Perform range sum queries on string as per given condition

Given a string S with lowercase alphabets only and Q queries where each query contains a pair {L, R}. For each query {L, R}, there exists a substring S[L, R], the task is to find the value of the product of the frequency of each character in substring with their position in alphabetical order. 
Note: Consider 1-based indexing.
Examples: 
 

Input: S = “abcd”, Q = { {2, 4}, {1, 3} } 
Output: 9 6 
Explanation: 
For 1st query, 
substring is S[2, 4] = “bcd”. Therefore the frequency of b, c, d are 1, 1, 1 in range 2 to 4. 
value = 2*(1) + 3*(1) + 4*(1) = 9.
For 2nd query, 
substring is S[1, 3] = “abc”. Therefore the frequency of a, b, c are 1, 1, 1 in range 1 to 3. 
value = 1*(1) + 2*(1) + 3*(1) = 6.

Input: S = “geeksforgeeks”, Q = { {3, 3}, {2, 6}, {1, 13} } 
Output: 5 46 133 
 

Naive Approach: The naive idea is to traverse for each ranges [L, R] in the query and keep the count of each character in an array. After traversing the range find the value of the expression 1*(occurrences of ‘a’) + 2*(occurrences of ‘b’) + 3*(occurrences of ‘c’) + ..+ 26*(occurrences of ‘z’)
Time Complexity: O(N*Q), where N is the length of the given string. 
Auxiliary Space: O(1)

Efficient Approach: The idea is to use the Prefix Sum of the whole string by which we can perform each query in constant time. Below are the steps: 
 

  1. Create an array arr[] of length equals to the length of the string.
  2. Traverse the given string and for each corresponding index i in the string, assign arr[i] the value of current character – ‘a’.
  3. Find the prefix sum of the array arr[]. This prefix sum array will given sum of occurrence of all characters till each index i.
  4. Now for each query(say {L, R}) the value of arr[R – 1] – arr[L – 2] will give the value of the given expression.

Below is the implementation of the above approach:
 



C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to perform range sum queries
// on string as per the given condition
void Range_sum_query(string S,
                     vector<pair<int, int> > Query)
{
    // Initialize N by string size
    int N = S.length();
  
    // Create array A[] for prefix sum
    int A[N];
  
    A[0] = S[0] - 'a' + 1;
  
    // Iterate till N
    for (int i = 1; i < N; i++) {
        A[i] = S[i] - 'a' + 1;
        A[i] = A[i] + A[i - 1];
    }
  
    // Traverse the queries
    for (int i = 0; i < Query.size(); i++) {
  
        if (Query[i].first == 1) {
  
            // Check if if L == 1 range
            // sum will be A[R-1]
            cout << A[(Query[i].second) - 1]
                 << endl;
        }
  
        else {
  
            // Condition if L > 1 range sum
            // will be A[R-1] - A[L-2]
            cout << A[(Query[i].second) - 1]
                        - A[(Query[i].first) - 2]
                 << endl;
        }
    }
}
  
// Driver Code
int main()
{
    // Given string
    string S = "abcd";
  
    vector<pair<int, int> > Query;
  
    // Given Queries
    Query.push_back(make_pair(2, 4));
    Query.push_back(make_pair(1, 3));
  
    // Function call
    Range_sum_query(S, Query);
    return 0;
}

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Java

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// Java program for the above approach
import java.util.*;
  
class GFG{
      
static class pair
    int first, second; 
    public pair(int first, int second) 
    
        this.first = first; 
        this.second = second; 
    
  
// Function to perform range sum queries
// on String as per the given condition
static void Range_sum_query(String S,
                            Vector<pair> Query)
{
      
    // Initialize N by String size
    int N = S.length();
  
    // Create array A[] for prefix sum
    int []A = new int[N];
  
    A[0] = S.charAt(0) - 'a' + 1;
  
    // Iterate till N
    for(int i = 1; i < N; i++)
    {
        A[i] = S.charAt(i) - 'a' + 1;
        A[i] = A[i] + A[i - 1];
    }
  
