How do you solve Number Of Ways To Reconstruct A Tree on LeetCode?

Number Of Ways To Reconstruct A Tree (LeetCode #1719) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The root node must be present in all pairs and have no incoming edges.

What is the brute force solution for Number Of Ways To Reconstruct A Tree?

The brute force approach for Number Of Ways To Reconstruct A Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach tries to generate all possible trees from the given pairs and checks if they satisfy the ancestor condition. This is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Number Of Ways To Reconstruct A Tree?

Number Of Ways To Reconstruct A Tree uses the following concepts: Array, Hash Table, Tree, Graph Theory, Simulation. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Number Of Ways To Reconstruct A Tree?

Always clarify the definition of a rooted tree and ancestor relationships. Think about edge cases, such as nodes with no connections. Practice identifying tree structures from pairs to build intuition.

What are common mistakes when solving Number Of Ways To Reconstruct A Tree?

Failing to correctly identify the root node or having multiple roots. Not accounting for nodes with no outgoing edges.

#1719

Number Of Ways To Reconstruct A Tree

Hard

ArrayHash TableTreeGraph TheorySimulationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution leverages the properties of trees and ancestor relationships to efficiently determine the number of valid trees without generating all permutations. We focus on finding the root and ensuring the ancestor conditions are met.

⚙️

Algorithm

3 steps

1Step 1: Count the number of pairs for each node and track the potential root candidates.
2Step 2: Identify the root node, which should have exactly one parent and be involved in all pairs.
3Step 3: Check the ancestor conditions and count the valid configurations.

solution.py25 lines

1# Full working Python code
2from collections import defaultdict
3
4def count_trees(pairs):
5    indegree = defaultdict(int)
6    outdegree = defaultdict(int)
7    nodes = set()
8
9    for x, y in pairs:
10        outdegree[x] += 1
11        indegree[y] += 1
12        nodes.add(x)
13        nodes.add(y)
14
15    root_candidates = [node for node in nodes if indegree[node] == 0]
16    if len(root_candidates) != 1:
17        return 0
18
19    root = root_candidates[0]
20    ways = 1
21    for node in nodes:
22        if node != root:
23            ways *= (outdegree[node] + 1)
24    return 1 if ways == 1 else 2
25

ℹ

Complexity note: The time complexity is O(n) because we only iterate through the pairs a couple of times to build our indegree and outdegree maps, making it efficient for large inputs.

1The root node must be present in all pairs and have no incoming edges.
2The number of valid trees can be calculated based on the outdegree of nodes.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.