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++

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// 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;
}

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Java

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// Java implementation 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);
    }
}

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Python3

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# 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 print the 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)

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C#

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// C# implementation 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

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Output:

22 
116

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