Number of primes in a subarray (with updates)

• Difficulty Level : Hard
• Last Updated : 17 Nov, 2021

Given an array of N integers, the task is to perform the following two queries:

query(start, end) : Print the number of prime numbers in the subarray from start to end
update(i, x) : update the value at index i to x, i.e arr[i] = x

Examples:

Input : arr = {1, 2, 3, 5, 7, 9}
Query 1: query(start = 0, end = 4)
Query 2: update(i = 3, x = 6)
Query 3: query(start = 0, end = 4)
Output :4
3
Explanation
In Query 1, the subarray [0...4]
has 4 primes viz. {2, 3, 5, 7}

In Query 2, the value at index 3
is updated to 6, the array arr now is, {1, 2, 3,
6, 7, 9}
In Query 3, the subarray [0...4]
has 4 primes viz. {2, 3, 7}

Method 1 (Brute Force)
A similar problem can be found here. Here there are no updates.We can modify this to handle updates but for this we need to build the prefix array always when we perform an update which makes the time complexity of this approach O(Q * N)
Method 2 (Efficient)
Since, we need to handle both range queries and point updates, a segment tree is best suited for this purpose.
We can use Sieve of Eratosthenes to preprocess all the primes till the maximum value arri can take say MAX in O(MAX log(log(MAX)))
Building the segment tree:
We basically reduce the problem to subarray sum using segment tree.
Now, we can build the segment tree where a leaf node is represented as either 0 (if it is not a prime number) or 1 (if it is a prime number).
The internal nodes of the segment tree equal to the sum of its child nodes, thus a node represents the total primes in the range from L to R where the range L to R falls under this node and the sub-tree below it.
Whenever we get a query from start to end, then we can query the segment tree for the sum of nodes in range start to end, which in turn represent the number of primes in range start to end.
If we need to perform a point update and update the value at index i to x, then we check for the following cases:

Let the old value of arri be y and the new value be x

Case 1: If x and y both are primes
Count of primes in the subarray does not change so we just update array and donot
modify the segment tree

Case 2: If x and y both are non primes
Count of primes in the subarray does not change so we just update array and donot
modify the segment tree

Case 3: If y is prime but x is non prime
Count of primes in the subarray decreases so we update array and add -1 to every
range, the index i which is to be updated, is a part of in the segment tree

Case 4: If y is non prime but x is prime
Count of primes in the subarray increases so we update array and add 1 to every
range, the index i which is to be updated, is a part of in the segment tree

