Given n strings, concatenate them in an order that produces the lexicographically smallest possible string.
Input : a = ["c", "cb", "cba"] Output : cbacbc Possible strings are ccbcba, ccbacb, cbccba, cbcbac, cbacbc and cbaccb. Among all these strings, cbacbc is the lexicographically smallest. Input : a = ["aa", "ab", "aaa"] Output : aaaaaab
One might think that sorting the given strings in the lexicographical order and then concatenating them produces the correct output. This approach produces the correct output for inputs like [“a”, “ab”, “abc”]. However, applying this method on [“c”, “cb”, “cba”] produces the wrong input and hence this approach is incorrect.
The correct approach is to use a regular sorting algorithm. When two strings a and b are compared to decide if they have to be swapped or not, do not check if a is lexicographically smaller than b or not. Instead check if appending b at the end of a produces a lexicographically smaller string or appending a at the end of b does. This approach works because we want the concatenated string to be lexicographically small, not the individual strings to be in the lexicographical order.
# Python 3 code to find the lexicographically
# smallest string
def lexSmallest(a, n):
# Sort strings using above compare()
a.sort(reverse = True)
# Concatenating sorted strings
answer = “”
for i in range( n):
answer += a[i]
# Driver code
if __name__ == “__main__”:
a = [ “c”, “cb”, “cba” ]
n = len(a)
# This code is contributed by ita_c
Time complexity : The above code runs inO(M * N * logN) where N is number of strings and M is maximum length of a string.
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