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z7Lo#t2g>f2p_ql<4fsJGZggR07}gTuaxA=mFRZtPmR0T_5&mK0cAt2v_8m9Cw-S?| zz~hjws0jToW4T45K0}qBMZO2r}sPeh9-Jl)o*?UR)iV4{T!a#m$jhg&0E<;kv+IQ{{sw zPhvSiJ%lI>uq7H2h$OF)+u)jEoG@K zRAboc3DZUQcwd!V2x1H$nN`ki2(cBO+y#&CQbsc{mo-#6LMw%K59Wr2(UMbQpPz?z z6Xv&IS4Q~E!zn+yBy@W)Qv@5k5Wc&ooV|Xd?rO#!m~r)MW05jh0Fxc27k9b24ZVJf zS3gH^^=s4@Um$6m$C^IX^*%8!+-<2MwEHD;+T&&w@}ZLR4RNaY0d%^8h%%fL&TqnK z7W$qb!~3}U>T?uw!s7f}tTu!*o5FZj2|b|{IszSehR}ol!pmIw=D%U}rQb!>)t7-_ z0(b33vT$KtSlV`qbJcnjG6B6_N?Kci1Uh}8nI;d9*Z=?lYe_^wRJau9K3arb<3ghemsa4lbz!yZLI9g8#J(fjb(cHGHc;}Fc4DYm<*kmek%Aa_ zvn7-~xRJWG7F1Wr1~8HlwmQm01e2kX_hBrAabH<&8(N7#3Vn4W5V0t^P}uCc72dLz zmb%)!dxnKaKl6|H)h~XQXa486c>Rx`!}DRbEVL7)(pIu!cy)D|t|}t~6XZvXtJ5%i)L z5{Z!WeLQ2B3?e2yWg~H#`&ODzN%{m{z*d})Gai9JFsPdASy#(A;s^M~ZHDEHA>+AL z3NeuPEX6=kqj-@=5N4S0dQ=h*QAfN}+?Yz7f{5T@QQVr1d`I3xAEE$SiBC^`JPe6d z0z5oYMu&#TWJ79gWqo^-n=MOghoHZwuoLLMgB|SP=NbP8i9JpB?5t&+00000NkvXX Hu0mjfzxw=J From 0aef492602166223d8b8c8f9adf74dfbe9a7b4ee Mon Sep 17 00:00:00 2001 From: Sayantan Date: Tue, 8 Oct 2019 20:51:40 +0530 Subject: [PATCH 2/9] Longest Palindromic Substring in Python --- .../p/python/longest_palindrome_substring.py | 33 +++++++++++++++++++ 1 file changed, 33 insertions(+) create mode 100644 archive/p/python/longest_palindrome_substring.py diff --git a/archive/p/python/longest_palindrome_substring.py b/archive/p/python/longest_palindrome_substring.py new file mode 100644 index 000000000..3b025d640 --- /dev/null +++ b/archive/p/python/longest_palindrome_substring.py @@ -0,0 +1,33 @@ +""" +Given a string S, find the longest palindromic substring in S. +""" +def longestPalindrome(string): + longest = "" + + centres = [len(string) - 1] + for diff in range(1, len(string)): + centres.append(centres[0] + diff) + centres.append(centres[0] - diff) + + for centre in centres: + + if(min(centre + 1, 2 * len(string) - 1 - centre) <= len(longest)): + break + if centre % 2 == 0: + left, right = (centre // 2) - 1, (centre // 2) + 1 + else: + left, right = centre // 2, (centre // 2) + 1 + + while left >= 0 and right < len(string) and string[left] == string[right]: + left -= 1 + right += 1 + + if right - left > len(longest): + longest = string[left + 1: right] + + return longest + +if __name__ == '__main__': + string = str(input("Enter String: ")) + sub = longestPalindrome(string) + print("Longest Palindromic Substring is: {}".format(sub)) \ No newline at end of file From 5ebee8f231c1e827e0967706470153e46a33ce75 Mon Sep 17 00:00:00 2001 From: Sayantan Date: Wed, 9 Oct 2019 21:52:01 +0530 Subject: [PATCH 3/9] Updated longest palindrome substring --- archive/p/python/longest_palindrome_substring.py | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/archive/p/python/longest_palindrome_substring.py b/archive/p/python/longest_palindrome_substring.py index 3b025d640..e72c75870 100644 --- a/archive/p/python/longest_palindrome_substring.py +++ b/archive/p/python/longest_palindrome_substring.py @@ -29,5 +29,10 @@ def longestPalindrome(string): if __name__ == '__main__': string = str(input("Enter String: ")) + if string == "" and string == None: + print("Incorrect input provided. Program Terminated") sub = longestPalindrome(string) - print("Longest Palindromic Substring is: {}".format(sub)) \ No newline at end of file + if len(sub) == 1: + print("No Palindromic substring present.") + else: + print("Longest Palindromic Substring is: {}".format(sub)) From f267991bb7a9ffcb0502ac98cb0f7550584115ae Mon Sep 17 00:00:00 2001 From: Sayantan Date: Wed, 9 Oct 2019 21:52:59 +0530 Subject: [PATCH 4/9] Documentation for Longest Palindromic Substring --- .../longest-palindrome-substring/index.md | 42 +++++++++++++++++++ 1 file changed, 42 insertions(+) create mode 100644 docs/projects/longest-palindrome-substring/index.md diff --git a/docs/projects/longest-palindrome-substring/index.md b/docs/projects/longest-palindrome-substring/index.md new file mode 100644 index 000000000..347139c48 --- /dev/null +++ b/docs/projects/longest-palindrome-substring/index.md @@ -0,0 +1,42 @@ +--- +title: Longest Palindromic Substring in Every Language +layout: default +date: 2019-10-08 +last-modified: 2018-10-09 +featured-image: +tags: [longest-palindrome-substring] +authors: Sayantan Paul(https://github.com/belikesayantan) +--- +Given a string, we need to find the smallest substring inside the main string which is a palindrome. +Palindrome is a phenomenon, where a string has same sequence of letters when read start --> end and end --> start. + +## Example + +Let's say we have a string, + +``` +s = 'paapaapap' +``` +Here, we have seven palindromic substrings. +``` +sub_1 = 'aa' +sub_2 = 'paap' +sub_3 = 'paapaap' +sub_4 = 'aapaa' +sub_5 = 'apap' +sub_6 = 'pap' +sub_7 = 'apaapa' +``` +Out of the seven, `sub_3 = 'paapaap'` is the longest. hence the output would be `'paapaap'` + +## Testing + +The following table contains various test cases that you can use to verify the correctness of your solution: + +| Description | Input | Output | +|-------------|-------|--------| +| No Input | |"Incorrect input provided. Program Terminated"| +|Empty String|""|"Incorrect input provided. Program Terminated"| +|Non-Palindromic string with initial capital letters|"Polip"|"No Palindromic substring present."| +|Palindromic string with disordered casing|"BoOroO"|"No Palindromic substring present."| +|Palindromic string with letters and numerics|"6eie6o6"|"Longest Palindromic Substring is: 6eie6"| From cb44f04a3e1afaefa2c1939e18364c342371dd69 Mon Sep 17 00:00:00 2001 From: Sayantan Paul Date: Wed, 9 Oct 2019 22:01:49 +0530 Subject: [PATCH 5/9] updated index.md --- docs/projects/longest-palindrome-substring/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/projects/longest-palindrome-substring/index.md b/docs/projects/longest-palindrome-substring/index.md index 347139c48..2114c0cac 100644 --- a/docs/projects/longest-palindrome-substring/index.md +++ b/docs/projects/longest-palindrome-substring/index.md @@ -5,7 +5,7 @@ date: 2019-10-08 last-modified: 2018-10-09 featured-image: tags: [longest-palindrome-substring] -authors: Sayantan Paul(https://github.com/belikesayantan) +authors: Sayantan Paul --- Given a string, we need to find the smallest substring inside the main string which is a palindrome. Palindrome is a phenomenon, where a string has same sequence of letters when read start --> end and end --> start. From 26a0692745793849a3d59a26b040caaf9f19d5f5 Mon Sep 17 00:00:00 2001 From: Sayantan Date: Thu, 10 Oct 2019 15:36:47 +0530 Subject: [PATCH 6/9] updated index.md --- .../longest-palindrome-substring/index.md | 30 ++++++++++++++++++- 1 file changed, 29 insertions(+), 1 deletion(-) diff --git a/docs/projects/longest-palindrome-substring/index.md b/docs/projects/longest-palindrome-substring/index.md index 347139c48..c6d336f83 100644 --- a/docs/projects/longest-palindrome-substring/index.md +++ b/docs/projects/longest-palindrome-substring/index.md @@ -7,9 +7,37 @@ featured-image: tags: [longest-palindrome-substring] authors: Sayantan Paul(https://github.com/belikesayantan) --- -Given a string, we need to find the smallest substring inside the main string which is a palindrome. +# Given a string, we need to find the smallest substring inside the main string which is a palindrome. Palindrome is a phenomenon, where a string