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Počet podreťazcov s počtom každého znaku ako k

Daný reťazec a celé číslo k nájdite počet podreťazcov, v ktorých sa všetky rôzne znaky vyskytujú presne k-krát. 

Príklady:  

  Input :   s = 'aabbcc' k = 2   Output :   6 The substrings are aa bb cc aabb bbcc and aabbcc.   Input :   s = 'aabccc' k = 2 Output : 3 There are three substrings aa cc and cc

Naivný prístup: Cieľom je prejsť cez všetky podreťazce. Opravíme prechod začiatočného bodu cez všetky podreťazce počnúc vybraným bodom, neustále zvyšujeme frekvencie všetkých znakov. Ak sa všetky frekvencie stanú k, zvýšime výsledok. Ak počet ľubovoľnej frekvencie presiahne k, zlomíme a zmeníme počiatočný bod. 



Nižšie je uvedená implementácia vyššie uvedeného prístupu:

C++
// C++ program to count number of substrings // with counts of distinct characters as k. #include    using namespace std; const int MAX_CHAR = 26; // Returns true if all values // in freq[] are either 0 or k. bool check(int freq[] int k) {  for (int i = 0; i < MAX_CHAR; i++)  if (freq[i] && freq[i] != k)  return false;  return true; } // Returns count of substrings where frequency // of every present character is k int substrings(string s int k) {  int res = 0; // Initialize result  // Pick a starting point  for (int i = 0; s[i]; i++) {  // Initialize all frequencies as 0  // for this starting point  int freq[MAX_CHAR] = { 0 };  // One by one pick ending points  for (int j = i; s[j]; j++) {    // Increment frequency of current char   int index = s[j] - 'a';  freq[index]++;  // If frequency becomes more than  // k we can't have more substrings  // starting with i  if (freq[index] > k)  break;  // If frequency becomes k then check  // other frequencies as well.  else if (freq[index] == k &&   check(freq k) == true)  res++;  }  }  return res; } // Driver code int main() {  string s = 'aabbcc';  int k = 2;  cout << substrings(s k) << endl;  s = 'aabbc';  k = 2;  cout << substrings(s k) << endl; } 
Java
// Java program to count number of substrings // with counts of distinct characters as k. import java.io.*; class GFG { static int MAX_CHAR = 26; // Returns true if all values // in freq[] are either 0 or k. static boolean check(int freq[] int k) {  for (int i = 0; i < MAX_CHAR; i++)  if (freq[i] !=0 && freq[i] != k)  return false;  return true; } // Returns count of substrings where frequency // of every present character is k static int substrings(String s int k) {  int res = 0; // Initialize result  // Pick a starting point  for (int i = 0; i< s.length(); i++)  {  // Initialize all frequencies as 0  // for this starting point  int freq[] = new int[MAX_CHAR];  // One by one pick ending points  for (int j = i; j<s.length(); j++)   {  // Increment frequency of current char   int index = s.charAt(j) - 'a';  freq[index]++;  // If frequency becomes more than  // k we can't have more substrings  // starting with i  if (freq[index] > k)  break;  // If frequency becomes k then check  // other frequencies as well.  else if (freq[index] == k &&   check(freq k) == true)  res++;  }  }  return res; } // Driver code public static void main(String[] args)  {  String s = 'aabbcc';  int k = 2;  System.out.println(substrings(s k));  s = 'aabbc';  k = 2;  System.out.println(substrings(s k)); } }  // This code has been contributed by 29AjayKumar 
Python3
# Python3 program to count number of substrings  # with counts of distinct characters as k.  MAX_CHAR = 26 # Returns true if all values  # in freq[] are either 0 or k. def check(freq k): for i in range(0 MAX_CHAR): if(freq[i] and freq[i] != k): return False return True # Returns count of substrings where  # frequency of every present character is k  def substrings(s k): res = 0 # Initialize result # Pick a starting point  for i in range(0 len(s)): # Initialize all frequencies as 0  # for this starting point freq = [0] * MAX_CHAR # One by one pick ending points for j in range(i len(s)): # Increment frequency of current char index = ord(s[j]) - ord('a') freq[index] += 1 # If frequency becomes more than  # k we can't have more substrings  # starting with i  if(freq[index] > k): break # If frequency becomes k then check  # other frequencies as well elif(freq[index] == k and check(freq k) == True): res += 1 return res # Driver Code if __name__ == '__main__': s = 'aabbcc' k = 2 print(substrings(s k)) s = 'aabbc'; k = 2; print(substrings(s k)) # This code is contributed  # by Sairahul Jella 
C#