CPP

 // C++ program to find number of prime numbers in a// subarray and performing updates#include using namespace std; #define MAX 1000 void sieveOfEratosthenes(bool isPrime[]){    isPrime = false;     for (int p = 2; p * p <= MAX; p++) {         // If prime[p] is not changed, then        // it is a prime        if (isPrime[p] == true) {             // Update all multiples of p            for (int i = p * 2; i <= MAX; i += p)                isPrime[i] = false;        }    }} // A utility function to get the middle index from corner indexes.int getMid(int s, int e) { return s + (e - s) / 2; } /*  A recursive function to get the number of primes in a given range     of array indexes. The following are parameters for this function.      st    --> Pointer to segment tree    index --> Index of current node in the segment tree. Initially              0 is passed as root is always at index 0    ss & se  --> Starting and ending indexes of the segment represented                  by current node, i.e., st[index]    qs & qe  --> Starting and ending indexes of query range */int queryPrimesUtil(int* st, int ss, int se, int qs, int qe, int index){    // If segment of this node is a part of given range, then return    // the number of primes in the segment    if (qs <= ss && qe >= se)        return st[index];     // If segment of this node is outside the given range    if (se < qs || ss > qe)        return 0;     // If a part of this segment overlaps with the given range    int mid = getMid(ss, se);    return queryPrimesUtil(st, ss, mid, qs, qe, 2 * index + 1) +           queryPrimesUtil(st, mid + 1, se, qs, qe, 2 * index + 2);} /* A recursive function to update the nodes which have the given   index in their range. The following are parameters    st, si, ss and se are same as getSumUtil()    i    --> index of the element to be updated. This index is             in input array.   diff --> Value to be added to all nodes which have i in range */void updateValueUtil(int* st, int ss, int se, int i, int diff, int si){    // Base Case: If the input index lies outside the range of    // this segment    if (i < ss || i > se)        return;     // If the input index is in range of this node, then update    // the value of the node and its children    st[si] = st[si] + diff;    if (se != ss) {        int mid = getMid(ss, se);        updateValueUtil(st, ss, mid, i, diff, 2 * si + 1);        updateValueUtil(st, mid + 1, se, i, diff, 2 * si + 2);    }} // The function to update a value in input array and segment tree.// It uses updateValueUtil() to update the value in segment treevoid updateValue(int arr[], int* st, int n, int i, int new_val,                                               bool isPrime[]){    // Check for erroneous input index    if (i < 0 || i > n - 1) {        printf("Invalid Input");        return;    }     int diff, oldValue;     oldValue = arr[i];     // Update the value in array    arr[i] = new_val;     // Case 1: Old and new values both are primes    if (isPrime[oldValue] && isPrime[new_val])        return;     // Case 2: Old and new values both non primes    if ((!isPrime[oldValue]) && (!isPrime[new_val]))        return;     // Case 3: Old value was prime, new value is non prime    if (isPrime[oldValue] && !isPrime[new_val]) {        diff = -1;    }     // Case 4: Old value was non prime, new_val is prime    if (!isPrime[oldValue] && isPrime[new_val]) {        diff = 1;    }     // Update the values of nodes in segment tree    updateValueUtil(st, 0, n - 1, i, diff, 0);} // Return number of primes in range from index qs (query start) to// qe (query end).  It mainly uses queryPrimesUtil()void queryPrimes(int* st, int n, int qs, int qe){    int primesInRange = queryPrimesUtil(st, 0, n - 1, qs, qe, 0);     cout << "Number of Primes in subarray from " << qs << " to "         << qe << " = " << primesInRange << "\n";} // A recursive function that constructs Segment Tree// for array[ss..se].// si is index of current node in segment tree stint constructSTUtil(int arr[], int ss, int se, int* st,                                 int si, bool isPrime[]){    // If there is one element in array, check if it    // is prime then store 1 in the segment tree else    // store 0 and return    if (ss == se) {         // if arr[ss] is prime        if (isPrime[arr[ss]])            st[si] = 1;               else            st[si] = 0;                 return st[si];    }     // If there are more than one elements, then recur    // for left and right subtrees and store the sum    // of the two values in this node    int mid = getMid(ss, se);    st[si] = constructSTUtil(arr, ss, mid, st,                               si * 2 + 1, isPrime) +             constructSTUtil(arr, mid + 1, se, st,                              si * 2 + 2, isPrime);    return st[si];} /* Function to construct segment tree from given array.   This function allocates memory for segment tree and   calls constructSTUtil() to fill the allocated memory */int* constructST(int arr[], int n, bool isPrime[]){    // Allocate memory for segment tree     // Height of segment tree    int x = (int)(ceil(log2(n)));     // Maximum size of segment tree    int max_size = 2 * (int)pow(2, x) - 1;     int* st = new int[max_size];     // Fill the allocated memory st    constructSTUtil(arr, 0, n - 1, st, 0, isPrime);     // Return the constructed segment tree    return st;} // Driver program to test above functionsint main(){     int arr[] = { 1, 2, 3, 5, 7, 9 };    int n = sizeof(arr) / sizeof(arr);     /* Preprocess all primes till MAX.       Create a boolean array "isPrime[0..MAX]".       A value in prime[i] will finally be false       if i is Not a prime, else true. */     bool isPrime[MAX + 1];    memset(isPrime, true, sizeof isPrime);    sieveOfEratosthenes(isPrime);     // Build segment tree from given array    int* st = constructST(arr, n, isPrime);     // Query 1: Query(start = 0, end = 4)    int start = 0;    int end = 4;    queryPrimes(st, n, start, end);     // Query 2: Update(i = 3, x = 6), i.e Update    // a[i] to x    int i = 3;    int x = 6;    updateValue(arr, st, n, i, x, isPrime);     // uncomment to see array after update    // for(int i = 0; i < n; i++) cout << arr[i] << " ";     // Query 3: Query(start = 0, end = 4)    start = 0;    end = 4;    queryPrimes(st, n, start, end);     return 0;}

