# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ implementation to find the sum ` `// of all composite numbers ` `// in the given range ` ` `  `#include ` ` `  `using` `namespace` `std; ` ` `  `// Prefix array to precompute ` `// the sum of all composite ` `// numbers ` `long` `long` `pref; ` ` `  `// 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[], ` `                    ``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], arr[i]); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// 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); ` `    ``return` `0; ` `} `

## Java

 `// 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); ` `    ``} ` `} `

## Python3

 `# 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) `

## C#

 `// 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``; ` ` `  `// 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 `

Output:

```22
116
```

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