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Range Queries for finding the Sum of all even parity numbers
  • Last Updated : 20 May, 2020

Given Q queries where each query consists of two numbers L and R which denotes a range [L, R]. The task is to find the sum of all Even Parity Numbers lying in the given range [L, R].

Parity of a number refers to whether it contains an odd or even number of 1-bits. The number has Even Parity if it contains even number of 1-bits.

Examples:

Input: Q = [ [1, 10], [121, 211] ]
Output:
33
7493
Explanation:
binary(1) = 01, parity = 1
binary(2) = 10, parity = 1
binary(3) = 11, parity = 2
binary(4) = 100, parity = 1
binary(5) = 101, parity = 2
binary(6) = 110, parity = 2
binary(7) = 111, parity = 3
binary(8) = 1000, parity = 1
binary(9) = 1001, parity = 2
binary(10) = 1010, parity = 2
From 1 to 10, 3, 5, 6, 9 and 10 are the Even Parity numbers. Therefore the sum is 33.
From 121 to 211 the sum of all the even parity numbers is 7493.

Input: Q = [ [ 10, 10 ], [ 258, 785 ], [45, 245], [ 1, 1000]]
Output:
10
137676
14595
250750



Approach:
The idea is to use a Prefix Sum Array. The sum of all Even Parity Numbers till that particular index is precomputed and stored in an array pref[] so that every query can be answered in O(1) time.

  1. Initialise the prefix array pref[].
  2. Iterate from 1 to N and check if the number has even parity or not:
    • If the number is Even Parity Number then, the current index of pref[] will store the sum of Even Parity Numbers found so far.
    • Else the current index of pref[] is same as the value at previous index of pref[].
  3. For Q queries the sum of all Even Parity Numbers for range [L, R] can be calculated as follows:
    sum = pref[R] - pref[L - 1]
    

Below is the implementation of the above approach

C++

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// C++ program to find the sum
// of all Even Parity numbers
// in the given range
  
#include <bits/stdc++.h>
using namespace std;
  
// pref[] array to precompute
// the sum of all Even
// Parity Numbers
int pref[100001] = { 0 };
  
// Function that returns true
// if count of set bits in
// x is even
int isEvenParity(int num)
{
    // Parity will store the
    // count of set bits
    int parity = 0;
    int x = num;
    while (x != 0) {
        if (x & 1)
            parity++;
        x = x >> 1;
    }
  
    if (parity % 2 == 0)
        return num;
    else
        return 0;
}
  
// Function to precompute the
// sum of all even parity
// numbers upto 100000
void preCompute()
{
    for (int i = 1; i < 100001; i++) {
  
        // isEvenParity()
        // return the number i
        // if i has even parity
        // else return 0
        pref[i] = pref[i - 1]
                  + isEvenParity(i);
    }
}
  
// Function to print sum
// for each query
void printSum(int L, int R)
{
    cout << (pref[R] - pref[L - 1])
         << endl;
}
  
// Function to print sum of all
// even parity numbers between
// [L, R]
void printSum(int arr[2][2], int Q)
{
  
    // Function that pre computes
    // the sum of all even parity
    // numbers
    preCompute();
  
    // Iterate over all Queries
    // to print sum
    for (int i = 0; i < Q; i++) {
        printSum(arr[i][0],
                 arr[i][1]);
    }
}
// Driver code
int main()
{
    // Queries
    int N = 2;
    int Q[2][2] = { { 1, 10 },
                    { 121, 211 } };
  
    // Function that print
    // the sum of all even parity
    // numbers in Range [L, R]
    printSum(Q, N);
  
    return 0;
}

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Java

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// Java program to find the sum
// of all Even Parity numbers
// in the given range
import java.io.*; 
import java.util.*; 
  
class GFG { 
      
// pref[] array to precompute
// the sum of all Even
// Parity Numbers
static int[] pref = new int[100001];
  
// Function that returns true
// if count of set bits in
// x is even
static int isEvenParity(int num)
{
      
    // Parity will store the
    // count of set bits
    int parity = 0;
    int x = num;
      
    while (x != 0)
    {
        if ((x & 1) == 1)
            parity++;
              
        x = x >> 1;
    }
      
    if (parity % 2 == 0)
        return num;
    else
        return 0;
}
  
// Function to precompute the
// sum of all even parity
// numbers upto 100000
static void preCompute()
{
    for(int i = 1; i < 100001; i++)
    {
  
       // isEvenParity()
       // return the number i
       // if i has even parity
       // else return 0
       pref[i] = pref[i - 1] + isEvenParity(i);
    }
}
  
// Function to print sum
// for each query
static void printSum(int L, int R)
{
    System.out.println(pref[R] - pref[L - 1]);
}
  
// Function to print sum of all
// even parity numbers between
// [L, R]
static void printSum(int arr[][], int Q)
{
      
    // Function that pre computes
    // the sum of all even parity
    // numbers
    preCompute();
  
    // Iterate over all Queries
    // to print sum
    for(int i = 0; i < Q; i++) 
    {
       printSum(arr[i][0], arr[i][1]);
    }
}
      
// Driver code 
public static void main(String[] args) 
      
    // Queries
    int N = 2;
    int[][] Q = { { 1, 10 }, 
                  { 121, 211 } };
  
    // Function that print
    // the sum of all even parity
    // numbers in Range [L, R]
    printSum(Q, N);
}
  
// This code is contributed by coder001

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C#

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// C# program to find the sum
// of all Even Parity numbers
// in the given range
using System;
  
class GFG { 
      
// pref[] array to precompute
// the sum of all Even
// Parity Numbers
static int[] pref = new int[100001];
  
// Function that returns true
// if count of set bits in
// x is even
static int isEvenParity(int num)
{
      
    // Parity will store the
    // count of set bits
    int parity = 0;
    int x = num;
      
    while (x != 0)
    {
        if ((x & 1) == 1)
            parity++;
              
        x = x >> 1;
    }
      
    if (parity % 2 == 0)
        return num;
    else
        return 0;
}
  
// Function to precompute the
// sum of all even parity
// numbers upto 100000
static void preCompute()
{
    for(int i = 1; i < 100001; i++)
    {
          
       // isEvenParity()
       // return the number i
       // if i has even parity
       // else return 0
       pref[i] = pref[i - 1] + isEvenParity(i);
    }
}
  
// Function to print sum
// for each query
static void printSum(int L, int R)
{
    Console.WriteLine(pref[R] - pref[L - 1]);
}
  
// Function to print sum of all
// even parity numbers between
// [L, R]
static void printSum(int[,] arr, int Q)
{
      
    // Function that pre computes
    // the sum of all even parity
    // numbers
    preCompute();
  
    // Iterate over all Queries
    // to print sum
    for(int i = 0; i < Q; i++) 
    {
       printSum(arr[i, 0], arr[i, 1]);
    }
}
      
// Driver code 
public static void Main() 
      
    // Queries
    int N = 2;
    int[,] Q = { { 1, 10 }, 
                 { 121, 211 } };
  
    // Function that print
    // the sum of all even parity
    // numbers in Range [L, R]
    printSum(Q, N);
}
  
// This code is contributed by AbhiThakur

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Output:

33
7493

Time Complexity: O(N), where N is the maximum element in the query.

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