    // Traverse the queries
    for(int i = 0; i < Query.size(); i++)
    {
        if (Query.get(i).first == 1)
        {
              
            // Check if if L == 1 range
            // sum will be A[R-1]
            System.out.print(
                A[(Query.get(i).second) - 1] + "\n");
        }
  
        else 
        {
              
            // Condition if L > 1 range sum
            // will be A[R-1] - A[L-2]
            System.out.print(
                A[(Query.get(i).second) - 1] -
                A[(Query.get(i).first) - 2] + "\n");
        }
    }
}
  
// Driver Code
public static void main(String[] args)
{
      
    // Given String
    String S = "abcd";
  
    Vector<pair> Query = new Vector<pair>();
  
    // Given Queries
    Query.add(new pair(2, 4));
    Query.add(new pair(1, 3));
  
    // Function call
    Range_sum_query(S, Query);
}
}
  
// This code is contributed by Rajput-Ji

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Python3

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# Python3 program for the above approach 
  
# Function to perform range sum queries
# on string as per the given condition
def Range_sum_query(S, Query):
  
    # Initialize N by string size
    N = len(S)
  
    # Create array A[] for prefix sum
    A = [0] * N
  
    A[0] = ord(S[0]) - ord('a') + 1
  
    # Iterate till N
    for i in range(1, N):
        A[i] = ord(S[i]) - ord('a') + 1
        A[i] = A[i] + A[i - 1]
  
    # Traverse the queries
    for i in range(len(Query)):
        if(Query[i][0] == 1):
  
            # Check if if L == 1 range
            # sum will be A[R-1]
            print(A[Query[i][1] - 1])
  
        else:
  
            # Condition if L > 1 range sum
            # will be A[R-1] - A[L-2]
            print(A[Query[i][1] - 1] -
                  A[Query[i][0] - 2])
  
# Driver Code
  
# Given string
S = "abcd"
  
Query = []
  
# Given Queries
Query.append([2, 4])
Query.append([1, 3])
  
# Function call 
Range_sum_query(S, Query)
  
# This code is contributed by Shivam Singh

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C#

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// C# program for the above approach
using System;
using System.Collections.Generic;
   
class GFG{
  
  class pair
  {
    public int first, second;
    public pair(int first, int second)
    {
      this.first = first;
      this.second = second;
    }
  }
  
  // Function to perform range sum queries
  // on String as per the given condition
  static void Range_sum_query(String S, List<pair> Query)
  {
  
    // Initialize N by String size
    int N = S.Length;
  
    // Create array []A for prefix sum
    int[] A = new int[N];
  
    A[0] = S[0] - 'a' + 1;
  
    // Iterate till N
    for (int i = 1; i < N; i++)
    {
      A[i] = S[i] - 'a' + 1;
      A[i] = A[i] + A[i - 1];
    }
  
    // Traverse the queries
    for (int i = 0; i < Query.Count; i++) 
    {
      if (Query[i].first == 1)
      {
  
        // Check if if L == 1 range
        // sum will be A[R-1]
        Console.Write(A[(Query[i].second) - 1] + "\n");
      }
  
      else 
      {
  
        // Condition if L > 1 range sum
        // will be A[R-1] - A[L-2]
        Console.Write(A[(Query[i].second) - 1] - 
                      A[(Query[i].first) - 2] + "\n");
      }
    }
  }
  
  // Driver Code
  public static void Main(String[] args)
  {
  
    // Given String
    String S = "abcd";
  
    List<pair> Query = new List<pair>();
  
    // Given Queries
    Query.Add(new pair(2, 4));
    Query.Add(new pair(1, 3));
  
    // Function call
    Range_sum_query(S, Query);
  }
}
  
// This code is contributed by gauravrajput1

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Output: 

9
6

 

Time Complexity: O(N), where N is the length of the given string. 
Auxiliary Space: O(1)
 

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