Range sum queries based on given conditions

Given an array arr[] of N integers and matrix Queries[][] consisting of Q queries of the form {m, a, b}. For each query the task is to find the sum of array elements according to the following conditions:

• If m = 1: Find the sum of the array elements in the range [a, b].
• If m = 2: Rearrange the array elements in increasing order and find the sum of the elements in the range [a, b] in the new array.

Examples:

Input: arr[] = {6, 4, 2, 7, 2, 7}, Q = 3, Queries[][3] = {{2, 3, 6}, {1, 3, 4}, {1, 1, 6}}
Output: 24 9 28
Explanation:
For Query 1:
m is 2, then array after sorting is arr[] = {2, 2, 4, 6, 7, 7} and sum of element in the range [3, 6] is 4 + 6 + 7 + 7 = 24.
For Query 2:
m is 1, then original array is arr[] = {6, 4, 2, 7, 2, 7} and sum of element in the range [3, 4] is 2 + 7 = 9.
For Query 3:
m is 1, then original array is arr[] = {6, 4, 2, 7, 2, 7} and sum of element in the range [1, 6] is 6 + 4 + 2 + 7 + 2 + 7 = 28.

Input: arr[] = {5, 5, 2, 3}, Q = 3, Queries[][10] = {{1, 2, 4}, {2, 1, 4}, {1, 1, 1}, {2, 1, 4}, {2, 1, 2},  {1, 1, 1}, {1, 3, 3}, {1, 1, 3}, {1, 4, 4}, {1, 2, 2}}
Output: 10 15 5 15 5 5 2 12 3 5

Naive Approach: The idea is to traverse the given queries and find the sum of all the elements according to the given conditions:

1. Choose the array according to the given m, if m is equal to 1 then choose the original array otherwise choose the other array where all the elements of the array arr[] are sorted.
2. Now calculate the sum of the array between the range [a, b].
3. Iterate a loop over the range to find the sum.
4. Print the sum for each query.

Below is the implementation of the above approach: 

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to calculate the sum
// between the given range as per
// value of m
int range_sum(vector<int> v, int a,
              int b)
{
    // Stores the sum
    int sum = 0;

    // Loop to calculate the sum
    for (int i = a - 1; i < b; i++) {
        sum += v[i];
    }

    // Return sum
    return sum;
}

// Function to find the sum of elements
// for each query
void findSum(vector<int>& v1, int q,
             int Queries[][3])
{
    // Take a dummy vector
    vector<int> v2;

    // Size of vector
    int n = sizeof(v1) / sizeof(int);

    // Copying the elements into
    // dummy vector
    for (int i = 0; i < n; i++) {
        v2.push_back(v1[i]);
    }

    // Sort the dummy vector
    sort(v2.begin(), v2.end());

    // Performs operations
    for (int i = 0; i < q; i++) {

        int m = Queries[i][0];
        int a = Queries[i][1];
        int b = Queries[i][2];

        if (m == 1) {

            // Function Call to find sum
            cout << range_sum(v1, a, b)
                 << ' ';
        }
        else if (m == 2) {

            // Function Call to find sum
            cout << range_sum(v2, a, b)
                 << ' ';
        }
    }
}

// Driver Code
int main()
{
    // Given arr[]
    vector<int> arr = { 6, 4, 2, 7, 2, 7 };

    int Q = 1;

    // Given Queries
    int Queries[][3] = { { 2, 3, 6 } };

    // Function Call
    findSum(arr, Q, Queries);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to calculate the sum
// between the given range as per
// value of m
static int range_sum(Vector<Integer> v, int a,
                                        int b)
{

    // Stores the sum
    int sum = 0;

    // Loop to calculate the sum
    for(int i = a - 1; i < b; i++)
    {
        sum += v.get(i);
    }

    // Return sum
    return sum;
}

static int range_sum(int []v, int a,
                     int b)
{

    // Stores the sum
    int sum = 0;

