What is the time complexity of LeetCode 2959. Number of Possible Sets of Closing Branches?

The Python solution on this page runs in O(2^n \times (n^3 + m)).

What is the space complexity of LeetCode 2959. Number of Possible Sets of Closing Branches?

The Python solution on this page uses O(n^2) auxiliary space.

Number of Possible Sets of Closing Branches — LeetCode 2959 Python Solution

HardBit ManipulationGraphEnumerationShortest PathHeap (Priority Queue)

Problem: #2959
Pattern: Heap / Priority Queue
Reading time: 5 min
Source: leetcode.com

The problem

There is a company with n branches across the country, some of which are connected by roads. Initially, all branches are reachable from each other by traveling some roads.

Example

Input: n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]
Output: 5
Explanation: The possible sets of closing branches are:

Python solution

Python

class Solution:
    def numberOfSets(self, n: int, maxDistance: int, roads: List[List[int]]) -> int:
        ans = 0
        for mask in range(1 << n):
            g = [[inf] * n for _ in range(n)]
            for u, v, w in roads:
                if mask >> u & 1 and mask >> v & 1:
                    g[u][v] = min(g[u][v], w)
                    g[v][u] = min(g[v][u], w)
            for k in range(n):
                if mask >> k & 1:
                    g[k][k] = 0
                    for i in range(n):
                        for j in range(n):
                            # g[i][j] = min(g[i][j], g[i][k] + g[k][j])
                            if g[i][k] + g[k][j] < g[i][j]:
                                g[i][j] = g[i][k] + g[k][j]
            if all(
                g[i][j] <= maxDistance
                for i in range(n)
                for j in range(n)
                if mask >> i & 1 and mask >> j & 1
            ):
                ans += 1
        return ans

Complexity

Measure	Complexity
Time	O(2^n \times (n^3 + m))
Space	O(n^2) auxiliary

Pattern: Heap / Priority Queue

Keep only the best k elements, or always pull the smallest, in log time. LeetCode 2959. Number of Possible Sets of Closing Branches is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Heap (Priority Queue).

The heap / priority queue guide has the Python template for the pattern and the 163 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2959. Number of Possible Sets of Closing Branches?: LeetCode 2959. Number of Possible Sets of Closing Branches is rated Hard on LeetCode.
What is the time complexity of LeetCode 2959. Number of Possible Sets of Closing Branches?: The Python solution on this page runs in O(2^n \times (n^3 + m)).
What is the space complexity of LeetCode 2959. Number of Possible Sets of Closing Branches?: The Python solution on this page uses O(n^2) auxiliary space.
What topics does LeetCode 2959. Number of Possible Sets of Closing Branches cover?: LeetCode 2959. Number of Possible Sets of Closing Branches is tagged Bit Manipulation, Graph, Enumeration, Shortest Path and Heap (Priority Queue) on LeetCode.