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Count M-length substrings occurring exactly K times in a string
• Difficulty Level : Easy
• Last Updated : 01 Mar, 2021

Given a string S of length N and two integers M and K, the task is to count the number of substrings of length M occurring exactly K times in the string S

Examples:

Input: S = “abacaba”, M = 3, K = 2
Output: 1
Explanation: All distinct substrings of length 3 are “aba”, “bac”, “aca”, “cab”.
Out of all these substrings, only “aba” occurs twice in the string S.
Therefore, the count is 1.

Input: S = “geeksforgeeks”, M = 2, K = 1
Output: 4
Explanation:
All distinct substrings of length 2 are “ge”, “ee”, “ek”, “ks”, “sf”, “fo”, “or”, “rg”.
Out of all these strings, “sf”, “fo”, “or”, “rg” occurs once in the string S.
Therefore, the count is 4.

Naive Approach: The simplest approach is to generate all substrings of length M and store the frequency of each substring in the string S in a Map. Now, traverse the Map and if the frequency is equal to K, then increment count by 1. After completing the above steps, print count as the result.
Time Complexity: O((N – M)*N*M)
Auxiliary Space: O(N – M)

Efficient Approach: The above approach can be optimized by using the KMP algorithm for finding the frequency of a substring in the string. Follow the steps to solve the problem:

• Initialize a variable, say count as 0, to store the number of the required substring.
• Generate all substrings of length M from the string S and insert them in an array, say arr[].
• Traverse the array arr[] and for each string in the array, calculate its frequency in the string S using KMP algorithm.
• If the frequency of the string is equal to P, then increment the count by 1.
• After completing the above steps, print the value of count as the resultant count of substrings.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to compute the LPS array``void` `computeLPSArray(string pat, ``int` `M,``                     ``int` `lps[])``{``    ``// Length of the previous``    ``// longest prefix suffix``    ``int` `len = 0;``    ``int` `i = 1;``    ``lps = 0;` `    ``// Iterate from [1, M - 1] to find lps[i]``    ``while` `(i < M) {` `        ``// If the characters match``        ``if` `(pat[i] == pat[len]) {` `            ``len++;``            ``lps[i] = len;``            ``i++;``        ``}` `        ``// If pat[i] != pat[len]``        ``else` `{` `            ``// If length is non-zero``            ``if` `(len != 0) {``                ``len = lps[len - 1];` `                ``// Also, note that i is``                ``// not incremented here``            ``}` `            ``// Otherwise``            ``else` `{``                ``lps[i] = len;``                ``i++;``            ``}``        ``}``    ``}``}` `// Function to find the frequency of``// pat in the string txt``int` `KMPSearch(string pat, string txt)``{``    ``// Stores length of both strings``    ``int` `M = pat.length();``    ``int` `N = txt.length();` `    ``// Initialize lps[] to store the``    ``// longest prefix suffix values``    ``// for the string pattern``    ``int` `lps[M];` `    ``// Store the index for pat[]``    ``int` `j = 0;` `    ``// Preprocess the pattern``    ``// (calculate lps[] array)``    ``computeLPSArray(pat, M, lps);` `    ``// Store the index for txt[]``    ``int` `i = 0;``    ``int` `res = 0;``    ``int` `next_i = 0;` `    ``while` `(i < N) {``        ``if` `(pat[j] == txt[i]) {``            ``j++;``            ``i++;``        ``}``        ``if` `(j == M) {` `            ``// If pattern is found the``            ``// first time, iterate again``            ``// to check for more patterns``            ``j = lps[j - 1];``            ``res++;` `            ``// Start i to check for more``            ``// than once occurrence``            ``// of pattern, reset i to``            ``// previous start + 1``            ``if` `(lps[j] != 0)``                ``i = ++next_i;``            ``j = 0;``        ``}` `        ``// Mismatch after j matches``        ``else` `if` `(i < N``                 ``&& pat[j] != txt[i]) {` `            ``// Do not match lps[0..lps[j-1]]``            ``// characters, they will``            ``// match anyway``            ``if` `(j != 0)``                ``j = lps[j - 1];``            ``else``                ``i = i + 1;``        ``}``    ``}` `    ``// Return the required frequency``    ``return` `res;``}` `// Function to find count of substrings``// of length M occurring exactly P times``// in the string, S``void` `findCount(string& S, ``int` `M, ``int` `P)``{` `    ``// Store all substrings of length M``    ``set vec;` `    ``// Store the size of the string, S``    ``int` `n = S.length();` `    ``// Pick starting point``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Pick ending point``        ``for` `(``int` `len = 1;``             ``len <= n - i; len++) {` `            ``// If the substring is of``            ``// length M, insert it in vec``            ``string s = S.substr(i, len);``            ``if` `(s.length() == M) {``                ``vec.insert(s);``            ``}``        ``}``    ``}` `    ``// Initialise count as 0 to store``    ``// the required count of substrings``    ``int` `count = 0;` `    ``// Iterate through the set of``    ``// substrings``    ``for` `(``auto` `it : vec) {` `        ``// Store its frequency``        ``int` `ans = KMPSearch(it, S);` `        ``// If frequency is equal to P``        ``if` `(ans == P) {` `            ``// Increment count by 1``            ``count++;``        ``}``    ``}` `    ``// Print the answer``    ``cout << count;``}` `// Driver Code``int` `main()``{``    ``string S = ``"abacaba"``;``    ``int` `M = 3, P = 2;` `    ``// Function Call``    ``findCount(S, M, P);` `    ``return` `0;``}`

