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Find the number of different numbers in the array after applying the given operation q times

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  • Difficulty Level : Medium
  • Last Updated : 25 Jun, 2022

Given an array of size N, initially consists of zeroes only. The task is to apply the given operation q times and find the number of different numbers in the array except for zeroes. 
Operation Format: update(l, r, x):: update a[i] = x for all (l <= i <= r). 

Examples: 

Input : N = 5, Q = 3, 
update(1, 3, 1) 
update(0, 1, 2) 
update(3, 3, 3) 
Output :
Explanation : Initially array is {0, 0, 0, 0, 0}. After 
applying the operation for the first time array becomes {0, 1, 1, 1, 0}. 
After applying the operation for the second time the array becomes 
{2, 2, 1, 1, 0}. After applying the operation for the third time the array 
becomes {2, 2, 1, 3, 0}. So, a number of different numbers expect zero are 3.

Input : N = 5, Q = 3, 
update(1, 1, 4) 
update(0, 1, 2) 
update(1, 4, 5) 
Output :
 

Approach : 
Each operation suggests a range update, hence try to update the array using lazy propagation. After applying the operation Q times using lazy propagation call a function that finds the number of different numbers in the array. This function uses a set to find the count of different numbers. 
The update and query operations are similar to what they are in a segment tree with some changes. Whenever an update query gets executed in a segment tree, all the nodes associated with the current node also get updated whereas in lazy propagation those nodes will only get updated when required i.e. we create an array lazy[] of size equal to the given array all of whose elements will be initialized to 0 which means there are no updates for any node initially and any non-zero value at lazy[i] indicates that node i has an update pending which will only be updated while querying (when required).

Below is the implementation of the above approach : 

C++




// CPP implementation for above approach
#include <bits/stdc++.h>
using namespace std;
 
#define N 100005
 
// To store the tree in lazy propagation
int lazy[4 * N];
 
// To store the different numbers
set<int> se;
 
// Function to update in the range [x, y) with given value
void update(int x, int y, int value, int id, int l, int r)
{
    // check out of bound
    if (x >= r or l >= y)
        return;
 
    // check for complete overlap
    if (x <= l && r <= y) {
        lazy[id] = value;
        return;
    }
 
    // find the mid number
    int mid = (l + r) / 2;
 
    // check for pending updates
    if (lazy[id])
        lazy[2 * id] = lazy[2 * id + 1] = lazy[id];
 
    // make lazy[id] = 0, so that it has no pending updates
    lazy[id] = 0;
 
    // call for two child nodes
    update(x, y, value, 2 * id, l, mid);
    update(x, y, value, 2 * id + 1, mid, r);
}
 
// Function to find non-zero integers in the range [l, r)
void query(int id, int l, int r)
{
    // if id contains positive number
    if (lazy[id]) {
        se.insert(lazy[id]);
        // There is no need to see the children,
        // because all the interval have same number
        return;
    }
 
    // check for out of bound
    if (r - l < 2)
        return;
 
    // find the middle number
    int mid = (l + r) / 2;
 
    // call for two child nodes
    query(2 * id, l, mid);
    query(2 * id + 1, mid, r);
}
 
// Driver code
int main()
{
    // size of the array and number of queries
    int n = 5, q = 3;
 
    // Update operation for l, r, x, id, 0, n
    update(1, 4, 1, 1, 0, n);
    update(0, 2, 2, 1, 0, n);
    update(3, 4, 3, 1, 0, n);
 
    // Query operation to get answer in the range [0, n-1]
    query(1, 0, n);
 
    // Print the count of non-zero elements
    cout << se.size() << endl;
 
    return 0;
}

Java




// Java implementation for above approach
import java.util.*;
 
class geeks
{
     
    static int N = 100005;
 
    // To store the tree in lazy propagation
    static int[] lazy = new int[4*N];
 
    // To store the different numbers
    static Set<Integer> se = new HashSet<Integer>();
 