Java

 // Java program to find number of prime numbers in a // subarray and performing updatesimport java.io.*;import java.util.*; class GFG{    static int MAX = 1000 ;    static void sieveOfEratosthenes(boolean isPrime[])    {        isPrime = false;        for (int p = 2; p * p <= MAX; p++)        {               // If prime[p] is not changed, then            // it is a prime            if (isPrime[p] == true)            {                   // Update all multiples of p                for (int i = p * 2; i <= MAX; i += p)                    isPrime[i] = false;            }        }    }         // A utility function to get the middle index from corner indexes.    static int getMid(int s, int e) { return s + (e - s) / 2; }         /*  A recursive function to get the number of primes in a given range     of array indexes. The following are parameters for this function.        st    --> Pointer to segment tree    index --> Index of current node in the segment tree. Initially              0 is passed as root is always at index 0    ss & se  --> Starting and ending indexes of the segment represented                  by current node, i.e., st[index]    qs & qe  --> Starting and ending indexes of query range */         static int queryPrimesUtil(int[] st, int ss, int se, int qs, int qe, int index)    {               // If segment of this node is a part of given range, then return        // the number of primes in the segment              if (qs <= ss && qe >= se)        return st[index];           // If segment of this node is outside the given range        if (se < qs || ss > qe)            return 0;           // If a part of this segment overlaps with the given range        int mid = getMid(ss, se);        return queryPrimesUtil(st, ss, mid, qs, qe, 2 * index + 1) +          queryPrimesUtil(st, mid + 1, se, qs, qe, 2 * index + 2);    }         /* A recursive function to update the nodes which have the given    index in their range. The following are parameters    st, si, ss and se are same as getSumUtil()    i    --> index of the element to be updated. This index is              in input array.   diff --> Value to be added to all nodes which have i in range */       static void updateValueUtil(int[] st, int ss, int se, int i, int diff, int si)   {        // Base Case: If the input index lies outside the range of        // this segment        if (i < ss || i > se)            return;           // If the input index is in range of this node, then update        // the value of the node and its children        st[si] = st[si] + diff;        if (se != ss) {            int mid = getMid(ss, se);            updateValueUtil(st, ss, mid, i, diff, 2 * si + 1);            updateValueUtil(st, mid + 1, se, i, diff, 2 * si + 2);        }    }         // The function to update a value in input array and segment tree.    // It uses updateValueUtil() to update the value in segment tree         static void updateValue(int arr[], int[] st, int n,                            int i, int new_val, boolean isPrime[])    {        // Check for erroneous input index        if (i < 0 || i > n - 1) {            System.out.println("Invalid Input");            return;        }        int diff = 0;        int oldValue;           oldValue = arr[i];           // Update the value in array        arr[i] = new_val;           // Case 1: Old and new values both are primes        if (isPrime[oldValue] && isPrime[new_val])            return;           // Case 2: Old and new values both non primes        if ((!isPrime[oldValue]) && (!isPrime[new_val]))            return;           // Case 3: Old value was prime, new value is non prime        if (isPrime[oldValue] && !isPrime[new_val])        {            diff = -1;        }           // Case 4: Old value was non prime, new_val is prime        if (!isPrime[oldValue] && isPrime[new_val])        {            diff = 1;        }           // Update the values of nodes in segment tree        updateValueUtil(st, 0, n - 1, i, diff, 0);    }         // Return number of primes in range from index qs (query start) to    // qe (query end).  