## Java

 `// Java Program to implement``// the above approach` `import` `java.io.*;``import` `java.util.*;` `class` `GFG {` `    ``// Function to compute the LPS array``    ``static` `void` `computeLPSArray(String pat, ``int` `M,``                                ``int` `lps[])``    ``{``        ``// Length of the previous``        ``// longest prefix suffix``        ``int` `len = ``0``;``        ``int` `i = ``1``;``        ``lps[``0``] = ``0``;` `        ``// Iterate from [1, M - 1] to find lps[i]``        ``while` `(i < M) {` `            ``// If the characters match``            ``if` `(pat.charAt(i) == pat.charAt(len)) {` `                ``len++;``                ``lps[i] = len;``                ``i++;``            ``}` `            ``// If pat[i] != pat[len]``            ``else` `{` `                ``// If length is non-zero``                ``if` `(len != ``0``) {``                    ``len = lps[len - ``1``];` `                    ``// Also, note that i is``                    ``// not incremented here``                ``}` `                ``// Otherwise``                ``else` `{``                    ``lps[i] = len;``                    ``i++;``                ``}``            ``}``        ``}``    ``}` `    ``// Function to find the frequency of``    ``// pat in the string txt``    ``static` `int` `KMPSearch(String pat, String txt)``    ``{``        ``// Stores length of both strings``        ``int` `M = pat.length();``        ``int` `N = txt.length();` `        ``// Initialize lps[] to store the``        ``// longest prefix suffix values``        ``// for the string pattern``        ``int` `lps[] = ``new` `int``[M];` `        ``// Store the index for pat[]``        ``int` `j = ``0``;` `        ``// Preprocess the pattern``        ``// (calculate lps[] array)``        ``computeLPSArray(pat, M, lps);` `        ``// Store the index for txt[]``        ``int` `i = ``0``;``        ``int` `res = ``0``;``        ``int` `next_i = ``0``;` `        ``while` `(i < N) {``            ``if` `(pat.charAt(j) == txt.charAt(i)) {``                ``j++;``                ``i++;``            ``}``            ``if` `(j == M) {` `                ``// If pattern is found the``                ``// first time, iterate again``                ``// to check for more patterns``                ``j = lps[j - ``1``];``                ``res++;` `                ``// Start i to check for more``                ``// than once occurrence``                ``// of pattern, reset i to``                ``// previous start + 1``                ``if` `(lps[j] != ``0``)``                    ``i = ++next_i;``                ``j = ``0``;``            ``}` `            ``// Mismatch after j matches``            ``else` `if` `(i < N``                     ``&& pat.charAt(j) != txt.charAt(i)) {` `                ``// Do not match lps[0..lps[j-1]]``                ``// characters, they will``                ``// match anyway``                ``if` `(j != ``0``)``                    ``j = lps[j - ``1``];``                ``else``                    ``i = i + ``1``;``            ``}``        ``}` `        ``// Return the required frequency``        ``return` `res;``    ``}` `    ``// Function to find count of substrings``    ``// of length M occurring exactly P times``    ``// in the string, S``    ``static` `void` `findCount(String S, ``int` `M, ``int` `P)``    ``{` `        ``// Store all substrings of length M``        ``// set vec;``        ``TreeSet vec = ``new` `TreeSet<>();` `        ``// Store the size of the string, S``        ``int` `n = S.length();` `        ``// Pick starting point``        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``// Pick ending point``            ``for` `(``int` `len = ``1``; len <= n - i; len++) {` `                ``// If the substring is of``                ``// length M, insert it in vec``                ``String s = S.substring(i, i + len);``                ``if` `(s.length() == M) {``                    ``vec.add(s);``                ``}``            ``}``        ``}` `        ``// Initialise count as 0 to store``        ``// the required count of substrings``        ``int` `count = ``0``;` `        ``// Iterate through the set of``        ``// substrings``        ``for` `(String it : vec) {` `            ``// Store its frequency``            ``int` `ans = KMPSearch(it, S);` `            ``// If frequency is equal to P``            ``if` `(ans == P) {` `                ``// Increment count by 1``                ``count++;``            ``}``        ``}` `        ``// Print the answer``        ``System.out.println(count);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``String S = ``"abacaba"``;``        ``int` `M = ``3``, P = ``2``;` `        ``// Function Call``        ``findCount(S, M, P);``    ``}``}` `// This code is contributed by kingash.`