// C# program to count number of substrings // with counts of distinct characters as k. using System; class GFG { static int MAX_CHAR = 26; // Returns true if all values // in freq[] are either 0 or k. static bool check(int []freq int k) {  for (int i = 0; i < MAX_CHAR; i++)  if (freq[i] != 0 && freq[i] != k)  return false;  return true; } // Returns count of substrings where frequency // of every present character is k static int substrings(String s int k) {  int res = 0; // Initialize result  // Pick a starting point  for (int i = 0; i < s.Length; i++)  {  // Initialize all frequencies as 0  // for this starting point  int []freq = new int[MAX_CHAR];  // One by one pick ending points  for (int j = i; j < s.Length; j++)   {  // Increment frequency of current char   int index = s[j] - 'a';  freq[index]++;  // If frequency becomes more than  // k we can't have more substrings  // starting with i  if (freq[index] > k)  break;  // If frequency becomes k then check  // other frequencies as well.  else if (freq[index] == k &&   check(freq k) == true)  res++;  }  }  return res; } // Driver code public static void Main(String[] args)  {  String s = 'aabbcc';  int k = 2;  Console.WriteLine(substrings(s k));  s = 'aabbc';  k = 2;  Console.WriteLine(substrings(s k)); } } /* This code contributed by PrinciRaj1992 */ 
PHP
 // PHP program to count number of substrings // with counts of distinct characters as k. $MAX_CHAR = 26; // Returns true if all values // in freq[] are either 0 or k. function check(&$freq $k) { global $MAX_CHAR; for ($i = 0; $i < $MAX_CHAR; $i++) if ($freq[$i] && $freq[$i] != $k) return false; return true; } // Returns count of substrings where frequency // of every present character is k function substrings($s $k) { global $MAX_CHAR; $res = 0; // Initialize result // Pick a starting point for ($i = 0; $i < strlen($s); $i++) { // Initialize all frequencies as 0 // for this starting point $freq = array_fill(0 $MAX_CHARNULL); // One by one pick ending points for ($j = $i; $j < strlen($s); $j++) { // Increment frequency of current char  $index = ord($s[$j]) - ord('a'); $freq[$index]++; // If frequency becomes more than // k we can't have more substrings // starting with i if ($freq[$index] > $k) break; // If frequency becomes k then check // other frequencies as well. else if ($freq[$index] == $k && check($freq $k) == true) $res++; } } return $res; } // Driver code $s = 'aabbcc'; $k = 2; echo substrings($s $k).'n'; $s = 'aabbc'; $k = 2; echo substrings($s $k).'n'; // This code is contributed by Ita_c. ?> 
JavaScript
<script> // Javascript program to count number of  // substrings with counts of distinct  // characters as k. let MAX_CHAR = 26; // Returns true if all values // in freq[] are either 0 or k. function check(freqk) {  for(let i = 0; i < MAX_CHAR; i++)  if (freq[i] != 0 && freq[i] != k)  return false;    return true; } // Returns count of substrings where frequency // of every present character is k function substrings(s k) {    // Initialize result  let res = 0;   // Pick a starting point  for(let i = 0; i< s.length; i++)  {    // Initialize all frequencies as 0  // for this starting point  let freq = new Array(MAX_CHAR);  for(let i = 0; i < freq.length ;i++)  {  freq[i] = 0;  }    // One by one pick ending points  for(let j = i; j < s.length; j++)  {    // Increment frequency of current char  let index = s[j].charCodeAt(0) -   'a'.charCodeAt(0);  freq[index]++;    // If frequency becomes more than  // k we can't have more substrings  // starting with i  if (freq[index] > k)  break;    // If frequency becomes k then check  // other frequencies as well.  else if (freq[index] == k &&  check(freq k) == true)  res++;  }  }  return res; } // Driver code let s = 'aabbcc'; let k = 2; document.write(substrings(s k) + '  
'
); s = 'aabbc'; k = 2; document.write(substrings(s k) + '
'
); // This code is contributed by avanitrachhadiya2155 </script>

Výstup
6 3

Časová zložitosť: O(n*n) kde n je dĺžka vstupného reťazca. Funkcia Check() spúšťa slučku konštantnej dĺžky od 0 do MAX_CHAR (tj; 26 vždy), takže táto funkcia check() beží v čase O(MAX_CHAR), takže časová zložitosť je O(MAX_CHAR*n*n)=O(n^2).
Pomocný priestor: O(1) 

Efektívny prístup: Pri veľmi pozornom pozorovaní môžeme vidieť, že to isté stačí skontrolovať pre podreťazce dĺžky Ktimes i forall iisin[1 D]                 , kde D                je počet odlišných znakov prítomných v danom reťazci.

argument:
Uvažujme podreťazec S_{i+1}S_{i+2}bodiek S_{i+p} dĺžky 'p'. Ak má tento podreťazec odlišné znaky 'm' a každý odlišný znak sa vyskytuje presne 'K'-krát, dĺžka podreťazca 'p' je daná ako p = Kkrát m. Keďže 'p              ' je vždy násobkom 'K' a 1le mle 26               pre daný reťazec stačí iterovať podreťazce, ktorých dĺžka je deliteľná 'K' a majú m 1 le m 26 rôznych znakov. Na iteráciu cez podreťazce s pevnou dĺžkou použijeme posuvné okno.