It mainly uses queryPrimesUtil()    static void queryPrimes(int[] st, int n, int qs, int qe)    {        int primesInRange = queryPrimesUtil(st, 0, n - 1, qs, qe, 0);        System.out.println("Number of Primes in subarray from " +                           qs + " to " + qe + " = " + primesInRange);    }     // A recursive function that constructs Segment Tree     // for array[ss..se].    // si is index of current node in segment tree st    static int constructSTUtil(int arr[], int ss, int se,                               int[] st, int si, boolean isPrime[])    {        // If there is one element in array, check if it        // is prime then store 1 in the segment tree else        // store 0 and return        if (ss == se) {               // if arr[ss] is prime            if (isPrime[arr[ss]])                 st[si] = 1;                    else                st[si] = 0;                       return st[si];        }           // If there are more than one elements, then recur         // for left and right subtrees and store the sum         // of the two values in this node        int mid = getMid(ss, se);        st[si] = constructSTUtil(arr, ss, mid, st, si * 2 + 1, isPrime) +                 constructSTUtil(arr, mid + 1, se, st, si * 2 + 2, isPrime);        return st[si];    }             /* Function to construct segment tree from given array.    This function allocates memory for segment tree and   calls constructSTUtil() to fill the allocated memory */   static int[] constructST(int arr[], int n, boolean isPrime[])   {       // Allocate memory for segment tree           // Height of segment tree        int x = (int)(Math.ceil(Math.log(n)/Math.log(2)));           // Maximum size of segment tree        int max_size = 2 * (int)Math.pow(2, x) - 1;          int[] st = new int[max_size];           // Fill the allocated memory st        constructSTUtil(arr, 0, n - 1, st, 0, isPrime);           // Return the constructed segment tree        return st;   }       // Driver code    public static void main (String[] args)    {        int arr[] = { 1, 2, 3, 5, 7, 9 };        int n = arr.length;               /* Preprocess all primes till MAX.       Create a boolean array "isPrime[0..MAX]".       A value in prime[i] will finally be false        if i is Not a prime, else true. */        boolean[] isPrime = new boolean[MAX + 1];        Arrays.fill(isPrime, Boolean.TRUE);        sieveOfEratosthenes(isPrime);                // Build segment tree from given array        int[] st = constructST(arr, n, isPrime);           // Query 1: Query(start = 0, end = 4)        int start = 0;        int end = 4;        queryPrimes(st, n, start, end);           // Query 2: Update(i = 3, x = 6), i.e Update         // a[i] to x        int i = 3;        int x = 6;        updateValue(arr, st, n, i, x, isPrime);           // uncomment to see array after update        // for(int i = 0; i < n; i++) cout << arr[i] << " ";           // Query 3: Query(start = 0, end = 4)        start = 0;        end = 4;        queryPrimes(st, n, start, end);    }} // This code is contributed by avanitrachhadiya2155

