KMP (Knuth-Morris-Pratt) algorithm introduction to algorithm 3rd, example 32.4

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本文介绍了KMP算法用于字符串匹配的过程，包括前缀数组的计算和算法的实现。通过实例演示了如何使用KMP算法在给定字符串中查找模式字符串，并提供了性能测试结果。

算法导论第三版 32.4 KMP

//KMP (Knuth-Morris-Pratt) algorithm introduction to algorithm 3rd, example 32.4

#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
#include <ostream>
#include <iterator>
#include <limits>
#include <complex>
#include "stopwatch.h"

std::vector<size_t> compute_prefix(const std::string & str)
{
std::vector<size_t> prefix(str.size(), 0);
size_t ip = 0;
for (size_t is = 1; is < str.size(); ++is)
{
while (ip > 0 && str[ip] != str[is])
{
ip = prefix[ip-1];
}
if (str[ip] == str[is])
{
++ip;
}
prefix[is] = ip;
}

return prefix;
}

std::vector<size_t> kmp_match(const std::string &s1, const std::string & s2, const std::vector<size_t> & prefixes)
{
std::vector<size_t> indexes;
size_t ip = 0;
for (size_t is = 0; is < s1.size(); ++is)
{
while (ip > 0 && s1[is] != s2[ip])
{
ip = prefixes[ip-1];
}

if (s1[is] == s2[ip])
{
++ip;
}
if (ip == prefixes.size())
{
ip = prefixes[ip-1];
indexes.push_back(is);
}
}

return indexes;
}

void test(std::string && s1, std::string && s2)
{
std::cout << "Match " << s1 << " with " << s2 << std::endl;
Stopwatch watch;
watch.start();
auto prefixes = compute_prefix(s2);
auto indexes = kmp_match(s1, s2, prefixes);
watch.stop();
std::cout << "prefix of " << s2 << " is ";
std::copy(prefixes.begin(), prefixes.end(), std::ostream_iterator<size_t>(std::cout, " "));
std::cout << std::endl;
std::cout << "Match string at index ";
std::copy(indexes.begin(), indexes.end(), std::ostream_iterator<size_t>(std::cout, " "));
std::cout << " use time " << watch.elapsed() << " ms\n" << std::endl;
}

int main()
{
std::cout << "start" << std::endl;
test(std::string("aaababaabaababaab"), std::string("aabab"));
test(std::string("bacbababacaabcbab"), std::string("ababaca"));
test(std::string("aaabaabaabaabaabaab"), std::string("aabaab"));

return 0;
}