Sub-strings that start and end with one character and have at least one other

Given a string str which contains only the characters x and y, the task is to count all the sub-strings that start and end with an x and have at least a single y.

Examples:

Input: str = “xyyxx”
Output: 2
“xyyx” and “xyyxx” are the only valid sub-strings.

Input: str = “xyy”
Output: 0



Approach:

  • Create an array countX[] where countX[i] stores the total x from i to n – 1.
  • Now, for every x in the string, find the first y that appears after this x.
  • And update count = count + countX[indexOf(y)] because with this x as the starting index, all sub-strings will be valid that will end at any x after the found y.
  • Return the count in the end.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;
  
// Function that returns the index of next occurrence
// of the character c in string str starting from index start
int nextIndex(string str, int start, char c)
{
  
    // Starting from start
    for (int i = start; i < str.length(); i++) {
  
        // If current character = c
        if (str[i] == c)
            return i;
    }
  
    // Not found
    return -1;
}
  
// Function to return the count of required sub-strings
int countSubStrings(string str)
{
    int i, n = str.length();
  
    // Stores running count of 'x' starting from the end
    int countX[n];
  
    int count = 0;
    for (i = n - 1; i >= 0; i--) {
        if (str[i] == 'x')
            count++;
        countX[i] = count;
    }
  
    // Next index of 'x' starting from index 0
    int nextIndexX = nextIndex(str, 0, 'x');
  
    // Next index of 'y' starting from index 0
    int nextIndexY = nextIndex(str, 0, 'y');
  
    // To store the count of required sub-strings
    count = 0;
    while (nextIndexX != -1 && nextIndexY != -1) {
  
        // If 'y' appears before 'x'
        // it won't contribute to a valid sub-string
        if (nextIndexX > nextIndexY) {
  
            // Find next occurrence of 'y'
            nextIndexY = nextIndex(str, nextIndexY + 1, 'y');
            continue;
        }
  
        // If 'y' appears after 'x'
        // every sub-string ending at an 'x' appearing after this 'y'
        // and starting with the current 'x' is a valid sub-string
        else {
            count += countX[nextIndexY];
  
            // Find next occurrence of 'x'
            nextIndexX = nextIndex(str, nextIndexX + 1, 'x');
        }
    }
  
    // Return the count
    return count;
}
  
// Driver code
int main()
{
  
    string s = "xyyxx";
  
    cout << countSubStrings(s);
}
  
// This code is contributed by ihritik

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Java

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// Java implementation of the approach
public class GFG {
  
    // Function that returns the index of next occurrence
    // of the character c in string str starting from index start
    static int nextIndex(String str, int start, char c)
    {
  
        // Starting from start
        for (int i = start; i < str.length(); i++) {
  
            // If current character = c
            if (str.charAt(i) == c)
                return i;
        }
  
        // Not found
        return -1;
    }
  
    // Function to return the count of required sub-strings
    static int countSubStrings(String str)
    {
        int i, n = str.length();
  
        // Stores running count of 'x' starting from the end
        int countX[] = new int[n];
  
        int count = 0;
        for (i = n - 1; i >= 0; i--) {
            if (str.charAt(i) == 'x')
                count++;
            countX[i] = count;
        }
  
        // Next index of 'x' starting from index 0
        int nextIndexX = nextIndex(str, 0, 'x');
  
        // Next index of 'y' starting from index 0
        int nextIndexY = nextIndex(str, 0, 'y');
  
        // To store the count of required sub-strings
        count = 0;
        while (nextIndexX != -1 && nextIndexY != -1) {
  
            // If 'y' appears before 'x'
            // it won't contribute to a valid sub-string
            if (nextIndexX > nextIndexY) {
  
                // Find next occurrence of 'y'
                nextIndexY = nextIndex(str, nextIndexY + 1, 'y');
                continue;
            }
  
            // If 'y' appears after 'x'
            // every sub-string ending at an 'x' appearing after this 'y'
            // and starting with the current 'x' is a valid sub-string
            else {
                count += countX[nextIndexY];
  
                // Find next occurrence of 'x'
                nextIndexX = nextIndex(str, nextIndexX + 1, 'x');
            }
        }
  
        // Return the count
        return count;
    }
  
    // Driver code
    public static void main(String[] args)
    {
  
        String s = "xyyxx";
  
        System.out.println(countSubStrings(s));
    }
}

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Python3

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# Python3 implementation of the approach
  
# Function that returns the index of next occurrence
# of the character c in string str starting from index start
def nextIndex(str, start, c):
  
  
    # Starting from start
    for i in range(start,len(str)): 
  
        # If current character = c
        if (str[i] == c):
            return i;
      
  
    # Not found
    return -1;
  
  
# Function to return the count of required sub-strings
def countSubStrings(str):
  
    n = len(str)
  
    # Stores running count of 'x' starting from the end
    countX=[0]*n;
  
    count = 0;
    for i in range(n-1,-1,-1): 
        if (str[i] == 'x'):
            count=count+1
        countX[i] = count
      
