Queries to search an element in an array and move it to front after every query

Last Updated : 27 Sep, 2022

Given an integer M which represents an array initially having numbers 1 to M. Also given is a Query array. For every query, search the number in the initial array and bring it to the front of the array. The task is to return the indexes of the searched element in the given array for every query.
Examples:

Input : Q[] = {3, 1, 2, 1}, M = 5
Output : [2, 1, 2, 1]
Explanations :
Since m = 5 the initial array is [1, 2, 3, 4, 5].
Query1: Search for 3 in the [1, 2, 3, 4, 5] and move it in the beginning. After moving, the array looks like [3, 1, 2, 4, 5]. 3 is at index 2.
Query2: Move 1 from [3, 1, 2, 4, 5] to the beginning of the array to make the array look like [1, 3, 2, 4, 5]. 1 is present at index 1.
Query3: Move 2 from [1, 3, 2, 4, 5] to the beginning of the array to make the array look like [2, 1, 3, 2, 4, 5]. 2 is present at index 2.
Query4: Move 1 from [2, 1, 3, 4, 5] to the beginning of the array to make the array look like [1, 2, 3, 4, 5]. 1 is present at index 1.

Input : Q[] = {4, 1, 2, 2}, M = 4
Output : 3, 1, 2, 0

Naive approach: The naive approach is to use a hash table to search for the element and linearly do shifts by performing swaps. The time complexity will be quadratic in nature for this approach.
Below is the naive implementation of the above approach:

C++

// C++ program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the indices
vector<int> processQueries(int Q[], int m, int n)
{
    int a[m + 1], pos[m + 1];
 
    for (int i = 1; i <= m; i++) {
        a[i - 1] = i;
        pos[i] = i - 1;
    }
 
    vector<int> ans;
 
    // iterate in the query array
    for (int i = 0; i < n; i++) {
        int q = Q[i];
 
        // store current element
        int p = pos[q];
 
        ans.push_back(p);
 
        for (int i = p; i > 0; i--) {
 
            // swap positions of the element
            swap(a[i], a[i - 1]);
 
            pos[a[i]] = i;
        }
 
        pos[a[0]] = 0;
    }
 
    // return the result
    return ans;
}
 
// Driver code
int main()
{
    // initialise array
    int Q[] = { 3, 1, 2, 1 };
    int n = sizeof(Q) / sizeof(Q[0]);
 
    int m = 5;
 
    vector<int> ans;
 
    // Function call
    ans = processQueries(Q, m, n);
 
    // Print answers to queries
    for (int i = 0; i < ans.size(); i++)
        cout << ans[i] << " ";
 
    return 0;
}

Java

// Java program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
import java.util.*;
 
class GFG{
  
// Function to find the indices
static Vector<Integer> processQueries(int Q[], int m, int n)
{
    int []a = new int[m + 1];
    int []pos = new int[m + 1];
  
    for (int i = 1; i <= m; i++) {
        a[i - 1] = i;
        pos[i] = i - 1;
    }
  
    Vector<Integer> ans = new Vector<Integer>();
  
    // iterate in the query array
    for (int i = 0; i < n; i++) {
        int q = Q[i];
  
        // store current element
        int p = pos[q];
  
        ans.add(p);
  
        for (int j = p; j > 0; j--) {
  
            // swap positions of the element
            a[j] = a[j] + a[j - 1];
            a[j - 1] = a[j] - a[j - 1];
            a[j] = a[j] - a[j - 1];
  
            pos[a[j]] = j;
        }
  
        pos[a[0]] = 0;
    }
  
    // return the result
    return ans;
}
  
// Driver code
public static void main(String[] args)
{
    // initialise array
    int Q[] = { 3, 1, 2, 1 };
    int n = Q.length;
  
    int m = 5;
  
    Vector<Integer> ans = new Vector<Integer>();
  
    // Function call
    ans = processQueries(Q, m, n);
  
    // Print answers to queries
    for (int i = 0; i < ans.size(); i++)
        System.out.print(ans.get(i)+ " ");
  
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 program to search the element 
# in an array for every query and 
# move the searched element to 
# the front after every query
 
# Function to find the indices 
def processQueries(Q, m, n) : 
 
    a = [0]*(m + 1); pos = [0]*(m + 1); 
 
    for i in range(1, m + 1) : 
        a[i - 1] = i; 
        pos[i] = i - 1; 
 
    ans = []; 
 
    # iterate in the query array 
    for i in range(n) :
        q = Q[i]; 
 
        # store current element 
        p = pos[q]; 
 
        ans.append(p); 
 
        for i in range(p,0,-1) : 
 