    // Function to update in the range [x, y) with given value
    public static void update(int x, int y, int value,
                            int id, int l, int r)
    {
 
        // check out of bound
        if (x >= r || l >= y)
            return;
     
        // check for complete overlap
        if (x <= l && r <= y)
        {
            lazy[id] = value;
            return;
        }
     
        // find the mid number
        int mid = (l + r) / 2;
     
        // check for pending updates
        if (lazy[id] != 0)
            lazy[2 * id] = lazy[2 * id + 1] = lazy[id];
     
        // make lazy[id] = 0, so that it has no pending updates
        lazy[id] = 0;
     
        // call for two child nodes
        update(x, y, value, 2 * id, l, mid);
        update(x, y, value, 2 * id + 1, mid, r);
    }
 
    // Function to find non-zero integers in the range [l, r)
    public static void query(int id, int l, int r)
    {
         
        // if id contains positive number
        if (lazy[id] != 0)
        {
            se.add(lazy[id]);
             
            // There is no need to see the children,
            // because all the interval have same number
            return;
        }
 
        // check for out of bound
        if (r - l < 2)
            return;
 
        // find the middle number
        int mid = (l + r) / 2;
 
        // call for two child nodes
        query(2 * id, l, mid);
        query(2 * id + 1, mid, r);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
         
        // size of the array and number of queries
        int n = 5, q = 3;
 
        // Update operation for l, r, x, id, 0, n
        update(1, 4, 1, 1, 0, n);
        update(0, 2, 2, 1, 0, n);
        update(3, 4, 3, 1, 0, n);
 
        // Query operation to get answer in the range [0, n-1]
        query(1, 0, n);
 
        // Print the count of non-zero elements
        System.out.println(se.size());
    }
}
 
// This code is contributed by
// sanjeev2552

Python3




# Python3 implementation for above approach
N = 100005
 
# To store the tree in lazy propagation
lazy = [0] * (4 * N);
 
# To store the different numbers
se = set()
 
# Function to update in the range [x, y)
# with given value
def update(x, y, value, id, l, r) :
     
    # check out of bound
    if (x >= r or l >= y):
        return;
 
    # check for complete overlap
    if (x <= l and r <= y) :
        lazy[id] = value;
        return;
 
    # find the mid number
    mid = (l + r) // 2;
 
    # check for pending updates
    if (lazy[id]) :
        lazy[2 * id] = lazy[2 * id + 1] = lazy[id];
 
    # make lazy[id] = 0,
    # so that it has no pending updates
    lazy[id] = 0;
 
    # call for two child nodes
    update(x, y, value, 2 * id, l, mid);
    update(x, y, value, 2 * id + 1, mid, r);
 
# Function to find non-zero integers
# in the range [l, r)
def query(id, l, r) :
     
    # if id contains positive number
    if (lazy[id]) :
         
        se.add(lazy[id]);
         
        # There is no need to see the children,
        # because all the interval have same number
        return;
     
    # check for out of bound
    if (r - l < 2) :
        return;
 
    # find the middle number
    mid = (l + r) // 2;
 
    # call for two child nodes
    query(2 * id, l, mid);
    query(2 * id + 1, mid, r);
 
# Driver code
if __name__ == "__main__" :
 
    # size of the array and number of queries
    n = 5; q = 3;
 
    # Update operation for l, r, x, id, 0, n
    update(1, 4, 1, 1, 0, n);
    update(0, 2, 2, 1, 0, n);
    update(3, 4, 3, 1, 0, n);
 
    # Query operation to get answer
    # in the range [0, n-1]
    query(1, 0, n);
 
    # Print the count of non-zero elements
    print(len(se));
     
# This code is contributed by AnkitRai01

C#




// C# implementation for above approach
using System;
using System.Collections.Generic;
     
public class geeks
{
     
    static int N = 100005;
 
    // To store the tree in lazy propagation
    static int[] lazy = new int[4*N];
 
    // To store the different numbers
    static HashSet<int> se = new HashSet<int>();
 