has same sequence of letters when read start --> end and end --> start. +## Requirements + +This problem can be solved using 3 methods. + +### Method 1 ( Brute Force ) +The simple approach is to check each substring whether the substring is a palindrome or not. We can run three loops, the outer two loops pick all substrings one by one by fixing the corner characters, the inner loop checks whether the picked substring is palindrome or not. + +- Time complexity: O (n3) +- Auxiliary complexity: O (1) + + +### Method 2 ( Dynamic Programming ) +The time complexity can be reduced by storing results of subproblems. We maintain a boolean table[n][n] that is filled in bottom up manner. The value of table[i][j] is true, if the substring is palindrome, otherwise false. To calculate table[i][j], we first check the value of table[i+1][j-1], if the value is true and str[i] is same as str[j], then we make table[i][j] true. Otherwise, the value of table[i][j] is made false. +- Time complexity: O ( n^2 ) +- Auxiliary Space: O ( n^2 ) + +### Method 3 +The time complexity of the Dynamic Programming based solution is O(n2) and it requires O(n2) extra space. We can find the longest palindrome substring in (n2) time with O(1) extra space. The idea is to generate all even length and odd length palindromes and keep track of the longest palindrome seen so far. + +#### Step to generate odd length palindrome: +Fix a centre and expand in both directions for longer palindromes. + + +#### Step to generate even length palindrome +Fix two centre ( low and high ) and expand in both directions for longer palindromes. +- Time complexity: O (n2) where n is the length of input string. +- Auxiliary Space: O ( 1 ) + ## Example Let's say we have a string, From 2b2bccfa5c6992fa15de8bdb58fccf94a12dd193 Mon Sep 17 00:00:00 2001 From: Sayantan Paul Date: Thu, 10 Oct 2019 15:48:40 +0530 Subject: [PATCH 7/9] added longest palindrome substring in README.md --- README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/README.md b/README.md index 4ccd5297d..34b3ec185 100644 --- a/README.md +++ b/README.md @@ -24,6 +24,7 @@ At any rate, if articles sound interesting, here are a few to get you started: - [Hello World in Every Language][2] - [Reverse a String in Every Language][3] - [The Coolest Programming Language Features][4] +- [Longest Palindromic Substring in Every Language][16] Alternatively, feel free to leverage the links in the README files spread throughout the repository. In addition, we have a rather extensive [wiki][5] which includes a table row for every language @@ -84,3 +85,4 @@ Thanks for your support! :relaxed: [13]: https://help.getadblock.com/support/solutions/articles/6000163989-how-do-i-pause-or-disable-adblock- [14]: https://twitter.com/RenegadeCoder94 [15]: https://gitter.im/TheRenegadeCoder/Lobby?utm_source=share-link&utm_medium=link&utm_campaign=share-link +[16]: https://therenegadecoder.com/code/longest-palindrome-substring-in-every-language/ From d4b52786bcf5dc35277358128e95ec1d25f6bec1 Mon Sep 17 00:00:00 2001 From: Jeremy Grifski Date: Thu, 10 Oct 2019 11:35:47 -0400 Subject: [PATCH 8/9] Reorganized index file Moved example to description section to conform to template. --- .../longest-palindrome-substring/index.md | 55 +++++++++++-------- 1 file changed, 32 insertions(+), 23 deletions(-) diff --git a/docs/projects/longest-palindrome-substring/index.md b/docs/projects/longest-palindrome-substring/index.md index 6dc70d281..4fd8e36ba 100644 --- a/docs/projects/longest-palindrome-substring/index.md +++ b/docs/projects/longest-palindrome-substring/index.md @@ -5,58 +5,67 @@ date: 2019-10-08 last-modified: 2018-10-09 