manacher_algorithm.cpp File Reference

Implementation of Manacher's Algorithm More...

#include <cassert>
#include <iostream>
#include <vector>
#include <cstring>

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Namespaces
namespace	strings
	Algorithms with strings.
namespace	manacher
	Functions for Manacher's Algorithm implementation.

Functions
std::string	strings::manacher::manacher (const std::string &prototype)
	A function that implements Manacher's algorithm. More...
static void	test ()
	Self-test implementations. More...
int	main ()
	Main function. More...

Detailed Description

Implementation of Manacher's Algorithm

Manacher's Algorithm is used to find the longest palindromic substring within a string in O(n) time. It exploits the property of a palindrome that its first half is symmetric to the last half, and thus if the first half is a palindrome, then last half is also a palindrome.

Author

Riti Kumari

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test();  // run self-test implementations
    return 0;
}

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manacher()

std::string strings::manacher::manacher

(

const std::string &

prototype

)

A function that implements Manacher's algorithm.

Parameters

prototype

is the string where algorithm finds a palindromic substring. This string can contain any character except @ # &

Returns

the largest palindromic substring

                                               {
    if (prototype.size() > 0) {
        // stuffing characters between the input string to handle cases with
        // even length palindrome
        std::string stuffed_string = "";
        for (auto str : prototype) {
            stuffed_string += str;
            stuffed_string += "#";
        }
        stuffed_string = "@#" + stuffed_string + "&";
 
        std::vector<uint64_t> palindrome_max_half_length(
            stuffed_string.size(),
            0);  // this array will consist of largest possible half length of
                 // palindrome centered at index (say i with respect to the
                 // stuffed string). This value will be lower bound of half
                 // length since single character is a palindrome in itself.
 
        uint64_t bigger_center =
            0;  // this is the index of the center of palindromic
                // substring which would be considered as the larger
                // palindrome, having symmetric halves
 
        uint64_t right = 0;  // this is the maximum length of the palindrome
                             // from 'bigger_center' to the rightmost end
 
        // i is considered as center lying within one half of the palindrone
        // which is centered at 'bigger_center'
        for (uint64_t i = 1; i < stuffed_string.size() - 1; i++) {
            if (i < right) {  // when i is before right end, considering
                              // 'bigger_center' as center of palindrome
                uint64_t opposite_to_i =
                    2 * bigger_center -
                    i;  // this is the opposite end of string, if
                        // centered at center, and having one end as i
 
                // finding the minimum possible half length among
                // the palindrome on having center at opposite end,
                // and the string between i and right end,
                // considering 'bigger_center' as center of palindrome
                palindrome_max_half_length[i] = std::min(
                    palindrome_max_half_length[opposite_to_i], right - i);
            }
 
            // expanding the palindrome across the maximum stored length in the
            // array, centered at i
            while (stuffed_string[i + (palindrome_max_half_length[i] + 1)] ==
                   stuffed_string[i - (palindrome_max_half_length[i] + 1)]) {
                palindrome_max_half_length[i]++;
            }
 
            // if palindrome centered at i exceeds the rightmost end of
            // palindrome centered at 'bigger_center', then i will be made the
            // 'bigger_center' and right value will also be updated with respect
            // to center i
            if (i + palindrome_max_half_length[i] > right) {
                bigger_center = i;
                right = i + palindrome_max_half_length[i];
            }
        }
 
        // now extracting the first largest palindrome
        uint64_t half_length = 0;   // half length of the largest palindrome
        uint64_t center_index = 0;  // index of center of the largest palindrome
 
        for (uint64_t i = 1; i < stuffed_string.size() - 1; i++) {
            if (palindrome_max_half_length[i] > half_length) {
                half_length = palindrome_max_half_length[i];
                center_index = i;
            }
        }
 
        std::string palindromic_substring =
            "";  // contains the resulting largest palindrome
 
        if (half_length > 0) {
            // extra information: when '#' is the center, then palindromic
            // substring will have even length, else palindromic substring will
            // have odd length
 
            uint64_t start =
                center_index - half_length +
                1;  // index of first character of palindromic substring
            uint64_t end =
                center_index + half_length -
                1;  // index of last character of palindromic substring
            for (uint64_t index = start; index <= end; index += 2) {
                palindromic_substring += stuffed_string[index];
            }
        } else {
            // if length = 0, then there does not exist any palindrome of length
            // > 1 so we can assign any character of length 1 from string as the
            // palindromic substring
            palindromic_substring = prototype[0];
        }
        return palindromic_substring;
 
    } else {
        // handling case when string is empty
        return "";
    }
}

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test()

static void test ( )

static

Self-test implementations.

Returns

void

                   {
    assert(strings::manacher::manacher("") == "");
    assert(strings::manacher::manacher("abababc") == "ababa");
    assert(strings::manacher::manacher("cbaabd") == "baab");
    assert(strings::manacher::manacher("DedzefDeD") == "DeD");
    assert(strings::manacher::manacher("XZYYXXYZXX") == "YXXY");
    assert(strings::manacher::manacher("1sm222m10abc") == "m222m");
    assert(strings::manacher::manacher("798989591") == "98989");
    assert(strings::manacher::manacher("xacdedcax") == "xacdedcax");
    assert(strings::manacher::manacher("xaccax") == "xaccax");
    assert(strings::manacher::manacher("a") == "a");
    assert(strings::manacher::manacher("xy") == "x");
    assert(strings::manacher::manacher("abced") == "a");
 
    std::cout << "All tests have passed!" << std::endl;
}

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