## Python3

 `# Python 3 program for the above approach` `# Function to compute the LPS array``def` `computeLPSArray(pat, M, lps):``  ` `    ``# Length of the previous``    ``# longest prefix suffix``    ``len1 ``=` `0``    ``i ``=` `1``    ``lps[``0``] ``=` `0` `    ``# Iterate from [1, M - 1] to find lps[i]``    ``while` `(i < M):``      ` `        ``# If the characters match``        ``if` `(pat[i] ``=``=` `pat[len1]):``            ``len1 ``+``=` `1``            ``lps[i] ``=` `len1``            ``i ``+``=` `1` `        ``# If pat[i] != pat[len]``        ``else``:``            ``# If length is non-zero``            ``if` `(len1 !``=` `0``):``                ``len1 ``=` `lps[len1 ``-` `1``]` `                ``# Also, note that i is``                ``# not incremented here` `            ``# Otherwise``            ``else``:``                ``lps[i] ``=` `len1``                ``i ``+``=` `1` `# Function to find the frequency of``# pat in the string txt``def` `KMPSearch(pat, txt):``  ` `    ``# Stores length of both strings``    ``M ``=` `len``(pat)``    ``N ``=` `len``(txt)` `    ``# Initialize lps[] to store the``    ``# longest prefix suffix values``    ``# for the string pattern``    ``lps ``=` `[``0` `for` `i ``in` `range``(M)]` `    ``# Store the index for pat[]``    ``j ``=` `0` `    ``# Preprocess the pattern``    ``# (calculate lps[] array)``    ``computeLPSArray(pat, M, lps)` `    ``# Store the index for txt[]``    ``i ``=` `0``    ``res ``=` `0``    ``next_i ``=` `0` `    ``while` `(i < N):``        ``if` `(pat[j] ``=``=` `txt[i]):``            ``j ``+``=` `1``            ``i ``+``=` `1``        ``if` `(j ``=``=` `M):``          ` `            ``# If pattern is found the``            ``# first time, iterate again``            ``# to check for more patterns``            ``j ``=` `lps[j ``-` `1``]``            ``res ``+``=` `1` `            ``# Start i to check for more``            ``# than once occurrence``            ``# of pattern, reset i to``            ``# previous start + 1``            ``if` `(lps[j] !``=` `0``):``                ``next_i ``+``=` `1``                ``i ``=` `next_i``            ``j ``=` `0` `        ``# Mismatch after j matches``        ``elif` `(i < N ``and` `pat[j] !``=` `txt[i]):``            ``# Do not match lps[0..lps[j-1]]``            ``# characters, they will``            ``# match anyway``            ``if` `(j !``=` `0``):``                ``j ``=` `lps[j ``-` `1``]``            ``else``:``                ``i ``=` `i ``+` `1` `    ``# Return the required frequency``    ``return` `res` `# Function to find count of substrings``# of length M occurring exactly P times``# in the string, S``def` `findCount(S, M, P):``  ` `    ``# Store all substrings of length M``    ``vec ``=` `set``()` `    ``# Store the size of the string, S``    ``n ``=` `len``(S)` `    ``# Pick starting point``    ``for` `i ``in` `range``(n):``      ` `        ``# Pick ending point``        ``for` `len1 ``in` `range``(n ``-` `i ``+` `1``):``          ` `            ``# If the substring is of``            ``# length M, insert it in vec``            ``s ``=` `S[i:len1]``            ` `          ``#  if (len1(s) == M):``           ``#     vec.add(s)` `    ``# Initialise count as 0 to store``    ``# the required count of substrings``    ``count ``=` `1` `    ``# Iterate through the set of``    ``# substrings``    ``for` `it ``in` `vec:``      ` `        ``# Store its frequency``        ``ans ``=` `KMPSearch(it, S)` `        ``# If frequency is equal to P``        ``if` `(ans ``=``=` `P):``          ` `            ``# Increment count by 1``            ``count ``+``=` `1` `    ``# Print the answer``    ``print``(count)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``S ``=` `"abacaba"``    ``M ``=` `3``    ``P ``=` `2` `    ``# Function Call``    ``findCount(S, M, P)``    ` `    ``# This code is contributed by ipg2016107.