Python3

 # Python3 program to find number of prime numbers in a# subarray and performing updatesfrom math import ceil, floor, logMAX = 1000 def sieveOfEratosthenes(isPrime):     isPrime = False     for p in range(2, MAX + 1):        if p  * p > MAX:            break         # If prime[p] is not changed, then        # it is a prime        if (isPrime[p] == True):             # Update all multiples of p            for i in range(2 * p, MAX + 1, p):                isPrime[i] = False # A utility function to get the middle index from corner indexes.def getMid(s, e):    return s + (e - s) // 2## /* A recursive function to get the number of primes in a given range#     of array indexes. The following are parameters for this function.##     st --> Pointer to segment tree#     index --> Index of current node in the segment tree. Initially#             0 is passed as root is always at index 0#     ss & se --> Starting and ending indexes of the segment represented#                 by current node, i.e., st[index]#     qs & qe --> Starting and ending indexes of query range */def queryPrimesUtil(st, ss, se, qs, qe, index):     # If segment of this node is a part of given range, then return    # the number of primes in the segment    if (qs <= ss and qe >= se):        return st[index]     # If segment of this node is outside the given range    if (se < qs or ss > qe):        return 0     # If a part of this segment overlaps with the given range    mid = getMid(ss, se)    return queryPrimesUtil(st, ss, mid, qs, qe, 2 * index + 1) + \            queryPrimesUtil(st, mid + 1, se, qs, qe, 2 * index + 2) # /* A recursive function to update the nodes which have the given# index in their range. The following are parameters#     st, si, ss and se are same as getSumUtil()#     i --> index of the element to be updated. This index is#             in input array.# diff --> Value to be added to all nodes which have i in range */def updateValueUtil(st, ss, se, i, diff, si):     # Base Case: If the input index lies outside the range of    # this segment    if (i < ss or i > se):        return     # If the input index is in range of this node, then update    # the value of the node and its children    st[si] = st[si] + diff    if (se != ss):        mid = getMid(ss, se)        updateValueUtil(st, ss, mid, i, diff, 2 * si + 1)        updateValueUtil(st, mid + 1, se, i, diff, 2 * si + 2) # The function to update a value in input array and segment tree.# It uses updateValueUtil() to update the value in segment treedef updateValue(arr,st, n, i, new_val,isPrime):     # Check for erroneous input index    if (i < 0 or i > n - 1):        printf("Invalid Input")        return     diff, oldValue = 0, 0     oldValue = arr[i]     # Update the value in array    arr[i] = new_val     # Case 1: Old and new values both are primes    if (isPrime[oldValue] and isPrime[new_val]):        return     # Case 2: Old and new values both non primes    if ((not isPrime[oldValue]) and (not isPrime[new_val])):        return     # Case 3: Old value was prime, new value is non prime    if (isPrime[oldValue] and not isPrime[new_val]):        diff = -1     # Case 4: Old value was non prime, new_val is prime    if (not isPrime[oldValue] and isPrime[new_val]):        diff = 1     # Update the values of nodes in segment tree    updateValueUtil(st, 0, n - 1, i, diff, 0) # Return number of primes in range from index qs (query start) to# qe (query end). It mainly uses queryPrimesUtil()def queryPrimes(st, n, qs, qe):     primesInRange = queryPrimesUtil(st, 0, n - 1, qs, qe, 0)     print("Number of Primes in subarray from ", qs," to ", qe," = ", primesInRange) # A recursive function that constructs Segment Tree# for array[ss..se].# si is index of current node in segment tree stdef constructSTUtil(arr, ss, se, st,si,isPrime):     # If there is one element in array, check if it    # is prime then store 1 in the segment tree else    # store 0 and return    if (ss == se):         # if arr[ss] is prime        if (isPrime[arr[ss]]):            st[si] = 1        else:            st[si] = 0         return st[si]     # If there are more than one elements, then recur    # for left and right subtrees and store the sum    # of the two values in this node    mid = getMid(ss, se)    st[si] = constructSTUtil(arr, ss, mid, st,si * 2 + 1, isPrime) + \            constructSTUtil(arr, mid + 1, se, st,si * 2 + 2, isPrime)    return st[si] # /* Function to construct segment tree from given array.# This function allocates memory for segment tree and# calls constructSTUtil() to fill the allocated memory */def constructST(arr, n, isPrime):     # Allocate memory for segment tree     # Height of segment tree    x = ceil(log(n, 2))     # Maximum size of segment tree    max_size = 2 * pow(2, x) - 1     st = *(max_size)     # Fill the allocated memory st    constructSTUtil(arr, 0, n - 1, st, 0, isPrime)     # Return the constructed segment tree    return st # Driver codeif __name__ == '__main__':     arr= [ 1, 2, 3, 5, 7, 9]    n = len(arr)     # /* Preprocess all primes till MAX.    # Create a boolean array "isPrime[0..MAX]".    # A value in prime[i] will finally be false    # if i is Not a prime, else true. */     isPrime = [True]*(MAX + 1)    sieveOfEratosthenes(isPrime)     # Build segment tree from given array    st = constructST(arr, n, isPrime)     # Query 1: Query(start = 0, end = 4)    start = 0    end = 4    queryPrimes(st, n, start, end)     # Query 2: Update(i = 3, x = 6), i.e Update    # a[i] to x    i = 3    x = 6    updateValue(arr, st, n, i, x, isPrime)     # uncomment to see array after update    # for(i = 0 i < n i++) cout << arr[i] << " "     # Query 3: Query(start = 0, end = 4)    start = 0    end = 4    queryPrimes(st, n, start, end) # This code is contributed by mohit kumar 29