    // Loop to calculate the sum
    for(int i = a - 1; i < b; i++)
    {
        sum += v[i];
    }

    // Return sum
    return sum;
}

// Function to find the sum of elements
// for each query
static void findSum(int []v1, int q,
                    int Queries[][])
{

    // Take a dummy vector
    Vector<Integer> v2 = new Vector<Integer>();

    // Size of vector
    int n = v1.length;

    // Copying the elements into
    // dummy vector
    for(int i = 0; i < n; i++)
    {
        v2.add(v1[i]);
    }

    // Sort the dummy vector
    Collections.sort(v2);

    // Performs operations
    for(int i = 0; i < q; i++)
    {
        int m = Queries[i][0];
        int a = Queries[i][1];
        int b = Queries[i][2];

        if (m == 1)
        {

            // Function call to find sum
            System.out.print(range_sum(
                v1, a, b) + " ");
        }
        else if (m == 2)
        {

            // Function call to find sum
            System.out.print(range_sum(
                v2, a, b) + " ");
        }
    }
}

// Driver Code
public static void main(String[] args)
{

    // Given arr[]
    int []arr = { 6, 4, 2, 7, 2, 7 };

    int Q = 1;

    // Given Queries
    int Queries[][] = { { 2, 3, 6 } };

    // Function call
    findSum(arr, Q, Queries);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program for the above approach

# Function to calculate the sum
# between the given range as per
# value of m
def range_sum(v, a, b):

    # Stores the sum
    Sum = 0

    # Loop to calculate the sum
    for i in range(a - 1, b):
        Sum += v[i]

    # Return sum
    return Sum

# Function to find the sum of elements
# for each query
def findSum(v1, q, Queries):

    # Take a dummy vector
    v2 = []

    # Size of vector
    n = len(v1)

    # Copying the elements into
    # dummy vector
    for i in range(n):
        v2.append(v1[i])

    # Sort the dummy vector
    v2.sort()

    # Performs operations
    for i in range(q):
        m = Queries[i][0]
        a = Queries[i][1]
        b = Queries[i][2]

        if (m == 1):

            # Function call to find sum
            print(range_sum(v1, a, b), end = " ")

        elif (m == 2):

            # Function call to find sum
            print(range_sum(v2, a, b), end = " ")

# Driver code

# Given arr[]
arr = [ 6, 4, 2, 7, 2, 7 ]

Q = 1

# Given Queries
Queries = [ [ 2, 3, 6 ] ]

# Function call
findSum(arr, Q, Queries)

# This code is contributed divyeshrabadiya07

C#

// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;

class GFG{

// Function to calculate the sum
// between the given range as per
// value of m
static int range_sum(ArrayList v, int a,
                                  int b)
{

    // Stores the sum
    int sum = 0;

    // Loop to calculate the sum
    for(int i = a - 1; i < b; i++)
    {
        sum += (int)v[i];
    }

    // Return sum
    return sum;
}

// Function to find the sum of elements
// for each query
static void findSum(ArrayList v1, int q,
                    int [,]Queries)
{

    // Take a dummy vector
    ArrayList v2 = new ArrayList();

    // Size of vector
    int n = v1.Count;

    // Copying the elements into
    // dummy vector
    for(int i = 0; i < n; i++)
    {
        v2.Add(v1[i]);
    }

    // Sort the dummy vector
    v2.Sort();

    // Performs operations
    for(int i = 0; i < q; i++)
    {
        int m = Queries[i, 0];
        int a = Queries[i, 1];
        int b = Queries[i, 2];

        if (m == 1)
        {

            // Function call to find sum
            Console.Write(range_sum(v1, a, b));
            Console.Write(' ');
        }
        else if (m == 2)
        {

            // Function call to find sum
            Console.Write(range_sum(v2, a, b));
            Console.Write(' ');
        }
    }
}

// Driver Code
public static void Main(string[] args)
{

    // Given arr[]
    ArrayList arr=new ArrayList(){ 6, 4, 2,
                                   7, 2, 7 };

    int Q = 1;

