Sum of all composite numbers lying in the range [L, R] for Q queries

Given Q queries in the form of 2D array arr[][] whose every row consists of two numbers L and R which denotes the range [L, R], the task is to find the sum of all Composite Numbers lying in range [L, R].

Input: arr[][] = {{10, 13}, {12, 21}}
Output:
22
116
Explanation:
From 10 to 13 only 10 and 12 is the composite number.
From 12 to 21, there are 7 composite numbers
12 + 14 + 15 + 16 + 18 + 20 + 21 = 116

Input: arr[][] = {{ 10, 10 }, { 258, 785 }, {45, 245 }, { 1, 1000}}
Output:
10
233196
23596
424372

Approach:
The idea is to use the prefix sum array. The sum of all composite number 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 is composite or not:
    • If the number is composite then, the current index of pref[] will store the sum of the number and the number at previous index of pref[].
    • Else the current index of pref[] is same as the value at previous index of pref[].
  3. For Q queries the sum of all composite numbers for range [L, R] can be found as follows:
    sum = pref[R] - pref[L - 1]
    

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation to find the sum
// of all composite numbers
// in the given range
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Prefix array to precompute
// the sum of all composite
// numbers
long long pref[100001];
  
// Function that return number
// num if num is composite
// else return 0
int isComposite(int n)
{
    // Corner cases
    if (n <= 1)
        return 0;
    if (n <= 3)
        return 0;
  
    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return n;
  
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return n;
  
    return 0;
}
  
// Function to precompute the
// sum of all Composite numbers
// upto 10^5
void preCompute()
{
    for (int i = 1; i <= 100000; ++i) {
  
        // isComposite()
        // return the number i
        // if i is Composite
        // else return 0
        pref[i] = pref[i - 1]
                + isComposite(i);
    }
}
  
// Function to print the sum
// for each query
void printSum(int L, int R)
{
    cout << pref[R] - pref[L - 1]
        << endl;
}
  
// Function to print sum of all
// Composite numbers between
// [L, R]
void printSumComposite(int arr[][2],
                    int Q)
{
  
    // Function that pre computes
    // the sum of all Composite
    // numbers
    preCompute();
  
    // Iterate over all Queries
    // to print the sum
    for (int i = 0; i < Q; i++) {
        printSum(arr[i][0], arr[i][1]);
    }
}
  
// Driver code
int main()
{
    // Queries
    int Q = 2;
    int arr[][2] = { { 10, 13 },
                      { 12, 21 } };
  
    // Function that print the
    // the sum of all composite
    // number in Range [L, R]
    printSumComposite(arr, Q);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implmentation to find the sum
// of all Composite numbers
// in the given range
  
import java.util.*;
  
class GFG {
  
    // Prefix array to precompute
    // the sum of all Composite
    // number
    static int[] pref = new int[100001];
  
    // Function that return number
    // num if num is Composite
    // else return 0
    static int isComposite(int n)
    {
        // Corner cases
        if (n <= 1)
            return 0;
  
        if (n <= 3)
            return 0;
  
        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n % 2 == 0 || n % 3 == 0)
            return n;
  
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return n;
  
        return 0;
    }
  
    // Function to precompute the
    // sum of all Composite numbers
    // upto 100000
    static void preCompute()
    {
        for (int i = 1; i <= 100000; ++i) {
  
            // checkComposite()
            // return the number i
            // if i is Composite
            // else return 0
            pref[i] = pref[i - 1]
                    + isComposite(i);
        }
    }
  
    // Function to print the sum
    // for each query
    static void printSum(int L, int R)
    {
        System.out.print(pref[R] - pref[L - 1]
                        + "\n");
    }
  
    // Function to print sum of all
    // Composite numbers between
    // [L, R]
    static void printSumComposite(int arr[][],
                                int Q)
    {
  
        // Function that pre computes
        // the sum of all Composite
        // numbers
        preCompute();
  
        // Iterate over all Queries
        // to print the 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 Q = 2;
        int arr[][] = { { 10, 13 },
                        { 12, 21 } };
  
        // Function that print the
        // the sum of all Composite
        // number in Range [L, R]
        printSumComposite(arr, Q);
    }
}

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python implementation to find the sum
# of all composite numbers
# in the given range
  
# Prefix array to precompute
# the sum of all composite
# number
pref =[0]*100001
  
# Function that return number
# num if num is composite
# else return 0
def isComposite(n): 
  
    # Corner cases 
    if (n <= 1): 
        return 0
    if (n <= 3): 
        return 0
  
    # This is checked so that we can skip 
    # middle five numbers in below loop 
    if (n % 2 == 0 or n % 3 == 0): 
        return n
    i = 5
    while(i * i <= n): 
          
        if (n % i == 0 or n % (i + 2) == 0): 
            return n
        i = i + 6
          
    return 0
  
# Function to precompute the
# sum of all composite numbers
# upto 100000
def preCompute():
    for i in range(1, 100001):
        # checkcomposite()
        # return the number i
        # if i is composite
        # else return 0
        pref[i] = pref[i - 1]+ isComposite(i)
      
  
  
# Function to print the sum
# for each query
def printSum(L, R):
    print(pref[R] - pref[L - 1])
  
  
# Function to prsum of all
# composite numbers between
def printSumcomposite(arr, Q):
      
    # Function that pre computes
    # the sum of all composite
    # numbers
    preCompute()
      
    # Iterate over all Queries
    # to prthe sum
    for i in range(Q):
        printSum(arr[i][0], arr[i][1])
      
  
  
# Driver code
if __name__ == "__main__":
    Q = 2
    arr = [[10, 13 ], [ 12, 21 ]]
      
    # Function that print the
    # the sum of all composite
    # number in Range [L, R]
    printSumcomposite(arr, Q)

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implmentation to find the sum
// of all Composite numbers
// in the given range
using System;
  
public class GFG{
  
// Prefix array to precompute
// the sum of all Composite
// number
static int[] pref = new int[100001];
  
// Function that return number
// num if num is Composite
// else return 0
static int isComposite(int n)
{
  
    // Corner cases
    if (n <= 1)
        return 0;
  
    if (n <= 3)
        return 0;
  
    // This is checked so that we can skip
    // middle five numbers in below loop
    if (n % 2 == 0 || n % 3 == 0)
        return n;
  
    for(int i = 5; i * i <= n; i = i + 6)
       if (n % i == 0 || n % (i + 2) == 0)
           return n;
  
    return 0;
}
  
// Function to precompute the
// sum of all Composite numbers
// upto 100000
static void preCompute()
{
    for(int i = 1; i <= 100000; ++i)
    {
       // CheckComposite()
       // return the number i
       // if i is Composite
       // else return 0
       pref[i] = pref[i - 1] + 
                 isComposite(i);
    }
}
  
// Function to print the sum
// for each query
static void printSum(int L, int R)
{
    Console.Write(pref[R] - 
                  pref[L - 1] + "\n");
}
  
// Function to print sum of all
// Composite numbers between
// [L, R]
static void printSumComposite(int [,]arr,
                              int Q)
{
  
    // Function that pre computes
    // the sum of all Composite
    // numbers
    preCompute();
  
    // Iterate over all Queries
    // to print the 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 Q = 2;
    int [,]arr = { { 10, 13 },
                   { 12, 21 } };
  
    // Function that print the
    // the sum of all Composite
    // number in Range [L, R]
    printSumComposite(arr, Q);
}
}
  
// This code is contributed by Princi Singh

chevron_right


Output:

22 
116

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : princi singh