            # swap positions of the element 
            a[i], a[i - 1] = a[i - 1],a[i];
            pos[a[i]] = i; 
 
        pos[a[0]] = 0; 
 
    # return the result 
    return ans; 
 
# Driver code 
if __name__ == "__main__" :
 
    # initialise array 
    Q = [ 3, 1, 2, 1 ]; 
    n = len(Q); 
 
    m = 5; 
 
    ans = []; 
 
    # Function call 
    ans = processQueries(Q, m, n); 
 
    # Print answers to queries 
    for i in range(len(ans)) :
        print(ans[i],end=" "); 
 
# This code is contributed by Yash_R

C#

// C# program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
using System;
using System.Collections.Generic;
 
public class GFG{
 
// Function to find the indices
static List<int> processQueries(int []Q, int m, int n)
{
    int []a = new int[m + 1];
    int []pos = new int[m + 1];
 
    for(int i = 1; i <= m; i++)
    {
       a[i - 1] = i;
       pos[i] = i - 1;
    }
     
    List<int> ans = new List<int>();
 
    // Iterate in the query array
    for(int i = 0; i < n; i++)
    {
       int q = Q[i];
 
       // Store current element
       int p = pos[q];
       ans.Add(p);
 
       for(int j = p; j > 0; j--)
       {
             
          // Swap positions of the element
          a[j] = a[j] + a[j - 1];
          a[j - 1] = a[j] - a[j - 1];
          a[j] = a[j] - a[j - 1];
 
          pos[a[j]] = j;
       }
       pos[a[0]] = 0;
    }
 
    // Return the result
    return ans;
}
 
// Driver code
public static void Main(String[] args)
{
    // Initialise array
    int []Q = { 3, 1, 2, 1 };
    int n = Q.Length;
    int m = 5;
 
    List<int> ans = new List<int>();
 
    // Function call
    ans = processQueries(Q, m, n);
 
    // Print answers to queries
    for(int i = 0; i < ans.Count; i++)
       Console.Write(ans[i] + " ");
 
}
}
// This code is contributed by sapnasingh4991

Javascript

<script>
 
// JavaScript program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
 
// Function to find the indices
function processQueries(Q,m,n)
{
    let a = new Array(m + 1);
    let pos = new Array(m + 1);
   
    for (let i = 1; i <= m; i++) {
        a[i - 1] = i;
        pos[i] = i - 1;
    }
   
    let ans = [];
   
    // iterate in the query array
    for (let i = 0; i < n; i++) {
        let q = Q[i];
   
        // store current element
        let p = pos[q];
   
        ans.push(p);
   
        for (let j = p; j > 0; j--) {
   
            // swap positions of the element
            a[j] = a[j] + a[j - 1];
            a[j - 1] = a[j] - a[j - 1];
            a[j] = a[j] - a[j - 1];
   
            pos[a[j]] = j;
        }
   
        pos[a[0]] = 0;
    }
   
    // return the result
    return ans;
}
 
// Driver code
 
// initialise array
let Q=[3, 1, 2, 1];
let n = Q.length;
let m = 5;
let ans=[];
// Function call
ans = processQueries(Q, m, n);
 
// Print answers to queries
for (let i = 0; i < ans.length; i++)
    document.write(ans[i]+ " ");
 
     
// This code is contributed by rag2127
 
</script>

Output:

2 1 2 1

Time complexity: O(n*p)
Auxiliary space: O(m)

Efficient Approach: An efficient method to solve the above problem is to use Fenwick Tree. Using the below 3 operations, the problem can be solved.

Push element in the front
Find the index of a number
Update the indexes of the rest of the elements.

Keep the elements in a sorted manner using the set data structure, and then follow the below-mentioned points:

Instead of pushing the element to the front i.e assigning an index 0 for every query.
We assign -1 for the first query, -2 for the second query, -3 for the third, and so on till -m.
Doing so, the range of index’s updates to [-m, m]
Perform a right shift for all values [-m, m] by a value of m, so our new range is [0, 2m]
Initialize a Fenwick tree of size 2m and set all the values from [1…m] i.e [m..2m]
For every query, find its position by finding the number of set elements lesser than the given query, once done set its position to 0 in the Fenwick tree.

