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58 lines
1.8 KiB
Python
58 lines
1.8 KiB
Python
# calculate palindromic length from center with incrementing difference
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def palindromic_length(center, diff, string):
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if (
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center - diff == -1
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or center + diff == len(string)
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or string[center - diff] != string[center + diff]
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):
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return 0
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return 1 + palindromic_length(center, diff + 1, string)
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def palindromic_string(input_string):
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"""
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Manacher’s algorithm which finds Longest Palindromic Substring in linear time.
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1. first this convert input_string("xyx") into new_string("x|y|x") where odd
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positions are actual input characters.
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2. for each character in new_string it find corresponding length and store,
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a. max_length
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b. max_length's center
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3. return output_string from center - max_length to center + max_length and remove
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all "|"
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"""
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max_length = 0
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# if input_string is "aba" than new_input_string become "a|b|a"
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new_input_string = ""
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output_string = ""
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# append each character + "|" in new_string for range(0, length-1)
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for i in input_string[: len(input_string) - 1]:
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new_input_string += i + "|"
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# append last character
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new_input_string += input_string[-1]
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# for each character in new_string find corresponding palindromic string
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for i in range(len(new_input_string)):
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# get palindromic length from i-th position
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length = palindromic_length(i, 1, new_input_string)
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# update max_length and start position
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if max_length < length:
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max_length = length
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start = i
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# create that string
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for i in new_input_string[start - max_length : start + max_length + 1]:
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if i != "|":
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output_string += i
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return output_string
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if __name__ == "__main__":
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n = input()
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print(palindromic_string(n))
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