Find sum in range L to R in given sequence of integers

Given an array arr[] of integers and a sequence of the form:

[ 2, 3, 0, 1, 6, 7, 4, 5, … ].

Also given two integer L and R such that 0 \le L \le R \le 10^{6}. The task is to find the sum of all numbers in given range from L to R.

Examples:

Input : L = 0, R = 5
Output : 19
Explanation : 
The arr[] is {2, 3, 0, 1, 6, 7}.
sum = arr[0] + arr[1] + arr[2] + arr[3] + arr[4] + arr[5]
sum = 2 + 3 + 0 + 1 + 6 + 7
Hence, the sum is 19.

Input : L = 2, R = 5
Output : 14
Explanation : 
The arr[] is {0, 1, 6, 7}.
sum = arr[2] + arr[3] + arr[4] + arr[5] 
sum = 0 + 1 + 6 + 7
Hence, the sum is 14.

Approach:



To solve the question mentioned above we first have to observe the sequence of the array and understand how is it generated. The given array is generated from a sequence of whole numbers which is [ 0, 1, 2, 3, 4, 5, 6, … ]. Initially we add 2 to the first two integers, then we subtract 2 from the next two integers and this goes on. So our newly formed array looks like [ 0+2, 1+2, 2-2, 3-2, 4+2, 5+2, 6-2, 7-2, … ]. Hence we generate this new sequence of integers up to R and store it in array. Finally, calculate the sum from indices in range L to R and return it.

Below is the implementation of the above approach:

C++

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// C++ program to find the
// sum in given range L to R
  
#include <bits/stdc++.h> 
using namespace std;
  
// Function to find the sum
// within the given range
int findSum(int L, int R)
{
    vector<int> arr; 
  
    // generating array from given sequence
    int i = 0;
    int x = 2;
    while (i <= R) {
        arr.push_back(i + x);
  
        if (i + 1 <= R)
            arr.push_back(i + 1 + x);
  
        x *= -1;
  
        i += 2;
    }
  
    // calculate the desired sum
    int sum = 0;
  
    for (int i = L; i <= R; ++i)
  
        sum += arr[i];
  
    // return the sum
    return sum;
}
  
// Driven code
int main()
{
  
    // initialise the range
    int L = 0, R = 5;
  
    cout << findSum(L, R);
  
    return 0;
}

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Java

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// Java program to find the
// sum in given range L to R
import java.util.*;
  
class GFG{
      
// Function to find the sum
// within the given range
public static int findSum(int L, int R)
{
    ArrayList<Integer> arr = new ArrayList<>(); 
  
    // Generating array from given sequence
    int i = 0;
    int x = 2;
    while (i <= R)
    {
        arr.add(i + x);
  
        if (i + 1 <= R)
            arr.add(i + 1 + x);
  
        x *= -1;
  
        i += 2;
    }
  
    // Calculate the desired sum
    int sum = 0;
  
    for(i = L; i <= R; ++i)
       sum += arr.get(i);
  
    // return the sum
    return sum;
}
  
// Driver code
public static void main(String[] args)
{
      
    // Initialise the range
    int L = 0, R = 5;
  
    System.out.println(findSum(L, R));
}
}
  
// This code is contributed by jrishabh99

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Python3

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# Python3 program to find the 
# sum in given range L to R 
  
# Function to find the sum 
# within the given range 
def findSum(L, R) : 
    arr = []
  
    # generating array from given sequence 
    i = 0
    x = 2
    k = 0
    while (i <= R) :
        arr.insert(k, i + x) 
        k += 1
        if (i + 1 <= R) :
            arr.insert(k, i + 1 + x)
        k += 1
        x *= -1
        i += 2
  
    # calculate the desired sum 
    sum = 0
  
    for i in range(L, R + 1) :
        sum += arr[i]
  
    # return the sum 
    return sum
  
# Driver code 
  
# initialise the range 
L = 0
R = 5
print(findSum(L, R))
  
# This code is contributed by Sanjit_Prasad

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C#

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// C# program to find the
// sum in given range L to R
using System;
using System.Collections;
  
class GFG{
      
// Function to find the sum
// within the given range
public static int findSum(int L, int R)
{
    ArrayList arr = new ArrayList(); 
  
    // Generating array from given sequence
    int i = 0;
    int x = 2;
    while (i <= R)
    {
        arr.Add(i + x);
  
        if (i + 1 <= R)
            arr.Add(i + 1 + x);
  
        x *= -1;
        i += 2;
    }
  
    // Calculate the desired sum
    int sum = 0;
  
    for(i = L; i <= R; ++i)
        sum += (int)arr[i];
  
    // return the sum
    return sum;
}
  
// Driver code
public static void Main(string[] args)
{
      
    // Initialise the range
    int L = 0, R = 5;
  
    Console.Write(findSum(L, R));
}
}
  
// This code is contributed by rutvik_56

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Output:

19

Time Complexity : O(N)

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