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Problem solution · Python

Incremental Even Weighted Cycle Queries

Incremental Even Weighted Cycle Queries: a Python solution using disjoint set union. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Disjoint set union
Source
Kamyu LeetCode Solutions
Length
45 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

Disjoint set union

For Incremental Even Weighted Cycle Queries, the implementation maintains connected components and merges them as relationships are processed.

  1. Give each element a component representative.
  2. Merge representatives when a connection is accepted.
  3. Answer connectivity or component queries from the compressed representatives.

Code notes

  • 45 lines of Python from the credited upstream file incremental-even-weighted-cycle-queries.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Account for every find and union operation; with path compression and ranked merging, the amortized cost is nearly constant per operation.

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 codeIncremental Even Weighted Cycle Queries · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n + e)# Space: O(n) # union findclass Solution(object):    def numberOfEdgesAdded(self, n, edges):        """        :type n: int        :type edges: List[List[int]]        :rtype: int        """        class UnionFind(object):  # Time: O(n * alpha(n)), Space: O(n)            def __init__(self, n):                self.set = range(n)                self.rank = [0]*n                self.parity = [0]*n  # added             def find_set(self, x):                stk = []                while self.set[x] != x:  # path compression                    stk.append(x)                    x = self.set[x]                prev = self.parity[x]  # added                while stk:                    self.parity[stk[-1]] ^= prev  # added                    prev = self.parity[stk[-1]]  # added                    self.set[stk.pop()] = x                return x             def union_set(self, x, y, w):                x0, y0 = x, y                x, y = self.find_set(x), self.find_set(y)                if x == y:                    return self.parity[x0]^w^self.parity[y0] == 0  # modified                if self.rank[x] > self.rank[y]:  # union by rank                    x, y = y, x                elif self.rank[x] == self.rank[y]:                    self.rank[y] += 1                self.set[x] = self.set[y]                self.parity[x] = self.parity[x0]^w^self.parity[y0]  # added                return True            uf = UnionFind(n)        return sum(uf.union_set(u, v, w) for u, v, w in edges)

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