Minimum changes required to make a Catalan Sequence
Last Updated :
12 May, 2021
Given an array arr[] of N integer elements, the task is to change the minimum number of elements of this array such that it contains first N terms of the Catalan Sequence. Thus, find the minimum changes required.
First few Catalan numbers are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …..
Examples:
Input: arr[] = {4, 1, 2, 33, 213, 5}
Output: 3
We have to replace 4, 33, 213 with 1, 14, 42 to make first 6 terms of Catalan sequence.
Input: arr[] = {1, 1, 2, 5, 41}
Output: 1
Simply change 41 with 14
Approach:
- Take an unordered multiset. Insert first N terms of Catalan sequence in this multiset.
- Traverse the array from left to right. Check if the array element if present in the multiset. If it is present, then remove that element from the multiset.
- After traversing the array, the minimum changes required will be equal to the size of the multiset.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
#define MAX 100000
#define ll long long int
ll catalan[MAX];
void catalanDP(ll n)
{
catalan[0] = catalan[1] = 1;
for ( int i = 2; i <= n; i++) {
catalan[i] = 0;
for ( int j = 0; j < i; j++)
catalan[i] += catalan[j] * catalan[i - j - 1];
}
}
int CatalanSequence( int arr[], int n)
{
catalanDP(n);
unordered_multiset< int > s;
int a = 1, b = 1;
int c;
s.insert(a);
if (n >= 2)
s.insert(b);
for ( int i = 2; i < n; i++) {
s.insert(catalan[i]);
}
unordered_multiset< int >::iterator it;
for ( int i = 0; i < n; i++) {
it = s.find(arr[i]);
if (it != s.end())
s.erase(it);
}
return s.size();
}
int main()
{
int arr[] = { 1, 1, 2, 5, 41 };
int n = sizeof (arr) / sizeof (arr[0]);
cout << CatalanSequence(arr, n);
return 0;
}
|
Java
import java.util.HashSet;
class GFG1
{
static int MAX = 100000 ;
static long catalan[] = new long [MAX];
static void catalanDP( long n)
{
catalan[ 0 ] = catalan[ 1 ] = 1 ;
for ( int i = 2 ; i <= n; i++)
{
catalan[i] = 0 ;
for ( int j = 0 ; j < i; j++)
{
catalan[i] += catalan[j] * catalan[i - j - 1 ];
}
}
}
static int CatalanSequence( int arr[], int n)
{
catalanDP(n);
HashSet<Integer> s = new HashSet<Integer>();
int a = 1 , b = 1 ;
int c;
s.add(a);
if (n >= 2 )
{
s.add(b);
}
for ( int i = 2 ; i < n; i++)
{
s.add(( int ) catalan[i]);
}
for ( int i = 0 ; i < n; i++)
{
if (s.contains(arr[i]))
{
s.remove(arr[i]);
}
}
return s.size();
}
public static void main(String[] args)
{
int arr[] = { 1 , 1 , 2 , 5 , 41 };
int n = arr.length;
System.out.print(CatalanSequence(arr, n));
}
}
|
Python3
MAX = 100000 ;
catalan = [ 0 ] * MAX ;
def catalanDP(n) :
catalan[ 0 ] = catalan[ 1 ] = 1 ;
for i in range ( 2 , n + 1 ) :
catalan[i] = 0 ;
for j in range (i) :
catalan[i] + = (catalan[j] *
catalan[i - j - 1 ]);
def CatalanSequence(arr, n) :
catalanDP(n);
s = set ();
a = 1 ; b = 1 ;
s.add(a);
if (n > = 2 ) :
s.add(b);
for i in range ( 2 , n) :
s.add(catalan[i]);
temp = set ()
for i in range (n) :
if arr[i] in s :
temp.add(arr[i])
s = s - temp ;
return len (s);
if __name__ = = "__main__" :
arr = [ 1 , 1 , 2 , 5 , 41 ];
n = len (arr)
print (CatalanSequence(arr, n));
|
C#
using System;
using System.Collections.Generic;
class GFG1
{
static int MAX = 100000;
static long [] catalan = new long [MAX];
static void catalanDP( long n)
{
catalan[0] = catalan[1] = 1;
for ( int i = 2; i <= n; i++)
{
catalan[i] = 0;
for ( int j = 0; j < i; j++)
{
catalan[i] += catalan[j] * catalan[i - j - 1];
}
}
}
static int CatalanSequence( int []arr, int n)
{
catalanDP(n);
HashSet< int > s = new HashSet< int >();
int a = 1, b = 1;
s.Add(a);
if (n >= 2)
{
s.Add(b);
}
for ( int i = 2; i < n; i++)
{
s.Add(( int )catalan[i]);
}
for ( int i = 0; i < n; i++)
{
if (s.Contains(arr[i]))
{
s.Remove(arr[i]);
}
}
return s.Count;
}
public static void Main()
{
int []arr = {1, 1, 2, 5, 41};
int n = arr.Length;
Console.WriteLine(CatalanSequence(arr, n));
}
}
|
PHP
<?php
$MAX = 1000;
$catalan = array_fill (0, $MAX , 0);
function catalanDP( $n )
{
global $catalan ;
$catalan [0] = $catalan [1] = 1;
for ( $i = 2; $i <= $n ; $i ++)
{
$catalan [ $i ] = 0;
for ( $j = 0; $j < $i ; $j ++)
{
$catalan [ $i ] += $catalan [ $j ] *
$catalan [ $i - $j - 1];
}
}
}
function CatalanSequence( $arr , $n )
{
global $catalan ;
catalanDP( $n );
$s = array ();
$a = $b = 1;
array_push ( $s , $a );
if ( $n >= 2)
{
array_push ( $s , $b );
}
for ( $i = 2; $i < $n ; $i ++)
{
array_push ( $s , $catalan [ $i ]);
}
$s = array_unique ( $s );
for ( $i = 0; $i < $n ; $i ++)
{
if (in_array( $arr [ $i ], $s ))
{
unset( $s [ array_search ( $arr [ $i ], $s )]);
}
}
return count ( $s );
}
$arr = array (1, 1, 2, 5, 41);
$n = count ( $arr );
print (CatalanSequence( $arr , $n ));
?>
|
Javascript
<script>
var MAX = 100000
var catalan = Array(MAX);
function catalanDP(n)
{
catalan[0] = catalan[1] = 1;
for ( var i = 2; i <= n; i++) {
catalan[i] = 0;
for ( var j = 0; j < i; j++)
catalan[i] += catalan[j] * catalan[i - j - 1];
}
}
function CatalanSequence(arr, n)
{
catalanDP(n);
var s = [];
var a = 1, b = 1;
var c;
s.push(a);
if (n >= 2)
s.push(b);
for ( var i = 2; i < n; i++) {
s.push(catalan[i]);
}
s.sort((a,b)=>b-a);
for ( var i =0; i<n; i++)
{
if (s.includes(arr[i]))
{
s.pop(arr[i]);
}
}
return s.length;
}
var arr = [1, 1, 2, 5, 41 ];
var n = arr.length;
document.write( CatalanSequence(arr, n));
</script>
|
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