# ---
# title: 1489. Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree
# id: problem1489
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Depth-first Search, Union Find
# link: <https://leetcode.com/problems/find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree/description/>
# hidden: true
# ---
# 
# Given a weighted undirected connected graph with `n` vertices numbered from
# `0` to `n - 1`, and an array `edges` where `edges[i] = [ai, bi, weighti]`
# represents a bidirectional and weighted edge between nodes `ai` and `bi`. A
# minimum spanning tree (MST) is a subset of the graph's edges that connects all
# vertices without cycles and with the minimum possible total edge weight.
# 
# Find _all the critical and pseudo-critical edges in the given graph 's minimum
# spanning tree (MST)_. An MST edge whose deletion from the graph would cause
# the MST weight to increase is called a  _critical edge_. On the other hand, a
# pseudo-critical edge is that which can appear in some MSTs but not all.
# 
# Note that you can return the indices of the edges in any order.
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2020/06/04/ex1.png)
# 
#     
#     
#     Input: n = 5, edges = [[0,1,1],[1,2,1],[2,3,2],[0,3,2],[0,4,3],[3,4,3],[1,4,6]]
#     Output: [[0,1],[2,3,4,5]]
#     Explanation: The figure above describes the graph.
#     The following figure shows all the possible MSTs:
#     ![](https://assets.leetcode.com/uploads/2020/06/04/msts.png)
#     Notice that the two edges 0 and 1 appear in all MSTs, therefore they are critical edges, so we return them in the first list of the output.
#     The edges 2, 3, 4, and 5 are only part of some MSTs, therefore they are considered pseudo-critical edges. We add them to the second list of the output.
#     
# 
# **Example 2:**
# 
# ![](https://assets.leetcode.com/uploads/2020/06/04/ex2.png)
# 
#     
#     
#     Input: n = 4, edges = [[0,1,1],[1,2,1],[2,3,1],[0,3,1]]
#     Output: [[],[0,1,2,3]]
#     Explanation: We can observe that since all 4 edges have equal weight, choosing any 3 edges from the given 4 will yield an MST. Therefore all 4 edges are pseudo-critical.
#     
# 
# 
# 
# **Constraints:**
# 
#   * `2 <= n <= 100`
#   * `1 <= edges.length <= min(200, n * (n - 1) / 2)`
#   * `edges[i].length == 3`
#   * `0 <= ai < bi < n`
#   * `1 <= weighti <= 1000`
#   * All pairs `(ai, bi)` are **distinct**.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
