Given an array arr[] consisting of N integers, the task is to find the minimum length of the prefix needed to be deleted such that the remaining array elements can be rearranged repeatedly by selecting the first or the last element one by one to form a sorted array.
Examples:
Input: arr[] = {6, 5, 4, 3, 4}
Output: 3
Explanation:
To make an array sorted according to the given condition, remove the first 3 elements.
After deletion, the array arr[] is modified to {3, 4}.
From the array arr[], selecting the first elements one by one, i.e. arr[0] -> arr[1], forms a sorted array {3, 4}.Input: arr[] = {1, 3, 4, 2}
Output: 3
Naive Approach: The simplest approach is to delete all possible lengths of the prefix from the given array and for every prefix, check if a sorted array can be formed from the remaining array elements by removal of those prefixes. If found to be true, then print the minimum length of the prefix deleted.
Time Complexity: O(N2)
Auxiliary Space: O(N)
Efficient Approach: The above approach can be optimized by observing that the resultant suffix must be of the form arr[1] ? arr[2] ? … ? arr[N – 2] ? arr[N – 1] where N is the length of the remaining array and the suffix is of the maximum length. Follow the steps below:
- Initialize a variable index to N – 1.
- Traverse the array from the end and stop at the point where arr[index – 1] ? arr[index].
- As the iteration proceeds, we keep decreasing the answer.
- After completing all the above steps, print the value of the index which is the minimum length of the prefix that must be deleted.
Below is the implementation of the above approach:
C++
// C++ program for above approach #include <bits/stdc++.h> using namespace std; // Function to find the minimum length // of prefix required to be deleted int findMinLength(vector< int >& arr) { // Stores index to be returned int index = ( int )arr.size() - 1; // Iterate until previous element // is <= current index while (index > 0 && arr[index] >= arr[index - 1]) { // Decrementing index index--; } // Return index return index; } // Driver Code int main() { // Given arr[] vector< int > arr = { 7, 8, 5, 0, -1, -1, 0, 1, 2, 3, 4 }; // Function Call cout << findMinLength(arr); return 0; } |
Java
// Java program for above approach import java.util.*; import java.io.*; class GFG{ // Function to find the minimum length // of prefix required to be deleted static int findMinLength( int [] arr) { // Stores index to be returned int index = ( int )arr.length - 1 ; // Iterate until previous element // is <= current index while (index > 0 && arr[index] >= arr[index - 1 ]) { // Decrementing index index--; } // Return index return index; } // Driver code public static void main(String args[]) { // Given arr[] int arr[]= { 7 , 8 , 5 , 0 , - 1 , - 1 , 0 , 1 , 2 , 3 , 4 }; int n = arr.length; // Function call System.out.println(findMinLength(arr)); } } // This code is contributed by bikram2001jha |
Python3
# Python3 program for above approach # Function to find the minimum length # of prefix required to be deleted def findMinLength(arr): # Stores index to be returned index = len (arr) - 1 ; # Iterate until previous element # is <= current index while (index > 0 and arr[index] > = arr[index - 1 ]): # Decrementing index index - = 1 ; # Return index return index; # Driver code if __name__ = = '__main__' : # Given arr arr = [ 7 , 8 , 5 , 0 , - 1 , - 1 , 0 , 1 , 2 , 3 , 4 ]; n = len (arr); # Function call print (findMinLength(arr)); # This code is contributed by Princi Singh |
C#
// C# program for above approach using System; class GFG{ // Function to find the minimum length // of prefix required to be deleted static int findMinLength( int [] arr) { // Stores index to be returned int index = ( int )arr.Length - 1; // Iterate until previous element // is <= current index while (index > 0 && arr[index] >= arr[index - 1]) { // Decrementing index index--; } // Return index return index; } // Driver code public static void Main(String []args) { // Given []arr int []arr = { 7, 8, 5, 0, -1, -1, 0, 1, 2, 3, 4 }; int n = arr.Length; // Function call Console.WriteLine(findMinLength(arr)); } } // This code is contributed by Amit Katiyar |
Javascript
<script> // Java Script program for above approach // Function to find the minimum length // of prefix required to be deleted function findMinLength( arr) { // Stores index to be returned let index = parseInt(arr.length) - 1; // Iterate until previous element // is <= current index while (index > 0 && arr[index] >= arr[index - 1]) { // Decrementing index index--; } // Return index return index; } // Driver code // Given arr[] let arr= [ 7, 8, 5, 0, -1, -1, 0, 1, 2, 3, 4 ]; let n = arr.length; // Function call document.write(findMinLength(arr)); //contributed by sravan kumar </script> |
4
Time Complexity: O(N)
Auxiliary Space: O(1)
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