Riešenie:

  • Nájdite počet odlišných znakov prítomných v danom reťazci. Nech je to D.
  • Pre každý i 1le ile D urobte nasledovné
    • Iterujte cez podreťazce dĺžky $i krát K$ pomocou posuvného okna.
    • Skontrolujte, či spĺňajú podmienku - Všetky odlišné znaky v podreťazci sa vyskytujú presne K-krát.
    • Ak podmienku splnia, počet sa zvýši.

Nižšie je uvedená implementácia vyššie uvedeného prístupu:

C++
#include    #include  #include  #include  int min(int a int b) { return a < b ? a : b; } using namespace std; bool have_same_frequency(map<char int>& freq int k) {  for (auto& pair : freq) {  if (pair.second != k && pair.second != 0) {  return false;  }  }  return true; } int count_substrings(string s int k) {  int count = 0;  int distinct = (set<char>(s.begin() s.end())).size();  for (int length = 1; length <= distinct; length++) {  int window_length = length * k;  map<char int> freq;  int window_start = 0;  int window_end = window_start + window_length - 1;  for (int i = window_start;  i <= min(window_end s.length() - 1); i++) {  freq[s[i]]++;  }  while (window_end < s.length()) {  if (have_same_frequency(freq k)) {  count++;  }  freq[s[window_start]]--;  window_start++;  window_end++;  if (window_length < s.length()) {  freq[s[window_end]]++;  }  }  }  return count; } int main() {  string s = 'aabbcc';  int k = 2;  cout << count_substrings(s k) << endl;  s = 'aabbc';  k = 2;  cout << count_substrings(s k) << endl;  return 0; } 
C
#include  #include  #include  int min(int a int b) { return a < b ? a : b; } bool have_same_frequency(int freq[] int k) {  for (int i = 0; i < 26; i++) {  if (freq[i] != 0 && freq[i] != k) {  return false;  }  }  return true; } int count_substrings(char* s int n int k) {  int count = 0;  int distinct = 0;  bool have[26] = { false };  for (int i = 0; i < n; i++) {  have[s[i] - 'a'] = true;  }  for (int i = 0; i < 26; i++) {  if (have[i]) {  distinct++;  }  }  for (int length = 1; length <= distinct; length++) {  int window_length = length * k;  int freq[26] = { 0 };  int window_start = 0;  int window_end = window_start + window_length - 1;  for (int i = window_start;  i <= min(window_end n - 1); i++) {  freq[s[i] - 'a']++;  }  while (window_end < n) {  if (have_same_frequency(freq k)) {  count++;  }  freq[s[window_start] - 'a']--;  window_start++;  window_end++;  if (window_end < n) {  freq[s[window_end] - 'a']++;  }  }  }  return count; } int main() {  char* s = 'aabbcc';  int k = 2;  printf('%dn' count_substrings(s 6 k));  s = 'aabbc';  k = 2;  printf('%dn' count_substrings(s 5 k));  return 0; } 
Java
import java.util.*; class GFG {  static boolean have_same_frequency(int[] freq int k)  {  for (int i = 0; i < 26; i++) {  if (freq[i] != 0 && freq[i] != k) {  return false;  }  }  return true;  }  static int count_substrings(String s int k)  {  int count = 0;  int distinct = 0;  boolean[] have = new boolean[26];  Arrays.fill(have false);  for (int i = 0; i < s.length(); i++) {  have[((int)(s.charAt(i) - 'a'))] = true;  }  for (int i = 0; i < 26; i++) {  if (have[i]) {  distinct++;  }  }  for (int length = 1; length <= distinct; length++) {  int window_length = length * k;  int[] freq = new int[26];  Arrays.fill(freq 0);  int window_start = 0;  int window_end  = window_start + window_length - 1;  for (int i = window_start;  i <= Math.min(window_end s.length() - 1);  i++) {  freq[((int)(s.charAt(i) - 'a'))]++;  }  while (window_end < s.length()) {  if (have_same_frequency(freq k)) {  count++;  }  freq[(  (int)(s.charAt(window_start) - 'a'))]--;  window_start++;  window_end++;  if (window_end < s.length()) {  freq[((int)(s.charAt(window_end)  - 'a'))]++;  }  }  }  return count;  }  public static void main(String[] args)  {  String s = 'aabbcc';  int k = 2;  System.out.println(count_substrings(s k));  s = 'aabbc';  k = 2;  System.out.println(count_substrings(s k));  } } 