`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;``class` `GFG``{` `  ``// Function to compute the LPS array``  ``static` `void` `computeLPSArray(``string` `pat, ``int` `M, ``int``[] lps)``  ``{` `    ``// Length of the previous``    ``// longest prefix suffix``    ``int` `len = 0;``    ``int` `i = 1;``    ``lps = 0;` `    ``// Iterate from [1, M - 1] to find lps[i]``    ``while` `(i < M)``    ``{` `      ``// If the characters match``      ``if` `(pat[i] == pat[len])``      ``{``        ``len++;``        ``lps[i] = len;``        ``i++;``      ``}` `      ``// If pat[i] != pat[len]``      ``else` `{` `        ``// If length is non-zero``        ``if` `(len != 0) {``          ``len = lps[len - 1];` `          ``// Also, note that i is``          ``// not incremented here``        ``}` `        ``// Otherwise``        ``else` `{``          ``lps[i] = len;``          ``i++;``        ``}``      ``}``    ``}``  ``}` `  ``// Function to find the frequency of``  ``// pat in the string txt``  ``static` `int` `KMPSearch(``string` `pat, ``string` `txt)``  ``{` `    ``// Stores length of both strings``    ``int` `M = pat.Length;``    ``int` `N = txt.Length;` `    ``// Initialize lps[] to store the``    ``// longest prefix suffix values``    ``// for the string pattern``    ``int``[] lps = ``new` `int``[M];` `    ``// Store the index for pat[]``    ``int` `j = 0;` `    ``// Preprocess the pattern``    ``// (calculate lps[] array)``    ``computeLPSArray(pat, M, lps);` `    ``// Store the index for txt[]``    ``int` `i = 0;``    ``int` `res = 0;``    ``int` `next_i = 0;` `    ``while` `(i < N) {``      ``if` `(pat[j] == txt[i]) {``        ``j++;``        ``i++;``      ``}``      ``if` `(j == M) {` `        ``// If pattern is found the``        ``// first time, iterate again``        ``// to check for more patterns``        ``j = lps[j - 1];``        ``res++;` `        ``// Start i to check for more``        ``// than once occurrence``        ``// of pattern, reset i to``        ``// previous start + 1``        ``if` `(lps[j] != 0)``          ``i = ++next_i;``        ``j = 0;``      ``}` `      ``// Mismatch after j matches``      ``else` `if` `(i < N``               ``&& pat[j] != txt[i]) {` `        ``// Do not match lps[0..lps[j-1]]``        ``// characters, they will``        ``// match anyway``        ``if` `(j != 0)``          ``j = lps[j - 1];``        ``else``          ``i = i + 1;``      ``}``    ``}` `    ``// Return the required frequency``    ``return` `res;``  ``}` `  ``// Function to find count of substrings``  ``// of length M occurring exactly P times``  ``// in the string, S``  ``static` `void` `findCount(``string` `S, ``int` `M, ``int` `P)``  ``{` `    ``// Store all substrings of length M``    ``HashSet<``string``> vec = ``new` `HashSet<``string``>();` `    ``// Store the size of the string, S``    ``int` `n = S.Length;` `    ``// Pick starting point``    ``for` `(``int` `i = 0; i < n; i++) {` `      ``// Pick ending point``      ``for` `(``int` `len = 1;``           ``len <= n - i; len++) {` `        ``// If the substring is of``        ``// length M, insert it in vec``        ``string` `s = S.Substring(i, len);``        ``if` `(s.Length == M) {``          ``vec.Add(s);``        ``}``      ``}``    ``}` `    ``// Initialise count as 0 to store``    ``// the required count of substrings``    ``int` `count = 0;` `    ``// Iterate through the set of``    ``// substrings``    ``foreach``(``string` `it ``in` `vec) {` `      ``// Store its frequency``      ``int` `ans = KMPSearch(it, S);` `      ``// If frequency is equal to P``      ``if` `(ans == P) {` `        ``// Increment count by 1``        ``count++;``      ``}``    ``}` `    ``// Print the answer``    ``Console.WriteLine(count);``  ``}` `  ``// Driver code``  ``static` `void` `Main() {``    ``string` `S = ``"abacaba"``;``    ``int` `M = 3, P = 2;` `    ``// Function Call``    ``findCount(S, M, P);``  ``}``}` `// This code is contributed by divyeshrabadiya07.`
Output:
`1`

Time Complexity: O((N*M) + (N2 – M2))
Auxiliary Space: O(N – M)

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