/
string-transformation.cpp
224 lines (208 loc) · 6.79 KB
/
string-transformation.cpp
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// Time: O(n + logk)
// Space: O(n)
// dp, math, kmp
class Solution {
public:
int numberOfWays(string s, string t, long long k) {
const int n = size(s);
vector<int> dp(2);
dp[1] = (((pow(n - 1, k, MOD) - pow(-1, k, MOD)) * pow(n, MOD - 2, MOD)) % MOD + MOD) % MOD;
dp[0] = (dp[1] + pow(-1, k, MOD)) % MOD;
int result = 0;
for (const auto& i : KMP(s + s.substr(0, size(s) - 1), t)) {
result = (result + dp[static_cast<int>(i != 0)]) % MOD;
}
return result;
}
private:
int64_t pow(int64_t a, int64_t b, int64_t m) {
a %= m;
int64_t result = 1;
while (b) {
if (b & 1) {
result = (result * a) % m;
}
a = (a * a) % m;
b >>= 1;
}
return result;
}
vector<int> KMP(const string& text, const string& pattern) {
vector<int> result;
const vector<int> prefix = getPrefix(pattern);
int j = -1;
for (int i = 0; i < text.length(); ++i) {
while (j > -1 && pattern[j + 1] != text[i]) {
j = prefix[j];
}
if (pattern[j + 1] == text[i]) {
++j;
}
if (j == pattern.length() - 1) {
result.emplace_back(i - j);
j = prefix[j];
}
}
return result;
}
vector<int> getPrefix(const string& pattern) {
vector<int> prefix(pattern.length(), -1);
int j = -1;
for (int i = 1; i < pattern.length(); ++i) {
while (j > -1 && pattern[j + 1] != pattern[i]) {
j = prefix[j];
}
if (pattern[j + 1] == pattern[i]) {
++j;
}
prefix[i] = j;
}
return prefix;
}
const int MOD = 1e9 + 7;
};
// Time: O(n + logk)
// Space: O(n)
// dp, matrix exponentiation, kmp
class Solution2 {
public:
int numberOfWays(string s, string t, long long k) {
const int n = size(s);
vector<vector<int>> T = {{ 0, 1},
{n - 1, (n - 1) - 1}};
const auto dp = matrixMult({{1, 0}}, matrixExpo(T, k))[0]; // [dp[0], dp[1]] * T^k
int result = 0;
for (const auto& i : KMP(s + s.substr(0, size(s) - 1), t)) {
result = (result + dp[static_cast<int>(i != 0)]) % MOD;
}
return result;
}
private:
vector<vector<int>> matrixExpo(const vector<vector<int>>& A, int64_t pow) {
vector<vector<int>> result(A.size(), vector<int>(A.size()));
vector<vector<int>> A_exp(A);
for (int i = 0; i < A.size(); ++i) {
result[i][i] = 1;
}
while (pow) {
if (pow % 2 == 1) {
result = matrixMult(result, A_exp);
}
A_exp = matrixMult(A_exp, A_exp);
pow /= 2;
}
return result;
}
vector<vector<int>> matrixMult(const vector<vector<int>>& A, const vector<vector<int>>& B) {
vector<vector<int>> result(A.size(), vector<int>(B[0].size()));
for (int i = 0; i < A.size(); ++i) {
for (int j = 0; j < B[0].size(); ++j) {
int64_t entry = 0;
for (int k = 0; k < B.size(); ++k) {
entry = (static_cast<int64_t>(A[i][k]) * B[k][j] % MOD + entry) % MOD;
}
result[i][j] = static_cast<int>(entry);
}
}
return result;
}
vector<int> KMP(const string& text, const string& pattern) {
vector<int> result;
const vector<int> prefix = getPrefix(pattern);
int j = -1;
for (int i = 0; i < text.length(); ++i) {
while (j > -1 && pattern[j + 1] != text[i]) {
j = prefix[j];
}
if (pattern[j + 1] == text[i]) {
++j;
}
if (j == pattern.length() - 1) {
result.emplace_back(i - j);
j = prefix[j];
}
}
return result;
}
vector<int> getPrefix(const string& pattern) {
vector<int> prefix(pattern.length(), -1);
int j = -1;
for (int i = 1; i < pattern.length(); ++i) {
while (j > -1 && pattern[j + 1] != pattern[i]) {
j = prefix[j];
}
if (pattern[j + 1] == pattern[i]) {
++j;
}
prefix[i] = j;
}
return prefix;
}
const int MOD = 1e9 + 7;
};
// Time: O(n + logk)
// Space: O(n)
// dp, matrix exponentiation, z-function
class Solution3 {
public:
int numberOfWays(string s, string t, long long k) {
const int n = size(s);
vector<vector<int>> T = {{ 0, 1},
{n - 1, (n - 1) - 1}};
const auto dp = matrixMult({{1, 0}}, matrixExpo(T, k))[0]; // [dp[0], dp[1]] * T^k
const auto& z = z_function(t + s + s.substr(0, size(s) - 1));
int result = 0;
for (int i = 0; i < n; ++i) {
if (z[i + size(t)] >= size(t)) {
result = (result + dp[static_cast<int>(i != 0)]) % MOD;
}
}
return result;
}
private:
vector<vector<int>> matrixExpo(const vector<vector<int>>& A, int64_t pow) {
vector<vector<int>> result(A.size(), vector<int>(A.size()));
vector<vector<int>> A_exp(A);
for (int i = 0; i < A.size(); ++i) {
result[i][i] = 1;
}
while (pow) {
if (pow % 2 == 1) {
result = matrixMult(result, A_exp);
}
A_exp = matrixMult(A_exp, A_exp);
pow /= 2;
}
return result;
}
vector<vector<int>> matrixMult(const vector<vector<int>>& A, const vector<vector<int>>& B) {
vector<vector<int>> result(A.size(), vector<int>(B[0].size()));
for (int i = 0; i < A.size(); ++i) {
for (int j = 0; j < B[0].size(); ++j) {
int64_t entry = 0;
for (int k = 0; k < B.size(); ++k) {
entry = (static_cast<int64_t>(A[i][k]) * B[k][j] % MOD + entry) % MOD;
}
result[i][j] = static_cast<int>(entry);
}
}
return result;
}
// Template: https://cp-algorithms.com/string/z-function.html
vector<int> z_function(const string& s) { // Time: O(n), Space: O(n)
vector<int> z(size(s));
for (int i = 1, l = 0, r = 0; i < size(z); ++i) {
if (i <= r) {
z[i] = min(r - i + 1, z[i - l]);
}
while (i + z[i] < size(z) && s[z[i]] == s[i + z[i]]) {
++z[i];
}
if (i + z[i] - 1 > r) {
l = i, r = i + z[i] - 1;
}
}
return z;
}
const int MOD = 1e9 + 7;
};