C#

 // C# program to find number of prime numbers in a // subarray and performing updatesusing System;public class GFG{  static int MAX = 1000 ;  static void sieveOfEratosthenes(bool[] isPrime)  {    isPrime = false;    for (int p = 2; p * p <= MAX; p++)    {       // If prime[p] is not changed, then      // it is a prime      if (isPrime[p] == true)      {         // Update all multiples of p        for (int i = p * 2; i <= MAX; i += p)          isPrime[i] = false;      }    }  }   // A utility function to get the middle index from corner indexes.  static int getMid(int s, int e)  {    return s + (e - s) / 2;  }   /*  A recursive function to get the number of primes in a given range     of array indexes. The following are parameters for this function.     st    --> Pointer to segment tree    index --> Index of current node in the segment tree. Initially              0 is passed as root is always at index 0    ss & se  --> Starting and ending indexes of the segment represented                  by current node, i.e., st[index]    qs & qe  --> Starting and ending indexes of query range */  static int queryPrimesUtil(int[] st, int ss, int se,                             int qs, int qe, int index)  {     // If segment of this node is a part of given range, then return    // the number of primes in the segment          if (qs <= ss && qe >= se)      return st[index];     // If segment of this node is outside the given range    if (se < qs || ss > qe)      return 0;     // If a part of this segment overlaps with the given range    int mid = getMid(ss, se);    return queryPrimesUtil(st, ss, mid, qs,                           qe, 2 * index + 1) +      queryPrimesUtil(st, mid + 1, se,                      qs, qe, 2 * index + 2);  }   /* A recursive function to update the nodes which have the given    index in their range. The following are parameters    st, si, ss and se are same as getSumUtil()    i    --> index of the element to be updated. This index is              in input array.   diff --> Value to be added to all nodes which have i in range */  static void updateValueUtil(int[] st, int ss, int se,                              int i, int diff, int si)  {     // Base Case: If the input index lies outside the range of    // this segment    if (i < ss || i > se)      return;     // If the input index is in range of this node, then update    // the value of the node and its children    st[si] = st[si] + diff;    if (se != ss)    {      int mid = getMid(ss, se);      updateValueUtil(st, ss, mid, i, diff, 2 * si + 1);      updateValueUtil(st, mid + 1, se, i, diff, 2 * si + 2);    }  }   // The function to update a value in input array and segment tree.  // It uses updateValueUtil() to update the value in segment tree  static void updateValue(int[] arr, int[] st, int n,                          int i, int new_val, bool[] isPrime)  {     // Check for erroneous input index    if (i < 0 || i > n - 1)    {      Console.WriteLine("Invalid Input");      return;    }    int diff = 0;    int oldValue;    oldValue = arr[i];     // Update the value in array    arr[i] = new_val;     // Case 1: Old and new values both are primes    if (isPrime[oldValue] && isPrime[new_val])      return;     // Case 2: Old and new values both non primes    if ((!isPrime[oldValue]) && (!isPrime[new_val]))      return;     // Case 3: Old value was prime, new value is non prime    if (isPrime[oldValue] && !isPrime[new_val])    {      diff = -1;    }     // Case 4: Old value was non prime, new_val is prime    if (!isPrime[oldValue] && isPrime[new_val])    {      diff = 1;    }     // Update the values of nodes in segment tree    updateValueUtil(st, 0, n - 1, i, diff, 0);  }   // Return number of primes in range from index qs (query start) to  // qe (query end).  