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Count of all sub-strings with sum of weights at most K
  • Last Updated : 06 Nov, 2020

Given a string S consisting of small English letters and a string W consisting of weight of all characters of English alphabet where for all i, 

0 \leq Qi \leq 9

. We have to find the total numbers of a unique substring with sum of weights at most K.
Examples: 

Input : P = “ababab”, Q = “12345678912345678912345678”, K=5 
Output :
Explanation : 
The unique substrings are: “a”, “ab”, “b”, “bc”, “c”, “d”, “e” 
Hence, the count is 7.

Input : P = “acbacbacaa”, Q = “12300045600078900012345000”, K=2 
Output :
Explanation :The unique substrings are: “a”, “b”, “aa” 
Hence, the count is 3. 
 



Approach: 
To solve the above problem, the main idea is to simply iterate through all the substrings and maintain a sum of the weight of all characters encountered so far. If the sum of characters is not greater than K, then insert it in a hashmap otherwise discard it and move forward with another substring. Finally, the result will be the size of the hashmap because it stores all the substring which have weight less than or equal to K.

Below is the implementation of the above approach:  

C++




// C++ implementation to Count all
// sub-strings with sum of weights at most K
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to count all substrings
int distinctSubstring(string& P, string& Q,
                      int K, int N)
{
 
    // Hashmap to store substrings
    unordered_set<string> S;
 
    // iterate over all substrings
    for (int i = 0; i < N; ++i) {
 
        // variable to maintain sum
        // of all characters encountered
        int sum = 0;
 
        // variable to maintain
        // substring till current position
        string s;
 
        for (int j = i; j < N; ++j) {
            // get position of
            // character in string W
            int pos = P[j] - 'a';
 
            // add weight to current sum
            sum += Q[pos] - '0';
 
            // add current character to substring
            s += P[j];
 
            // check if sum of characters
            // is <=K insert in Hashmap
            if (sum <= K) {
                S.insert(s);
            }
            else {
                break;
            }
        }
    }
 
    return S.size();
}
 
// Driver code
int main()
{
    // initialise string
    string S = "abcde";
 
    // initialise weight
    string W = "12345678912345678912345678";
 
    int K = 5;
 
    int N = S.length();
 
    cout << distinctSubstring(S, W, K, N);
 
    return 0;
}


Java




// Java implementation to count all
// sub-strings with sum of weights at most K
import java.io.*;
import java.util.*;
 
class GFG{
 
// Function to count all substrings
static int distinctSubstring(String P, String Q,
                             int K, int N)
{
     
    // Hashmap to store substrings
    Set<String> S = new HashSet<>();
 
    // Iterate over all substrings
    for(int i = 0; i < N; ++i)
    {
         
        // Variable to maintain sum
        // of all characters encountered
        int sum = 0;
 
        // Variable to maintain substring
        // till current position
        String s = "";
 
        for(int j = i; j < N; ++j)
        {
             
            // Get position of
            // character in string W
            int pos = P.charAt(j) - 'a';
 
            // Add weight to current sum
            sum += Q.charAt(pos) - '0';
 
            // Add current character to substring
            s += P.charAt(j);
 
            // Check if sum of characters
            // is <=K insert in Hashmap
            if (sum <= K)
            {
                S.add(s);
            }
            else
            {
                break;
            }
        }
    }
    return S.size();
}
 
// Driver Code
public static void main(String args[])
{
     
    // Initialise string
    String S = "abcde";
 
    // Initialise weight
    String W = "12345678912345678912345678";
 
    int K = 5;
    int N = S.length();
 
    System.out.println(distinctSubstring(S, W, K, N));
}
}
 
// This code is contributed by offbeat


Python3




# Python3 implementation to Count all
# sub-strings with sum of weights at most K
 
# Function to count all substrings
def distinctSubstring(P, Q, K, N):
 
    # Hashmap to store substrings
    S = set()
 
    # iterate over all substrings
    for i in range(N):
 
        # variable to maintain sum
        # of all characters encountered
        sum = 0
 
        # variable to maintain
        # substring till current position
        s = ""
 
        for j in range(i, N):
 
            # get position of
            # character in string W
            pos = ord(P[j]) - 97
 
            # add weight to current sum
            sum += ord(Q[pos]) - 48
 
            # add current character to substring
            s += P[j]
 
            # check if sum of characters
            # is <=K insert in Hashmap
            if (sum <= K):
                S.add(s)
 
            else:
                break
 
    return len(S)
 
# Driver code
if __name__ == '__main__':
    # initialise string
    S = "abcde"
 
    # initialise weight
    W = "12345678912345678912345678"
 
    K = 5
 
    N = len(S)
 
    print(distinctSubstring(S, W, K, N))
 
# This code is contributed by Surendra_Gangwar


C#




// C# implementation to count all sub-strings
// with sum of weights at most K 
using System;
using System.Collections.Generic;
 
class GFG{
     
// Function to count all substrings 
static int distinctSubstring(string P, string Q, 
                             int K, int N) 
     
    // Hashmap to store substrings 
    HashSet<string> S = new HashSet<string>();
   
    // Iterate over all substrings 
    for(int i = 0; i < N; ++i)
    
         
        // Variable to maintain sum 
        // of all characters encountered 
        int sum = 0; 
         
        // Variable to maintain substring
        // till current position 
        string s = ""
   
        for(int j = i; j < N; ++j)
        {
             
            // Get position of 
            // character in string W 
            int pos = P[j] - 'a'
   
            // Add weight to current sum 
            sum += Q[pos] - '0'
             
            // Add current character to
            // substring 
            s += P[j]; 
   
            // Check if sum of characters 
            // is <=K insert in Hashmap 
            if (sum <= K)
            {
                S.Add(s); 
            
            else
            
                break
            
        
    
    return S.Count; 
 
// Driver code
static void Main()
{
     
    // Initialise string 
    string S = "abcde"
   
    // Initialise weight 
    string W = "12345678912345678912345678"
   
    int K = 5; 
    int N = S.Length; 
   
    Console.WriteLine(distinctSubstring(S, W, K, N)); 
}
}
 
// This code is contributed by divyeshrabadiya07


Output: 

7




 

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