    // Function to update in the range [x, y) with given value
    public static void update(int x, int y, int value,
                            int id, int l, int r)
    {
 
        // check out of bound
        if (x >= r || l >= y)
            return;
     
        // check for complete overlap
        if (x <= l && r <= y)
        {
            lazy[id] = value;
            return;
        }
     
        // find the mid number
        int mid = (l + r) / 2;
     
        // check for pending updates
        if (lazy[id] != 0)
            lazy[2 * id] = lazy[2 * id + 1] = lazy[id];
     
        // make lazy[id] = 0, so that it has no pending updates
        lazy[id] = 0;
     
        // call for two child nodes
        update(x, y, value, 2 * id, l, mid);
        update(x, y, value, 2 * id + 1, mid, r);
    }
 
    // Function to find non-zero integers in the range [l, r)
    public static void query(int id, int l, int r)
    {
         
        // if id contains positive number
        if (lazy[id] != 0)
        {
            se.Add(lazy[id]);
             
            // There is no need to see the children,
            // because all the interval have same number
            return;
        }
 
        // check for out of bound
        if (r - l < 2)
            return;
 
        // find the middle number
        int mid = (l + r) / 2;
 
        // call for two child nodes
        query(2 * id, l, mid);
        query(2 * id + 1, mid, r);
    }
 
    // Driver Code
    public static void Main(String[] args)
    {
         
        // size of the array and number of queries
        int n = 5, q = 3;
 
        // Update operation for l, r, x, id, 0, n
        update(1, 4, 1, 1, 0, n);
        update(0, 2, 2, 1, 0, n);
        update(3, 4, 3, 1, 0, n);
 
        // Query operation to get answer in the range [0, n-1]
        query(1, 0, n);
 
        // Print the count of non-zero elements
        Console.WriteLine(se.Count);
    }
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
 
// JavaScript implementation for above approach
 
var N = 100005;
// To store the tree in lazy propagation
var lazy = Array(4*N).fill(0);
// To store the different numbers
var se = new Set();
// Function to update in the range [x, y) with given value
function update(x, y, value, id, l, r)
{
    // check out of bound
    if (x >= r || l >= y)
        return;
 
    // check for complete overlap
    if (x <= l && r <= y)
    {
        lazy[id] = value;
        return;
    }
 
    // find the mid number
    var mid = parseInt((l + r) / 2);
 
    // check for pending updates
    if (lazy[id] != 0)
        lazy[2 * id] = lazy[2 * id + 1] = lazy[id];
 
    // make lazy[id] = 0, so that it has no pending updates
    lazy[id] = 0;
 
    // call for two child nodes
    update(x, y, value, 2 * id, l, mid);
    update(x, y, value, 2 * id + 1, mid, r);
}
// Function to find non-zero integers in the range [l, r)
function query(id, l, r)
{
     
    // if id contains positive number
    if (lazy[id] != 0)
    {
        se.add(lazy[id]);
         
        // There is no need to see the children,
        // because all the interval have same number
        return;
    }
    // check for out of bound
    if (r - l < 2)
        return;
    // find the middle number
    var mid = parseInt((l + r) / 2);
    // call for two child nodes
    query(2 * id, l, mid);
    query(2 * id + 1, mid, r);
}
 
// Driver Code
// size of the array and number of queries
var n = 5, q = 3;
// Update operation for l, r, x, id, 0, n
update(1, 4, 1, 1, 0, n);
update(0, 2, 2, 1, 0, n);
update(3, 4, 3, 1, 0, n);
// Query operation to get answer in the range [0, n-1]
query(1, 0, n);
// Print the count of non-zero elements
document.write(se.size);
 
 
</script>

Output: 

3

 

Time Complexity: O(N*logN), as we are using two recursive calls and in each recursive call, we are decrementing mid by floor division of 2.

Auxiliary Space: O(N), as we are using the implicit extra space for the recursive stack for the recursive calls.


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