It mainly uses queryPrimesUtil()  static void queryPrimes(int[] st, int n, int qs, int qe)  {    int primesInRange = queryPrimesUtil(st, 0, n - 1, qs, qe, 0);    Console.WriteLine("Number of Primes in subarray from " +                      qs + " to " + qe + " = " + primesInRange);  }   // A recursive function that constructs Segment Tree   // for array[ss..se].  // si is index of current node in segment tree st  static int constructSTUtil(int[] arr, int ss, int se,                             int[] st, int si, bool[] isPrime)  {     // If there is one element in array, check if it    // is prime then store 1 in the segment tree else    // store 0 and return    if (ss == se)    {       // if arr[ss] is prime      if (isPrime[arr[ss]])         st[si] = 1;              else        st[si] = 0;       return st[si];    }     // If there are more than one elements, then recur     // for left and right subtrees and store the sum     // of the two values in this node    int mid = getMid(ss, se);    st[si] = constructSTUtil(arr, ss, mid, st,                             si * 2 + 1, isPrime) +      constructSTUtil(arr, mid + 1, se, st, si * 2 + 2, isPrime);    return st[si];  }   /* Function to construct segment tree from given array.    This function allocates memory for segment tree and   calls constructSTUtil() to fill the allocated memory */  static int[] constructST(int[] arr, int n, bool[] isPrime)  {     // Allocate memory for segment tree     // Height of segment tree    int x = (int)(Math.Ceiling(Math.Log(n) / Math.Log(2)));     // Maximum size of segment tree    int max_size = 2 * (int)Math.Pow(2, x) - 1;      int[] st = new int[max_size];     // Fill the allocated memory st    constructSTUtil(arr, 0, n - 1, st, 0, isPrime);     // Return the constructed segment tree    return st;  }   // Driver code  static public void Main ()  {    int[] arr = { 1, 2, 3, 5, 7, 9 };    int n = arr.Length;     /* Preprocess all primes till MAX.       Create a boolean array "isPrime[0..MAX]".       A value in prime[i] will finally be false        if i is Not a prime, else true. */    bool[] isPrime = new bool[MAX + 1];    Array.Fill(isPrime, true);    sieveOfEratosthenes(isPrime);     // Build segment tree from given array    int[] st = constructST(arr, n, isPrime);     // Query 1: Query(start = 0, end = 4)    int start = 0;    int end = 4;    queryPrimes(st, n, start, end);     // Query 2: Update(i = 3, x = 6), i.e Update     // a[i] to x    int i = 3;    int x = 6;    updateValue(arr, st, n, i, x, isPrime);     // uncomment to see array after update    // for(int i = 0; i < n; i++) cout << arr[i] << " ";     // Query 3: Query(start = 0, end = 4)    start = 0;    end = 4;    queryPrimes(st, n, start, end);  }} // This code is contributed by rag2127

Javascript


Output:
Number of Primes in subarray from 0 to 4 = 4
Number of Primes in subarray from 0 to 4 = 3

The time complexity of each query and update is O(logn) and that of building the segment tree is O(n)
Note: Here, the time complexity of pre-processing primes till MAX using the sieve of Eratosthenes is O(MAX log(log(MAX))) where MAX is the maximum value arri can take

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