// https://www.infoarena.ro/problema/strmatch
#include <array>
#include <algorithm>
#include <cstring>
#include <functional>
#include <iostream>
#include <fstream>
#include <regex>
#include <vector>
#define ALG 9
#if ALG == 1 || ALG == 2
/**
* @brief KMP algorithm, finds max 1000 occurences of a in b.
* next[i] represents the longest prefix of a that is a suffix of a_i.
* This implementation assumes a and b are indexed from 0.
*
* One improvement, for real-time restraints, is to create the next table
* for each character in the alphabet, so that the lookup time for a mismatch
* is constant.
*
* Complexity: O(A+B) time, O(A) space for ALG 1 and O(A+S) space for ALG 2,
* where S is the size of the alphabet
*/
auto strmatch(const std::string& a, const std::string& b) -> std::pair<int, std::array<int, 1000>>
{
#if ALG == 2
int marked[128]; // represents the LAST position of the character in a
std::fill_n(marked, 128, -1);
marked[a[0]] = 0;
#endif
// precompute next array
std::vector<int> next(a.size());
next[0] = -1;
for (int i = 1, k = -1; i < a.size(); ++i) {
#if ALG == 2
marked[a[i]] = i;
#endif
// if the prefix cannot be extended to match the current suffix,
// go back to next[k], ensuring that the prexix of a_k is still a
// suffix of a_{i-1} (because a_k was already a suffix of a_{i-1})
while (k >= 0 && a[k + 1] != a[i])
k = next[k];
// extend the prefix
if (a[k + 1] == a[i])
++k;
next[i] = k;
}
// KMP pattern matching - same algorithm as for precomputing the next array
std::array<int, 1000> positions;
int len = 0;
for (int i = 0, q = -1; i < b.size(); ++i) {
#if ALG == 2
// S. Boyer and J. Moore 1974 improvement for large alphabets: we check
// first the last element of the pattern and if it does not match, we
// just skip by the length of the pattern; otherwise, we skip by the
// minimum amount that is consistent with the match.
if (q == -1) {
int pos = i + a.size() - 1;
if (pos < b.size()) {
if (marked[b[pos]] == -1) {
i = pos;
continue;
}
i = pos - marked[b[pos]];
}
else
break;
}
// for smaller alphabets that can be stored in a small array of markers,
// we can do this check for each character in b, at each step of the
// loop
if (marked[b[i]] == -1) {
q = -1;
continue;
}
#endif
// if the prefix cannot be extended to match the current character
// in b, go back to next[q], ensuring that the prefix of a_q is
// still a suffix to b_{i-1} (because the next[q] step guarantees
// that a_next[q] will be a suffix of a_q, and thus b_i by
// transitivity)
while (q >= 0 && a[q + 1] != b[i])
q = next[q];
// extend the match
if (a[q + 1] == b[i])
++q;
// found a full match
if (q + 1 == a.size()) {
if (len < 1000)
positions[len] = i - a.size() + 1;
++len;
}
}
return { len, positions };
}
#endif
#if ALG == 3 || ALG == 4 || ALG == 5
/**
* @brief Uses standard library searchers:
* - default searcher: implementation defined complexity
* - Boyer Moore searcher: search complexity is worst case O(A*B) when the
* pattern appears in text and best case O(B/A) when it does not; preprocessing
* is O(A); time complexity is O(S+A)
* - Boyer Moore Horspool searcher: simpler variant that only uses bad character
* heuristic; it improves the average case performance to O(B) on random text
*
* See: https://www.cppstories.com/2018/08/searchers/
*
* Unfortunately, std::search finds only one occurence, thus for multiple,
* overlapping searches you are limited to incrementing +1 instead of skipping
* whole sequences of b. Bottom line is these standard library searchers are
* only suitable for single searches or non-overlapping occurences.
*
* Complexity: see above
*/
auto strmatch(const std::string& a, const std::string& b) -> std::pair<int, std::array<int, 1000>>
{
#if ALG == 3
const std::default_searcher searcher(a.begin(), a.end());
#elif ALG == 4
const std::boyer_moore_searcher searcher(a.begin(), a.end());
#elif ALG == 5
const std::boyer_moore_horspool_searcher searcher(a.begin(), a.end());
#endif
std::array<int, 1000> positions;
int len = 0;
auto it = std::search(b.begin(), b.end(), searcher);
while (it != b.end()) {
if (len < 1000)
positions[len] = it - b.begin();
++len;
it = std::search(it + 1, b.end(), searcher);
}
return { len, positions };
}
#endif
#if ALG == 6
/**
* @brief Uses std::string::find, which has implementation defined complexity.
*
* See:
* https://stackoverflow.com/questions/43657530/using-stdsearch-over-stringfind
*
* Complexity: unknown
*/
auto strmatch(const std::string& a, const std::string& b) -> std::pair<int, std::array<int, 1000>>
{
std::array<int, 1000> positions;
int len = 0;
auto pos = b.find(a);
while (pos != std::string::npos) {
if (len < 1000)
positions[len] = pos;
++len;
pos = b.find(a, pos + 1);
}
return { len, positions };
}
#endif
#if ALG == 7
/**
* @brief Uses std::regex_iterator with an overlapping pattern.