Below is the implementation of the above approach:

C++

// C++ program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
#include <bits/stdc++.h>
using namespace std;
 
// Function to update the fenwick tree
void update(vector<int>& tree, int i, int val)
{
    // update the next element
    while (i < tree.size()) {
        tree[i] += val;
 
        // move to the next
        i += (i & (-i));
    }
}
 
// Function to  get the
// sum from the fenwick tree
int getSum(vector<int>& tree, int i)
{
    int s = 0;
 
    // keep adding till we have not
    // reached the root of the tree
    while (i > 0) {
        s += tree[i];
 
        // move to the parent
        i -= (i & (-i));
    }
    return s;
}
 
// function to process the queries
vector<int> processQueries(vector<int>& queries, int m)
{
    vector<int> res, tree((2 * m) + 1, 0);
 
    // Hash-table
    unordered_map<int, int> hmap;
 
    // Iterate and increase the frequency
    // count in the fenwick tree
    for (int i = 1; i <= m; ++i) {
        hmap[i] = i + m;
        update(tree, i + m, 1);
    }
    // Traverse for all queries
    for (int querie : queries) {
 
        // Get the sum from the fenwick tree
        res.push_back(getSum(tree, hmap[querie]) - 1);
 
        // remove it from the fenwick tree
        update(tree, hmap[querie], -1);
 
        // Add it back at the first index
        update(tree, m, 1);
 
        hmap[querie] = m;
 
        m--;
    }
 
    // return the final result
    return res;
}
 
// Driver code
int main()
{
    // initialise the Queries
    vector<int> Queries = { 4, 1, 2, 2 };
 
    // initialise M
    int m = 4;
 
    vector<int> ans;
 
    ans = processQueries(Queries, m);
 
    for (int i = 0; i < ans.size(); i++)
        cout << ans[i] << " ";
 
    return 0;
}

Java

// Java program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
import java.util.*;
class GFG{
 
// Function to update the fenwick tree
static void update(int []tree, int i, int val)
{
    // update the next element
    while (i < tree.length) 
    {
        tree[i] += val;
 
        // move to the next
        i += (i & (-i));
    }
}
 
// Function to  get the
// sum from the fenwick tree
static int getSum(int []tree, int i)
{
    int s = 0;
 
    // keep adding till we have not
    // reached the root of the tree
    while (i > 0)
    {
        s += tree[i];
 
        // move to the parent
        i -= (i & (-i));
    }
    return s;
}
 
// function to process the queries
static Vector<Integer> processQueries(int []queries, 
                                      int m)
{
    Vector<Integer>res = new Vector<>();
    int []tree = new int[(2 * m) + 1];
 
    // Hash-table
    HashMap<Integer,Integer> hmap  = new HashMap<>();
 
    // Iterate and increase the frequency
    // count in the fenwick tree
    for (int i = 1; i <= m; ++i)
    {
        hmap.put(i, i+m);
        update(tree, i + m, 1);
    }
   
    // Traverse for all queries
    for (int querie : queries) 
    {
 
        // Get the sum from the fenwick tree
        res.add(getSum(tree, hmap.get(querie) - 1));
 
        // remove it from the fenwick tree
        update(tree, hmap.get(querie), -1);
 
        // Add it back at the first index
        update(tree, m, 1);
 
        hmap.put(querie, m);
 
        m--;
    }
 
    // return the final result
    return res;
}
 
// Driver code
public static void main(String[] args)
{
    // initialise the Queries
    int []Queries = { 4, 1, 2, 2 };
 
    // initialise M
    int m = 4;
 
    Vector<Integer> ans;
 
    ans = processQueries(Queries, m);
 
    System.out.print(ans);
}
}
 
// This code is contributed by Rohit_ranjan

Python3

# Python3 program to search the element
# in an array for every query and
# move the searched element to
# the front after every query
 
# Function to update the fenwick tree
def update(tree, i, val):
 
    # Update the next element
    while (i < len(tree)):
        tree[i] += val
 
        # Move to the next
        i += (i & (-i))
 
# Function to get the
# sum from the fenwick tree
def getSum(tree, i):
 
    s = 0
 
    # Keep adding till we have not
    # reached the root of the tree
    while (i > 0):
        s += tree[i]
 
        # Move to the parent
        i -= (i & (-i))
    return s
 
# Function to process the queries
def processQueries(queries, m):
 
    res = []
    tree = [0] * (2 * m + 1)
 
    # Hash-table
    hmap = {}
 
    # Iterate and increase the frequency
    # count in the fenwick tree
    for i in range(1, m + 1):
        hmap[i] = i + m
        update(tree, i + m, 1)
     