featured-image: tags: [longest-palindrome-substring] -authors: Sayantan Paul +authors: + - Sayantan Paul --- -# Given a string, we need to find the smallest substring inside the main string which is a palindrome. + +Given a string, we need to find the smallest substring inside the main string which is a palindrome. + +## Description + Palindrome is a phenomenon, where a string has same sequence of letters when read start --> end and end --> start. +Let's say we have a string, + +``` +s = 'paapaapap' +``` + +Here, we have seven palindromic substrings. + +``` +sub_1 = 'aa' +sub_2 = 'paap' +sub_3 = 'paapaap' +sub_4 = 'aapaa' +sub_5 = 'apap' +sub_6 = 'pap' +sub_7 = 'apaapa' +``` + +Out of the seven, `sub_3 = 'paapaap'` is the longest. hence the output would be `'paapaap'` + ## Requirements This problem can be solved using 3 methods. ### Method 1 ( Brute Force ) + The simple approach is to check each substring whether the substring is a palindrome or not. We can run three loops, the outer two loops pick all substrings one by one by fixing the corner characters, the inner loop checks whether the picked substring is palindrome or not. - Time complexity: O (n3) - Auxiliary complexity: O (1) - ### Method 2 ( Dynamic Programming ) + The time complexity can be reduced by storing results of subproblems. We maintain a boolean table[n][n] that is filled in bottom up manner. The value of table[i][j] is true, if the substring is palindrome, otherwise false. To calculate table[i][j], we first check the value of table[i+1][j-1], if the value is true and str[i] is same as str[j], then we make table[i][j] true. Otherwise, the value of table[i][j] is made false. - Time complexity: O ( n^2 ) - Auxiliary Space: O ( n^2 ) ### Method 3 + The time complexity of the Dynamic Programming based solution is O(n2) and it requires O(n2) extra space. We can find the longest palindrome substring in (n2) time with O(1) extra space. The idea is to generate all even length and odd length palindromes and keep track of the longest palindrome seen so far. #### Step to generate odd length palindrome: -Fix a centre and expand in both directions for longer palindromes. +Fix a centre and expand in both directions for longer palindromes. #### Step to generate even length palindrome + Fix two centre ( low and high ) and expand in both directions for longer palindromes. - Time complexity: O (n2) where n is the length of input string. - Auxiliary Space: O ( 1 ) -## Example - -Let's say we have a string, - -``` -s = 'paapaapap' -``` -Here, we have seven palindromic substrings. -``` -sub_1 = 'aa' -sub_2 = 'paap' -sub_3 = 'paapaap' -sub_4 = 'aapaa' -sub_5 = 'apap' -sub_6 = 'pap' -sub_7 = 'apaapa' -``` -Out of the seven, `sub_3 = 'paapaap'` is the longest. hence the output would be `'paapaap'` - ## Testing The following table contains various test cases that you can use to verify the correctness of your solution: From 8e1677b423d0e0a4840e101e90b28362930d9fe4 Mon Sep 17 00:00:00 2001 From: Sayantan Paul Date: Thu, 10 Oct 2019 21:23:38 +0530 Subject: [PATCH 9/9] Update README.md --- archive/p/python/README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/archive/p/python/README.md b/archive/p/python/README.md index ef17ca06c..9c0aba70b 100644 --- a/archive/p/python/README.md +++ b/archive/p/python/README.md @@ -17,6 +17,7 @@ Welcome to Sample Programs in Python! - [Insertion Sort in Python][34] - [Job Sequencing with Deadlines in Python][30] - [Longest Common Subsequence][26] +- [Longest Palindromic Subsequence][42] - [Merge Sort in Python][35] - [Prime Number in Python][36] - [Quick Sort in Python][37]

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