +Difficulty: Medium +https://leetcode.com/problems/number-of-connected-components-in-an-undirected-graph/ + +────────────────────────────────────────────────── + +You have a graph of n nodes. You are given an integer n and an array +edges where edges[i] = [ai, bi] indicates that there is an edge +between ai and bi in the graph. + +Return the number of connected components in the graph. + + + +Example 1: + +Input: n = 5, edges = [[0,1],[1,2],[3,4]] +Output: 2 + +Example 2: + +Input: n = 5, edges = [[0,1],[1,2],[2,3],[3,4]] +Output: 1 + + + +Constraints: + + • 1 <= n <= 2000 + + • 1 <= edges.length <= 5000 + + • edges[i] = [ai, bi] + + • ai != bi + + • There are no repeated edges. +""" + + +class Solution: + def countComponents(self, n: int, edges: list[list[int]]) -> int: + par = [i for i in range(n + 1)] + rank = [1] * (n + 1) + + def find(n): + res = n + while res != par[res]: + par[res] = par[par[res]] + res = par[res] + return res + + def union(n1, n2): + p1, p2 = find(n1), find(n2) + if p1 == p2: + return 0 + if rank[p1] > rank[p2]: + par[p2] = p1 + rank[p1] += rank[p2] + else: + par[p1] = p2 + rank[p2] += rank[p1] + return 1 + + res = n + for n1, n2 in edges: + res -= union(n1, n2) + return res