Given an array arr[] of size N, consisting of 0s initially, and a positive integer K, the task is to print the array elements by performing the following operations exactly K times.
- For every ith operation select the rightmost longest subarray consisting of all 0s and replace the mid element of the subarray by i.
- If two middle elements exist, then check if i is an even number or not. If found to be true, then replace the rightmost middle element with i.
- Otherwise, replace the leftmost middle element with i.
- Initialize a Priority Queue, say pq, to store the subarrays of the form { X, Y} where X denotes the length of the subarray and Y denotes the starting index of the subarray.
- Initially maximum length of the subarray with all 0s is N and start index of the subarray is 0. Therefore, Insert { N, 0 } into pq.
- Iterate over the range [1, K] using variable i. For every ith operation pop the top element from pq and check if length of the popped element is an odd number or not. If found to be true then replace the mid element of the subarray with i.
- Otherwise, if i is an even number then replace the rightmost mid element of the subarray with i. Otherwise, replace the leftmost mid element of the subarray with i.
- After replacing the mid element with i, insert the left half of the subarray and right half of the subarray containing all 0s into pq.
- Finally, print the array elements.
Below is the implementation of the above approach:
C++
// C++ program to implement// the above approach#include <bits/stdc++.h>using namespace std;
// Function to print array by replacing the mid// of the rightmost longest subarray with count// of operations performed on the arrayvoid ReplaceArray(int arr[], int N, int K)
{ // Stores subarray of the form { X, Y },
// where X is the length and Y is start
// index of the subarray
priority_queue<vector<int> > pq;
// Insert the array arr[]
pq.push({ N, 0 });
// Stores index of mid
// element of the subarray
int mid;
// Iterate over the range [1, N]
for (int i = 1; i <= K; i++) {
// Stores top element of pq
vector<int> sub = pq.top();
// Pop top element of pq
pq.pop();
// If length of the subarray
// is an odd number
if (sub[0] % 2 == 1) {
// Update mid
mid = sub[1] + sub[0] / 2;
// Replacing arr[mid] with i
arr[mid] = i;
// Insert left half of
// the subarray into pq
pq.push({ sub[0] / 2,
sub[1] });
// Insert right half of
// the subarray into pq
pq.push({ sub[0] / 2,
(mid + 1) });
}
// If length of the current
// subarray is an even number
else {
// If i is
// an odd number
if (i % 2 == 1) {
// Update mid
mid = sub[1] + sub[0] / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.push({ sub[0] / 2 - 1,
sub[1] });
// Insert right half of
// the subarray into pq
pq.push({ sub[0] / 2, mid });
}
// If i is an even number
else {
// Update mid
mid = sub[1] + sub[0] / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.push({ sub[0] / 2,
sub[1] });
// Insert right half of
// the subarray into pq
pq.push({ sub[0] / 2 - 1,
(mid + 1) });
}
}
}
// Print array elements
for (int i = 0; i < N; i++)
cout << arr[i] << " ";
}// Driver Codeint main()
{ int arr[] = { 0, 0, 0, 0, 0 };
int N = sizeof(arr) / sizeof(arr[0]);
int K = 3;
ReplaceArray(arr, N, K);
} |
Java
import java.util.*;
class Tuple
{ public int x, y;
public Tuple(int a, int b)
{
x = a;
y = b;
}
}class GFG {
// Function to print array by replacing the mid
// of the rightmost longest subarray with count
// of operations performed on the array
static void replaceArray(int[] arr, int N, int K) {
// Stores subarray of the form { X, Y },
// where X is the length and Y is start
// index of the subarray
List<Tuple> pq = new ArrayList<>();
// Insert the array arr[]
pq.add(new Tuple(N, 0));
// Stores index of mid
// element of the subarray
int mid;
// Iterate over the range [1, N]
for (int i = 1; i <= K; i++) {
// Stores top element of pq
Tuple sub = pq.get(0);
// Pop top element of pq
pq.remove(0);
// If length of the subarray
// is an odd number
if (sub.x % 2 == 1) {
// Update mid
mid = sub.y + sub.x / 2;
// Replacing arr[mid] with i
arr[mid] = i;
// Insert left half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2, sub.y));
// Insert right half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2, (mid + 1)));
}
// If length of the current
// subarray is an even number
else {
// If i is
// an odd number
if (i % 2 == 1) {
// Update mid
mid = sub.y + sub.x / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2 - 1, sub.y));
// Insert right half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2, mid));
}
// If i is an even number
else {
// Update mid
mid = sub.y + sub.x / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2, sub.y));
// Insert right half of
// the subarray into pq
pq.add(new Tuple(sub.x / 2 - 1, (mid + 1)));
}
}
pq.sort((a, b) -> (a.x != b.x) ?