  
    # Next index of 'x' starting from index 0
    nextIndexX = nextIndex(str, 0, 'x')
  
    # Next index of 'y' starting from index 0
    nextIndexY = nextIndex(str, 0, 'y')
  
    # To store the count of required sub-strings
    count = 0;
    while (nextIndexX != -1 and nextIndexY != -1):
  
        # If 'y' appears before 'x'
        # it won't contribute to a valid sub-string
        if (nextIndexX > nextIndexY):
  
            # Find next occurrence of 'y'
            nextIndexY = nextIndex(str, nextIndexY + 1, 'y')
            continue
          
  
        # If 'y' appears after 'x'
        # every sub-string ending at an 'x' appearing after this 'y'
        # and starting with the current 'x' is a valid sub-string
        else :
            count += countX[nextIndexY]
  
            # Find next occurrence of 'x'
            nextIndexX = nextIndex(str, nextIndexX + 1, 'x');
          
      
  
    # Return the count
    return count
  
  
# Driver code
  
  
s = "xyyxx";
  
print(countSubStrings(s));
  
  
# This code is contributed by ihritik

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C#

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// C# implementation of the approach 
  
using System;
  
public class GFG { 
  
    // Function that returns the index of next occurrence 
    // of the character c in string str starting from index start 
    static int nextIndex(string str, int start, char c) 
    
  
        // Starting from start 
        for (int i = start; i < str.Length; i++) { 
  
            // If current character = c 
            if (str[i] == c) 
                return i; 
        
  
        // Not found 
        return -1; 
    
  
    // Function to return the count of required sub-strings 
    static int countSubStrings(string str) 
    
        int i, n = str.Length ; 
  
        // Stores running count of 'x' starting from the end 
        int []countX = new int[n]; 
  
        int count = 0; 
        for (i = n - 1; i >= 0; i--) { 
            if (str[i] == 'x'
                count++; 
            countX[i] = count; 
        
  
        // Next index of 'x' starting from index 0 
        int nextIndexX = nextIndex(str, 0, 'x'); 
  
        // Next index of 'y' starting from index 0 
        int nextIndexY = nextIndex(str, 0, 'y'); 
  
        // To store the count of required sub-strings 
        count = 0; 
        while (nextIndexX != -1 && nextIndexY != -1) { 
  
            // If 'y' appears before 'x' 
            // it won't contribute to a valid sub-string 
            if (nextIndexX > nextIndexY) { 
  
                // Find next occurrence of 'y' 
                nextIndexY = nextIndex(str, nextIndexY + 1, 'y'); 
                continue
            
  
            // If 'y' appears after 'x' 
            // every sub-string ending at an 'x' appearing after this 'y' 
            // and starting with the current 'x' is a valid sub-string 
            else
                count += countX[nextIndexY]; 
  
                // Find next occurrence of 'x' 
                nextIndexX = nextIndex(str, nextIndexX + 1, 'x'); 
            
        
  
        // Return the count 
        return count; 
    
  
    // Driver code 
    public static void Main() 
    
  
        string s = "xyyxx"
  
        Console.WriteLine(countSubStrings(s)); 
    
    // This code is contributed by Ryuga

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PHP

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<?php 
// PHP implementation of the approach
   
// Function that returns the index of next occurrence
// of the character c in string str starting from index start
function nextIndex($str, $start, $c)
{
   
    // Starting from start
    for ($i = $start; $i < strlen($str); $i++) {
   
        // If current character = c
        if ($str[$i] == $c)
            return $i;
    }
   
    // Not found
    return -1;
}
   
// Function to return the count of required sub-strings
function countSubStrings($str)
{
    $n = strlen($str);
   
    // Stores running count of 'x' starting from the end
    $countX = array(0,$n,NULL);
   
    $count = 0;
    for ($i = $n - 1; $i >= 0; $i--) {
        if ($str[$i] == 'x')
            $count++;
        $countX[$i] = $count;
    }
   
    // Next index of 'x' starting from index 0
    $nextIndexX = nextIndex($str, 0, 'x');
   
    // Next index of 'y' starting from index 0
    $nextIndexY = nextIndex($str, 0, 'y');
   
    // To store the count of required sub-strings
    $count = 0;
    while ($nextIndexX != -1 && $nextIndexY != -1) {
   
        // If 'y' appears before 'x'
        // it won't contribute to a valid sub-string
        if ($nextIndexX > $nextIndexY) {
   
            // Find next occurrence of 'y'
            $nextIndexY = nextIndex($str, $nextIndexY + 1, 'y');
            continue;
        }
   
        // If 'y' appears after 'x'
        // every sub-string ending at an 'x' appearing after this 'y'
        // and starting with the current 'x' is a valid sub-string
        else {
            $count += $countX[$nextIndexY];
   
            // Find next occurrence of 'x'
            $nextIndexX = nextIndex($str, $nextIndexX + 1, 'x');
        }
    }
   
    // Return the count
    return $count;
}
   
// Driver code
  
$s = "xyyxx";
echo countSubStrings($s);
?>

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Output:

2


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