    // Given Queries
    int [,]Queries = { { 2, 3, 6 } };

    // Function call
    findSum(arr, Q, Queries);
}
}

// This code is contributed by rutvik_56

Javascript

<script>

// Javascript program for the above approach

// Function to calculate the sum
// between the given range as per
// value of m
function range_sum(v, a, b)
{

    // Stores the sum
    let sum = 0;

    // Loop to calculate the sum
    for(let i = a - 1; i < b; i++)
    {
        sum += v[i];
    }

    // Return sum
    return sum;
}

// Function to find the sum of elements
// for each query
function findSum(v1, q, Queries)
{

    // Take a dummy vector
    let v2 = [];

    // Size of vector
    let n = v1.length;

    // Copying the elements into
    // dummy vector
    for(let i = 0; i < n; i++)
    {
        v2.push(v1[i]);
    }

    // Sort the dummy vector
    v2.sort(function(a, b){return a - b;});

    // Performs operations
    for(let i = 0; i < q; i++)
    {
        let m = Queries[i][0];
        let a = Queries[i][1];
        let b = Queries[i][2];

        if (m == 1)
        {

            // Function call to find sum
            document.write(range_sum(
                v1, a, b) + " ");
        }
        else if (m == 2)
        {

            // Function call to find sum
            document.write(range_sum(
                v2, a, b) + " ");
        }
    }
}

// Driver Code

// Given arr[]
let arr = [ 6, 4, 2, 7, 2, 7 ];
let Q = 1;

// Given Queries
let Queries = [ [ 2, 3, 6 ] ];

// Function call
findSum(arr, Q, Queries);

// This code is contributed by avanitrachhadiya2155

</script>

Output:

24

Time Complexity: O(N²)
Auxiliary Space: O(N)

Efficient Approach: The above approach can be optimized by reducing one loop using the prefix sum array. Below are the steps:

• Create the other array brr[] to store the elements of the given array arr[] in sorted order.
• Find the prefix sum of both the arrays arr[] and brr[].
• Traverse the given queries and if the query is of type 1 then the sum of the element in the range [a, b] is given by:

arr[b – 1] – arr[a – 2]

• If the query is of type 2 then the sum of the element in the range [a, b] is given by:

brr[b – 1] – arr[a – 2]

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to calculate the sum
// between the given range as per
// value of m
int range_sum(vector<int>& arr, int a,
              int b)
{
    // Stores the sum
    int sum = 0;

    // Condition for a to print the
    // sum between ranges [a, b]
    if (a - 2 < 0)
        sum = arr[b - 1];
    else
        sum = arr[b - 1] - arr[a - 2];

    // Return sum
    return sum;
}

// Function to precalculate the sum
// of both the vectors
void precompute_sum(vector<int>& arr,
                    vector<int>& brr)
{
    int N = (int)arr.size();

    // Make Prefix sum array
    for (int i = 1; i <= N; i++) {
        arr[i] = arr[i] + arr[i - 1];
        brr[i] = brr[i] + brr[i - 1];
    }
}

// Function to compute the result
// for each query
void find_sum(vector<int>& arr, int q,
              int Queries[][3])
{
    // Take a dummy vector and copy
    // the element of arr in brr
    vector<int> brr(arr);

    int N = (int)arr.size();

    // Sort the dummy vector
    sort(brr.begin(), brr.end());

    // Compute prefix sum of both vectors
    precompute_sum(arr, brr);

    // Performs operations
    for (int i = 0; i < q; i++) {

        int m = Queries[i][0];
        int a = Queries[i][1];
        int b = Queries[i][2];

        if (m == 1) {

            // Function Call to find sum
            cout << range_sum(arr, a, b)
                 << ' ';
        }
        else if (m == 2) {

            // Function Call to find sum
            cout << range_sum(brr, a, b)
                 << ' ';
        }
    }
}

