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Problem solution · Python

Count Connected Subgraphs with Even Node Sum

Count Connected Subgraphs with Even Node Sum: a Python solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Depth-first search
Source
Kamyu LeetCode Solutions
Length
75 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Count Connected Subgraphs with Even Node Sum, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 75 lines of Python from the credited upstream file count-connected-subgraphs-with-even-node-sum.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCount Connected Subgraphs with Even Node Sum · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O((n + e) * 2^n)# Space: O(n + e) # bitmask, dfsclass Solution(object):    def evenSumSubgraphs(self, nums, edges):        """        :type nums: List[int]        :type edges: List[List[int]]        :rtype: int        """        def even(mask):            def popcount(x):                return bin(x).count('1')             return not popcount(mask&odd_mask)%2            def connected(mask):            i = next(i for i in xrange(len(nums)) if mask&(1<<i))            mask ^= 1<<i            stk = [i]            while stk:                u = stk.pop()                for v in adj[u]:                    if not mask&(1<<v):                        continue                    mask ^= 1<<v                    stk.append(v)            return not mask         adj = [[] for _ in xrange(len(nums))]        for u, v in edges:            adj[u].append(v)            adj[v].append(u)        odd_mask = reduce(lambda accu, x: accu|(1<<x), (i for i in xrange(len(nums)) if nums[i]), 0)        return sum(even(mask) and connected(mask) for mask in xrange(1, 1<<len(nums)))  # Time:  O((n + e) * 2^n)# Space: O(n + e)# bitmask, dfsclass Solution2(object):    def evenSumSubgraphs(self, nums, edges):        """        :type nums: List[int]        :type edges: List[List[int]]        :rtype: int        """        def even(mask):            parity = 0            for i in xrange(len(nums)):                if not mask&(1<<i):                    continue                parity ^= nums[i]            return not parity            def connected(mask):            i = next(i for i in xrange(len(nums)) if mask&(1<<i))            mask ^= 1<<i            stk = [i]            while stk:                u = stk.pop()                for v in adj[u]:                    if not mask&(1<<v):                        continue                    mask ^= 1<<v                    stk.append(v)            return not mask         adj = [[] for _ in xrange(len(nums))]        for u, v in edges:            adj[u].append(v)            adj[v].append(u)        return sum(even(mask) and connected(mask) for mask in xrange(1, 1<<len(nums)))

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