*
* Complexity: unknown (but bad af)
*/
auto strmatch(const std::string& a, const std::string& b) -> std::pair<int, std::array<int, 1000>>
{
std::array<int, 1000> positions;
int len = 0;
std::regex pattern("(?=(" + a + ")).");
auto begin = std::sregex_iterator(b.begin(), b.end(), pattern);
auto end = std::sregex_iterator();
for (auto it = begin; it != end; ++it) {
if (len < 1000)
positions[len] = it->position();
++len;
}
return { len, positions };
}
#endif
#if ALG == 8 || ALG == 9
/**
* @brief Rabin-Karp algorithm, with a rolling hash. Note that many
* implementations use Rabin fingerprints for the hashing.
* This type of algorithm is inferior to KMP and Boyer-Moore, but can be useful
* in multiple patterns searching.
*
* The ALG 9 variant uses 2 hashes to have stronger confidence and removes the
* comparison check in this case, making it linear worst-case.
*
* Complexity: time O(A*B) worst-case but average O(A+B); space O(A+B)
*
*/
auto strmatch(const std::string& a, const std::string& b) -> std::pair<int, std::array<int, 1000>>
{
std::array<int, 1000> positions;
auto a_size = a.size(), b_size = b.size();
if (a_size > b_size)
return { 0, positions };
#if ALG == 8
auto fast_exp = [](unsigned b, unsigned p) {
unsigned res = 1;
while (p) {
while (!(p & 1))
b *= b, p >>= 1;
res *= b, --p;
}
return res;
};
#else
static const unsigned mod1 = 100007, mod2 = 100021, p = 73;
auto fast_exp = [](unsigned b, unsigned p, unsigned mod) {
unsigned res = 1;
while (p) {
while (!(p & 1))
b = (b * b) % mod, p >>= 1;
res = (res * b) % mod, --p;
}
return res;
};
#endif
#if ALG == 8
auto hash = [](std::string s, size_t len) {
// string hash version of Daniel J. Bernstein (this is NOT a good one-way function tho)
// https://stackoverflow.com/questions/11546791/what-is-the-best-hash-function-for-rabin-karp-algorithm
unsigned h = 0; // can also be replaced with 5381
for (int i = 0; i < len; ++i)
h = h * 33 + s[i];
return h;
};
#else
auto hash = [](std::string s, size_t len) {
unsigned h1 = 0, h2 = 0;
for (int i = 0; i < len; ++i) {
h1 = (h1 * p + s[i]) % mod1;
h2 = (h2 * p + s[i]) % mod2;
}
return std::pair<int, int>{ h1, h2 };
};
#endif
// precompute hash of a (and first hash of b also)
auto ha = hash(a, a_size), hb = hash(b, a_size);
// rolling hash version
#if ALG == 8
/**
h = h[m,n-1] * 33 + c = h[m,n]
h' = h[m+1,n] * 33 + c' = h[m+1,n+1]
h' = h[m,n] * 33 + c' - x, x = ?
x = (h[m,n] - h[m+1,n]) * 33
h[m,n] = c_n + c_n-1 * 33 + c_n-2 * 33^2 + ... + c_m+1 * 33^n-m-1 + c_m * 33^n-m + h0 * 33^n-m+1
h[m+1,n] = c_n + c_n-1 * 33 + c_n-2 * 33^2 + ... + c_m+1 * 33^n-m-1 + h0 * 33^n-m
h[m,n] - h[m+1,n] = c_m*33^n-m + h0 * 33^n-m * 32
x = 33^n-m * (c_m + 32 * h0)
*/
unsigned p33 = fast_exp(33, a_size);
auto hash_rolling = [&b, a_size, p33, hb](int idx) {
static auto h = hb;
return h = h * 33 + b[idx] - p33 * (b[idx - a_size]);
};
#else
unsigned p1 = fast_exp(p, a_size - 1, mod1), p2 = fast_exp(p, a_size - 1, mod2);
auto hash_rolling = [&b, a_size, hb, p1, p2](int idx) {
static auto h = hb;
h.first = ((h.first - (b[idx - a_size] * p1) % mod1 + mod1) * p + b[idx]) % mod1;
h.second = ((h.second - (b[idx - a_size] * p2) % mod2 + mod2) * p + b[idx]) % mod2;
return h;
};
#endif
int len = 0;
for (int i = a_size; i <= b_size; ++i) {
if (ha == hb) {
#if ALG == 8
// hashes match, we have to compare the strings thoroughly
if (!std::memcmp(a.c_str(), b.c_str() + i - a_size, a_size)) {
#endif
if (len < 1000)
positions[len] = i - a_size;
++len;
#if ALG == 8
}
#endif
}
if (i < b_size)
hb = hash_rolling(i);
}
return { len, positions };
}
#endif
int main()
{
try {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
std::ifstream in("strmatch.in");
std::ofstream out("strmatch.out");
if (!in.is_open())
throw std::runtime_error("input file not found");
std::string a, b;
in >> a >> b;
auto [len, positions] = strmatch(a, b);
out << len << '\n';
for (int i = 0; i < std::min(1000, len); ++i)
out << positions[i] << ' ';
}
catch (const std::exception& e) {
std::cerr << e.what();
return EXIT_FAILURE;
}
}