// Driver Code
int main()
{
    // Given arr[]
    vector<int> arr = { 0, 6, 4, 2, 7, 2, 7 };

    // Number of queries
    int Q = 1;

    // Given queries
    int Queries[][3] = { { 2, 3, 6 } };

    // Function Call
    find_sum(arr, Q, Queries);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to calculate the sum
// between the given range as per
// value of m
static int range_sum(int []arr, int a,
                     int b)
{

    // Stores the sum
    int sum = 0;

    // Condition for a to print the
    // sum between ranges [a, b]
    if (a - 2 < 0)
        sum = arr[b - 1];
    else
        sum = arr[b - 1] - arr[a - 2];

    // Return sum
    return sum;
}

// Function to precalculate the sum
// of both the vectors
static void precompute_sum(int []arr,
                           int []brr)
{
    int N = (int)arr.length;

    // Make Prefix sum array
    for(int i = 1; i < N; i++)
    {
        arr[i] = arr[i] + arr[i - 1];
        brr[i] = brr[i] + brr[i - 1];
    }
}

// Function to compute the result
// for each query
static void find_sum(int []arr, int q,
                     int Queries[][])
{

    // Take a dummy vector and copy
    // the element of arr in brr
    int []brr = arr.clone();

    int N = (int)arr.length;

    // Sort the dummy vector
    Arrays.sort(brr);

    // Compute prefix sum of both vectors
    precompute_sum(arr, brr);

    // Performs operations
    for(int i = 0; i < q; i++)
    {
        int m = Queries[i][0];
        int a = Queries[i][1];
        int b = Queries[i][2];

        if (m == 1)
        {

            // Function call to find sum
            System.out.print(range_sum(
                arr, a, b) + " ");
        }
        else if (m == 2)
        {

            // Function call to find sum
            System.out.print(range_sum(
                brr, a, b) + " ");
        }
    }
}

// Driver Code
public static void main(String[] args)
{

    // Given arr[]
    int []arr = { 0, 6, 4, 2, 7, 2, 7 };

    // Number of queries
    int Q = 1;

    // Given queries
    int Queries[][] = { { 2, 3, 6 } };

    // Function call
    find_sum(arr, Q, Queries);
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program for
# the above approach

# Function to calculate
# the sum between the
# given range as per value
# of m
def range_sum(arr, a, b):

    # Stores the sum
    sum = 0

    # Condition for a to
    # print the sum between
    # ranges [a, b]
    if (a - 2 < 0):
        sum = arr[b - 1]
    else:
        sum = (arr[b - 1] -
               arr[a - 2])

    # Return sum
    return sum

# Function to precalculate
# the sum of both the vectors
def precompute_sum(arr, brr):

    N = len(arr)

    # Make Prefix sum array
    for i in range(1, N):
        arr[i] = arr[i] + arr[i - 1]
        brr[i] = brr[i] + brr[i - 1]

# Function to compute
# the result for each query
def find_sum(arr, q, Queries):

    # Take a dummy vector
    # and copy the element
    # of arr in brr
    brr = arr.copy()

    N = len(arr)

    # Sort the dummy vector
    brr.sort()

    # Compute prefix sum of
    # both vectors
    precompute_sum(arr, brr)

    # Performs operations
    for i in range(q):

        m = Queries[i][0]
        a = Queries[i][1]
        b = Queries[i][2]

        if (m == 1):

            # Function Call to
            # find sum
            print (range_sum(arr,
                             a, b),
                   end = ' ')

        elif (m == 2):

            # Function Call to
            # find sum
            print (range_sum(brr,
                             a, b),
                   end = ' ')

# Driver Code
if __name__ == "__main__":

    # Given arr[]
    arr = [0, 6, 4,
           2, 7, 2, 7]

    # Number of queries
    Q = 1

    # Given queries
    Queries = [[2, 3, 6]]

    # Function Call
    find_sum(arr, Q, Queries)

# This code is contributed by Chitranayal

C#

// C# program for
// the above approach
using System;
class GFG{

// Function to calculate the sum
// between the given range as per
// value of m
static int range_sum(int []arr,
                     int a,
                     int b)
{
  // Stores the sum
  int sum = 0;