Python3
from collections import defaultdict def have_same_frequency(freq: defaultdict k: int): return all([freq[i] == k or freq[i] == 0 for i in freq]) def count_substrings(s: str k: int) -> int: count = 0 distinct = len(set([i for i in s])) for length in range(1 distinct + 1): window_length = length * k freq = defaultdict(int) window_start = 0 window_end = window_start + window_length - 1 for i in range(window_start min(window_end + 1 len(s))): freq[s[i]] += 1 while window_end < len(s): if have_same_frequency(freq k): count += 1 freq[s[window_start]] -= 1 window_start += 1 window_end += 1 if window_end < len(s): freq[s[window_end]] += 1 return count if __name__ == '__main__': s = 'aabbcc' k = 2 print(count_substrings(s k)) s = 'aabbc' k = 2 print(count_substrings(s k)) 
C#
using System; class GFG{ static bool have_same_frequency(int[] freq int k) {  for(int i = 0; i < 26; i++)   {  if (freq[i] != 0 && freq[i] != k)   {  return false;  }  }  return true; } static int count_substrings(string s int k) {  int count = 0;  int distinct = 0;  bool[] have = new bool[26];  Array.Fill(have false);    for(int i = 0; i < s.Length; i++)   {  have[((int)(s[i] - 'a'))] = true;  }    for(int i = 0; i < 26; i++)   {  if (have[i])   {  distinct++;  }  }    for(int length = 1; length <= distinct; length++)   {  int window_length = length * k;  int[] freq = new int[26];  Array.Fill(freq 0);  int window_start = 0;  int window_end = window_start +   window_length - 1;    for(int i = window_start;  i <= Math.Min(window_end s.Length - 1);  i++)   {  freq[((int)(s[i] - 'a'))]++;  }  while (window_end < s.Length)   {  if (have_same_frequency(freq k))  {  count++;  }  freq[((int)(s[window_start] - 'a'))]--;  window_start++;  window_end++;    if (window_end < s.Length)   {  freq[((int)(s[window_end] - 'a'))]++;  }  }  }  return count; } // Driver code public static void Main(string[] args) {  string s = 'aabbcc';  int k = 2;  Console.WriteLine(count_substrings(s k));    s = 'aabbc';  k = 2;  Console.WriteLine(count_substrings(s k)); } } // This code is contributed by gaurav01 
JavaScript
<script> function have_same_frequency(freqk) {  for (let i = 0; i < 26; i++) {  if (freq[i] != 0 && freq[i] != k) {  return false;  }  }  return true; } function count_substrings(sk) {  let count = 0;  let distinct = 0;  let have = new Array(26);  for(let i=0;i<26;i++)  {  have[i]=false;  }  for (let i = 0; i < s.length; i++) {  have[((s[i].charCodeAt(0) -   'a'.charCodeAt(0)))] = true;  }  for (let i = 0; i < 26; i++) {  if (have[i]) {  distinct++;  }  }  for (let length = 1; length <= distinct; length++) {  let window_length = length * k;  let freq = new Array(26);  for(let i=0;i<26;i++)  freq[i]=0;  let window_start = 0;  let window_end  = window_start + window_length - 1;  for (let i = window_start;  i <= Math.min(window_end s.length - 1);  i++) {  freq[((s[i].charCodeAt(0) -   'a'.charCodeAt(0)))]++;  }  while (window_end < s.length) {  if (have_same_frequency(freq k)) {  count++;  }  freq[(  (s[window_start].charCodeAt(0) -   'a'.charCodeAt(0)))]--;  window_start++;  window_end++;  if (window_end < s.length) {  freq[(s[window_end].charCodeAt(0)  - 'a'.charCodeAt(0))]++;  }  }  }  return count; } let s = 'aabbcc'; let k = 2; document.write(count_substrings(s k)+'  
'
); s = 'aabbc'; k = 2; document.write(count_substrings(s k)+'
'
); // This code is contributed by rag2127 </script>

Výstup
6 3

Časová zložitosť: O(N * D) kde D je počet odlišných znakov prítomných v reťazci a N je dĺžka reťazca.
Pomocný priestor: O(N) 

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