Count Subtrees With Max Distance Between Cities — LeetCode 1617 Python Solution

HardBit ManipulationTreeDynamic ProgrammingBitmaskEnumeration

Problem: #1617
Pattern: Bit Manipulation
Reading time: 6 min
Source: leetcode.com

The problem

There are n cities numbered from 1 to n. You are given an array edges of size n-1, where edges[i] = [ui, vi] represents a bidirectional edge between cities ui and vi.

Example

Input: n = 4, edges = [[1,2],[2,3],[2,4]]
Output: [3,4,0]
Explanation: The subtrees with subsets {1,2}, {2,3} and {2,4} have a max distance of 1.

Python solution

Python

class Solution:
    def countSubgraphsForEachDiameter(
        self, n: int, edges: List[List[int]]
    ) -> List[int]:
        def dfs(u: int, d: int = 0):
            nonlocal mx, nxt, msk
            if mx < d:
                mx, nxt = d, u
            msk ^= 1 << u
            for v in g[u]:
                if msk >> v & 1:
                    dfs(v, d + 1)

        g = defaultdict(list)
        for u, v in edges:
            u, v = u - 1, v - 1
            g[u].append(v)
            g[v].append(u)
        ans = [0] * (n - 1)
        nxt = mx = 0
        for mask in range(1, 1 << n):
            if mask & (mask - 1) == 0:
                continue
            msk, mx = mask, 0
            cur = msk.bit_length() - 1
            dfs(cur)
            if msk == 0:
                msk, mx = mask, 0
                dfs(nxt)
                ans[mx - 1] += 1
        return ans

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1617. Count Subtrees With Max Distance Between Cities is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1617. Count Subtrees With Max Distance Between Cities?: LeetCode 1617. Count Subtrees With Max Distance Between Cities is rated Hard on LeetCode.
What topics does LeetCode 1617. Count Subtrees With Max Distance Between Cities cover?: LeetCode 1617. Count Subtrees With Max Distance Between Cities is tagged Bit Manipulation, Tree, Dynamic Programming, Bitmask and Enumeration on LeetCode.