- a.x + b.x :
- a.y + b.y);
}
// Print array elements
for (int i = 0; i < N; i++)
System.out.print( arr[i] + " ");
}
// Driver Code
public static void main(String[] args)
{
int[] arr = { 0, 0, 0, 0, 0 };
int N = arr.length;
int K = 3;
replaceArray(arr, N, K);
}
}// This code is contributed by phasing17. |
Python3
# Python3 program to implement# the above approach# Function to print array by replacing the mid# of the rightmost longest subarray with count# of operations performed on the arraydef ReplaceArray(arr, N, K):
# Stores subarray of the form X, Y ,
# where X is the length and Y is start
# index of the subarray
pq = [];
# Insert the array arr[]
pq.append([ N, 0 ]);
# Stores index of mid
# element of the subarray
mid = 0
# Iterate over the range [1, N]
for i in range(1, 1 + N):
# Stores top element of pq
sub = pq[-1]
# Pop top element of pq
pq.pop();
# If length of the subarray
# is an odd number
if (sub[0] % 2 == 1) :
# Update mid
mid = int(sub[1] + int(sub[0] / 2));
# Replacing arr[mid] with i
arr[mid] = i;
# Insert left half of
# the subarray into pq
pq.append([ int(sub[0] / 2), sub[1] ]);
# Insert right half of
# the subarray into pq
pq.append([ int(sub[0] / 2), (mid + 1) ]);
# If length of the current
# subarray is an even number
else :
# If i is
# an odd number
if (i % 2 == 1) :
# Update mid
mid = sub[1] + int(sub[0] / 2);
# Replacing mid element
# with i
arr[mid - 1] = i;
# Insert left half of
# the subarray into pq
pq.append([ int(sub[0] / 2) - 1, sub[1] ]);
# Insert right half of
# the subarray into pq
pq.append([ int(sub[0] / 2), mid ]);
# If i is an even number
else :
# Update mid
mid = sub[1] + int(sub[0] / 2);
# Replacing mid element
# with i
arr[mid - 1] = i;
# Insert left half of
# the subarray into pq
pq.append([ int(sub[0] / 2), sub[1] ]);
# Insert right half of
# the subarray into pq
pq.append([ int(sub[0] / 2) - 1, (mid + 1) ]);
pq.sort()
# Print array elements
print(*arr)
# Driver Codearr = [ 0, 0, 0, 0, 0 ];
N = len(arr)
K = 3
ReplaceArray(arr, N, K);# This code is contributed by phasing17. |
C#
// C# program to implement// the above approachusing System;
using System.Linq;
using System.Collections.Generic;
class GFG
{ // Function to print array by replacing the mid
// of the rightmost longest subarray with count
// of operations performed on the array
static void ReplaceArray(int[] arr, int N, int K)
{
// Stores subarray of the form { X, Y },
// where X is the length and Y is start
// index of the subarray
var pq = new List<Tuple<int, int>>();
// Insert the array arr[]
pq.Add(Tuple.Create(N, 0));
// Stores index of mid
// element of the subarray
int mid;
// Iterate over the range [1, N]
for (int i = 1; i <= K; i++)
{
// Stores top element of pq
var sub = pq[0];
// Pop top element of pq
pq.RemoveAt(0);
// If length of the subarray
// is an odd number
if (sub.Item1 % 2 == 1) {
// Update mid
mid = sub.Item2 + sub.Item1 / 2;
// Replacing arr[mid] with i
arr[mid] = i;
// Insert left half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2,
sub.Item2));
// Insert right half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2,
(mid + 1)));
}
// If length of the current
// subarray is an even number
else {
// If i is
// an odd number
if (i % 2 == 1) {
// Update mid
mid = sub.Item2 + sub.Item1 / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2 - 1,
sub.Item2));
// Insert right half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2, mid));
}
// If i is an even number
else {
// Update mid
mid = sub.Item2 + sub.Item1 / 2;
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2,
sub.Item2));
// Insert right half of
// the subarray into pq
pq.Add(Tuple.Create(sub.Item1 / 2 - 1,
(mid + 1)));
}
}
pq = pq.OrderBy(p => -p.Item1).ThenBy(p => -p.Item2).ToList();
}
// Print array elements
for (int i = 0; i < N; i++)
Console.Write( arr[i] + " ");
}
// Driver Code
public static void Main(string[] args)
{
int[] arr = { 0, 0, 0, 0, 0 };
int N = arr.Length;
int K = 3;
ReplaceArray(arr, N, K);
}
} |
Javascript
// JS program to implement// the above approach// Function to print array by replacing the mid// of the rightmost longest subarray with count// of operations performed on the arrayfunction ReplaceArray(arr, N, K)
{ // Stores subarray of the form { X, Y },
// where X is the length and Y is start
// index of the subarray
let pq = [];
// Insert the array arr[]
pq.push([ N, 0 ]);
// Stores index of mid
// element of the subarray
let mid;
// Iterate over the range [1, N]
for (let i = 1; i <= K; i++) {
// Stores top element of pq
let sub = pq[pq.length - 1]
// Pop top element of pq
pq.pop();
// If length of the subarray
// is an odd number
if (sub[0] % 2 == 1) {
// Update mid
mid = Math.floor(sub[1] + Math.floor(sub[0] / 2));
// Replacing arr[mid] with i
arr[mid] = i;
// Insert left half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2),
sub[1] ]);
// Insert right half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2),
(mid + 1) ]);
}
// If length of the current
// subarray is an even number
else {
// If i is
// an odd number
if (i % 2 == 1) {
// Update mid
mid = sub[1] + Math.floor(sub[0] / 2);
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2) - 1,
sub[1] ]);
// Insert right half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2), mid ]);
}
// If i is an even number
else {
// Update mid
mid = sub[1] + Math.floor(sub[0] / 2);
// Replacing mid element
// with i
arr[mid - 1] = i;
// Insert left half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2),
sub[1] ]);
// Insert right half of
// the subarray into pq
pq.push([ Math.floor(sub[0] / 2) - 1,
(mid + 1) ]);
}
}
pq.sort()
}
// Print array elements
console.log(arr.join(" "))
}// Driver Codelet arr = [ 0, 0, 0, 0, 0 ];let N = arr.lengthlet K = 3ReplaceArray(arr, N, K);// This code is contributed by phasing17. |
Output
3 0 1 2 0
Time Complexity: O(K * log(N))
Auxiliary Space: O(N)