  // Condition for a to print the
  // sum between ranges [a, b]
  if (a - 2 < 0)
    sum = arr[b - 1];
  else
    sum = arr[b - 1] - arr[a - 2];

  // Return sum
  return sum;
}

// Function to precalculate the sum
// of both the vectors
static void precompute_sum(int []arr,
                           int []brr)
{
  int N = (int)arr.Length;

  // Make Prefix sum array
  for(int i = 1; i < N; i++)
  {
    arr[i] = arr[i] + arr[i - 1];
    brr[i] = brr[i] + brr[i - 1];
  }
}

// Function to compute the result
// for each query
static void find_sum(int []arr, int q,
                     int [,]Queries)
{
  // Take a dummy vector and copy
  // the element of arr in brr
  int []brr = new int[arr.Length];
  arr.CopyTo(brr, 0);

  int N = (int)arr.Length;

  // Sort the dummy vector
  Array.Sort(brr);

  // Compute prefix sum of both vectors
  precompute_sum(arr, brr);

  // Performs operations
  for(int i = 0; i < q; i++)
  {
    int m = Queries[i, 0];
    int a = Queries[i, 1];
    int b = Queries[i, 2];

    if (m == 1)
    {
      // Function call to find sum
      Console.Write(range_sum(
                    arr, a, b) + " ");
    }
    else if (m == 2)
    {
      // Function call to find sum
      Console.Write(range_sum(
                    brr, a, b) + " ");
    }
  }
}

// Driver Code
public static void Main(String[] args)
{
  // Given []arr
  int []arr = {0, 6, 4, 2, 7, 2, 7};

  // Number of queries
  int Q = 1;

  // Given queries
  int [,]Queries = {{2, 3, 6}};

  // Function call
  find_sum(arr, Q, Queries);
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript program for the above approach

// Function to calculate the sum
// between the given range as per
// value of m
function range_sum(arr,a,b)
{
    // Stores the sum
    let sum = 0;

    // Condition for a to print the
    // sum between ranges [a, b]
    if (a - 2 < 0)
        sum = arr[b - 1];
    else
        sum = arr[b - 1] - arr[a - 2];

    // Return sum
    return sum;
}

// Function to precalculate the sum
// of both the vectors
function precompute_sum(arr,brr)
{
    let N = arr.length;

    // Make Prefix sum array
    for(let i = 1; i < N; i++)
    {
        arr[i] = arr[i] + arr[i - 1];
        brr[i] = brr[i] + brr[i - 1];
    }
}

// Function to compute the result
// for each query
function find_sum(arr,q,Queries)
{
    // Take a dummy vector and copy
    // the element of arr in brr
    let brr = [...arr];

    let N = arr.length;

    // Sort the dummy vector
    brr.sort(function(a,b){return a-b;});

    // Compute prefix sum of both vectors
    precompute_sum(arr, brr);

    // Performs operations
    for(let i = 0; i < q; i++)
    {
        let m = Queries[i][0];
        let a = Queries[i][1];
        let b = Queries[i][2];

        if (m == 1)
        {

            // Function call to find sum
            document.write(range_sum(
                arr, a, b) + " ");
        }
        else if (m == 2)
        {

            // Function call to find sum
            document.write(range_sum(
                brr, a, b) + " ");
        }
    }
}

// Driver Code
let arr=[0, 6, 4, 2, 7, 2, 7];
// Number of queries
let Q = 1;

// Given queries
let Queries = [[ 2, 3, 6 ]];

// Function call
find_sum(arr, Q, Queries);


// This code is contributed by rag2127
</script>

Output:

19

Time Complexity: O(N*log N)
Auxiliary Space: O(N)