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Problem solution · Python

Longest Palindromic Path in Graph

Longest Palindromic Path in Graph: a Python solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Dynamic programming
Source
Kamyu LeetCode Solutions
Length
50 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

Dynamic programming

For Longest Palindromic Path in Graph, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 50 lines of Python from the credited upstream file longest-palindromic-path-in-graph.py.
  • The implementation visibly relies on sequence storage, cached states.
  • No explicit loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

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 codeLongest Palindromic Path in Graph · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n^4 * 2^n)# Space: O(n + e) # bitmasks, dp, freq tableclass Solution(object):    def maxLen(self, n, edges, label):        """        :type n: int        :type edges: List[List[int]]        :type label: str        :rtype: int        """        def popcount(x):            return bin(x).count('1')         if len(edges) == n*(n-1)//2:  # to improve performance            cnt = [0]*26            for x in label:                cnt[ord(x)-ord('a')] += 1            return 2*sum(c//2 for c in cnt)+1*any(c%2 for c in cnt)         adj = [[] for _ in xrange(n)]        for u, v in edges:            adj[u].append(v)            adj[v].append(u)        dp = [[[False]*n for _ in xrange(n)]for _ in xrange(1<<n)]        for u in xrange(n):            dp[1<<u][u][u] = True        for u, v in edges:            if label[u] == label[v]:                dp[(1<<u)|(1<<v)][min(u, v)][max(u, v)] = True        result = 0        for mask in xrange(1, 1<<n):            for u in xrange(n):                for v in xrange(u, n):                    if not dp[mask][u][v]:                        continue                    result = max(result, popcount(mask))                    for nu in adj[u]:                        if mask&(1<<nu):                            continue                        for nv in adj[v]:                            if mask&(1<<nv):                                continue                            if nu == nv:                                continue                            if label[nu] == label[nv]:                                dp[mask|(1<<nu)|(1<<nv)][min(nu, nv)][max(nu, nv)] = True        return result

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