    # Traverse for all queries
    for querie in queries:
 
        # Get the sum from the fenwick tree
        res.append(getSum(tree, hmap[querie]) - 1)
 
        # Remove it from the fenwick tree
        update(tree, hmap[querie], -1)
 
        # Add it back at the first index
        update(tree, m, 1)
 
        hmap[querie] = m
        m -= 1
 
    # Return the final result
    return res
 
# Driver code
if __name__ == "__main__":
     
    # Initialise the Queries
    Queries = [ 4, 1, 2, 2 ]
 
    # Initialise M
    m = 4
 
    ans = processQueries(Queries, m)
 
    for i in range(len(ans)):
        print(ans[i], end = " ")
 
# This code is contributed by chitranayal

C#

// C# program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
using System;
using System.Collections.Generic;
class GFG{
 
// Function to update the fenwick tree
static void update(int []tree, 
                   int i, int val)
{
    // update the next element
    while (i < tree.Length) 
    {
        tree[i] += val;
 
        // move to the next
        i += (i & (-i));
    }
}
 
// Function to  get the
// sum from the fenwick tree
static int getSum(int []tree, int i)
{
    int s = 0;
 
    // keep adding till we have not
    // reached the root of the tree
    while (i > 0)
    {
        s += tree[i];
 
        // move to the parent
        i -= (i & (-i));
    }
    return s;
}
 
// function to process the queries
static List<int> processQueries(int []queries, 
                                int m)
{
    List<int>res = new List<int>();
    int []tree = new int[(2 * m) + 1];
 
    // Hash-table
    Dictionary<int,
               int> hmap  = new Dictionary<int,
                                           int>();
 
    // Iterate and increase the frequency
    // count in the fenwick tree
    for (int i = 1; i <= m; ++i)
    {
        hmap.Add(i, i+m);
        update(tree, i + m, 1);
    }
   
    // Traverse for all queries
    foreach (int querie in queries) 
    {
        // Get the sum from the fenwick tree
        res.Add(getSum(tree, hmap[querie] - 1));
 
        // remove it from the fenwick tree
        update(tree, hmap[querie], -1);
 
        // Add it back at the first index
        update(tree, m, 1);
        if(hmap.ContainsKey(querie))
            hmap[querie] = m;
        else
            hmap.Add(querie, m);
 
        m--;
    }
 
    // return the readonly result
    return res;
}
 
// Driver code
public static void Main(String[] args)
{
    // initialise the Queries
    int []Queries = {4, 1, 2, 2};
 
    // initialise M
    int m = 4;
 
    List<int> ans;
    ans = processQueries(Queries, m);
    foreach (int i in ans)
        Console.Write(i + " ");
}
}
 
// This code is contributed by shikhasingrajput

Javascript

<script>
// Javascript program to search the element
// in an array for every query and
// move the searched element to
// the front after every query
     
    // Function to update the fenwick tree
    function update(tree,i,val)
    {
        // update the next element
    while (i < tree.length)
    {
        tree[i] += val;
  
        // move to the next
        i += (i & (-i));
    }
    }
     
    // Function to  get the
// sum from the fenwick tree
    function getSum(tree,i)
    {
        let s = 0;
  
    // keep adding till we have not
    // reached the root of the tree
    while (i > 0)
    {
        s += tree[i];
  
        // move to the parent
        i -= (i & (-i));
    }
    return s;
    }
     
    // function to process the queries
    function processQueries(queries,m)
    {
        let res = [];
    let tree = new Array((2 * m) + 1);
     for(let i=0;i<tree.length;i++)
    {
        tree[i]=0;
    }
    // Hash-table
    let hmap  = new Map();
  
    // Iterate and increase the frequency
    // count in the fenwick tree
    for (let i = 1; i <= m; ++i)
    {
        hmap.set(i, i+m);
        update(tree, i + m, 1);
    }
    
    // Traverse for all queries
    for (let querie=0;querie< queries.length;querie++)
    {
  
        // Get the sum from the fenwick tree
        res.push(getSum(tree, hmap.get(queries[querie]) - 1));
  
        // remove it from the fenwick tree
        update(tree, hmap.get(queries[querie]), -1);
  
        // Add it back at the first index
        update(tree, m, 1);
  
        hmap.set(queries[querie], m);
  
        m--;
    }
  
    // return the final result
    return res;
    }
     
    // Driver code
    let Queries=[4, 1, 2, 2];
    // initialise M
    let m = 4;
  
    let ans;
  
    ans = processQueries(Queries, m);
  
    document.write(ans.join(" "));
     
     
 
// This code is contributed by avanitrachhadiya2155
</script>

Output:

3 1 2 0

Time complexity: O(nlogn)
Auxiliary space: O(n)

Javascript Program for Search an element in a sorted and rotated array

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