53 lines
2.0 KiB
Python
53 lines
2.0 KiB
Python
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from collections import defaultdict
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class Solution:
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def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
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'''
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Key idea: if (a, b) indexes can be swapped and (b, c) indexes can
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be swapped, then (a, c) can be swapped so infinite swap across (a, b, c).
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Can be expanded to cover any other letters that are swappable.
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'''
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# Make the adjacency list
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swapmap = defaultdict(list)
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for i, j in pairs:
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swapmap[i].append(j)
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swapmap[j].append(i)
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def dfs(s, vertex, chars, vertices):
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chars.append(s[vertex])
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vertices.append(vertex)
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visited.add(vertex)
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for neighbor in swapmap[vertex]:
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if neighbor not in visited:
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dfs(s, neighbor, chars, vertices)
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output = [''] * len(s)
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visited = set()
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for vertex, _ in enumerate(s):
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if vertex not in visited:
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connected_chars = []
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connected_vertices = []
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dfs(s, vertex, connected_chars, connected_vertices)
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# This might seem confusing but remember that if we find one character
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# with the `vertex` connected (i.e swappable) with other characters, then
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# they can all be swapped with each other infinite times. Our goal is to
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# get the lexicographically smallest string (i.e most sorted) from doing
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# these allowed swaps. Hence, we can go ahead and safely sort the chars
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# obtained from DFS of vertex.
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connected_chars.sort()
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connected_vertices.sort()
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for i, connected_vertex in enumerate(connected_vertices):
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output[connected_vertex] = connected_chars[i]
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return ''.join(output)
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