Maximum number of partitions that can be sorted individually to make sorted

Given an array arr[] of size n such that elements of arr[] in range [0, 1, ..n-1]. Our task is to divide the array into maximum number of partitions that can be sorted individually, then concatenated to make the whole array sorted.

Examples :

Input : arr[] = [2, 1, 0, 3]
Output : 2
If divide arr[] into two partitions
{2, 1, 0} and {3}, sort then and concatenate
then, we get the whole array sorted.

Input : arr[] = [2, 1, 0, 3, 4, 5]
Output : 4
The maximum number of partitions are four, we
get these partitions as {2, 1, 0}, {3}, {4} 
and {5}

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is based on the fact that if an element arr[i] is maximum of prefix arr[0..i], then we can make a partition ending with arr[i].

C++

// CPP program to find Maximum number of partitions 
// such that we can get a sorted array. 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find maximum partitions. 
int maxPartitions(int arr[], int n) 
{ 
    int ans = 0, max_so_far = 0; 
    for (int i = 0; i < n; ++i) { 
  
        // Find maximum in prefix arr[0..i] 
        max_so_far = max(max_so_far, arr[i]); 
  
        // If maximum so far is equal to index, 
        // we can make a new partition ending at 
        // index i. 
        if (max_so_far == i) 
            ans++; 
    } 
    return ans; 
} 
  
// Driver code 
int main() 
{ 
    int arr[] = { 1, 0, 2, 3, 4 }; 
    int n = sizeof(arr) / sizeof(arr[0]); 
    cout << maxPartitions(arr, n); 
    return 0; 
} 

Java

// java program to find Maximum number of partitions 
// such that we can get a sorted array 
  
import java.io.*; 
  
class GFG  
{ 
    // Function to find maximum partitions. 
    static int maxPartitions(int arr[], int n) 
    { 
        int ans = 0, max_so_far = 0; 
        for (int i = 0; i < n; ++i) { 
      
            // Find maximum in prefix arr[0..i] 
            max_so_far = Math.max(max_so_far, arr[i]); 
      
            // If maximum so far is equal to index, 
            // we can make a new partition ending at 
            // index i. 
            if (max_so_far == i) 
                ans++; 
        } 
        return ans; 
    } 
      
    // Driver code 
    public static void main (String[] args)  
    { 
        int arr[] = { 1, 0, 2, 3, 4 }; 
        int n = arr.length; 
        System.out.println (maxPartitions(arr, n)); 
              
    } 
}  
  
// This code is contributed by vt_m. 

Python3

# Python3 program to find Maximum 
# number of partitions such that 
# we can get a sorted array. 
  
# Function to find maximum partitions. 
def maxPartitions(arr, n): 
  
    ans = 0; max_so_far = 0
    for i in range(0, n):  
  
        # Find maximum in prefix arr[0..i] 
        max_so_far = max(max_so_far, arr[i]) 
  
        # If maximum so far is equal to  
        # index, we can make a new partition  
        # ending at index i. 
        if (max_so_far == i): 
            ans += 1
      
    return ans 
  
# Driver code 
arr = [1, 0, 2, 3, 4]  
n = len(arr) 
print(maxPartitions(arr, n)) 
  
# This code is contributed by Smitha Dinesh Semwal. 

C#

// C# program to find Maximum number of partitions 
// such that we can get a sorted array 
using System; 
  
class GFG  
{ 
    // Function to find maximum partitions. 
    static int maxPartitions(int []arr, int n) 
    { 
        int ans = 0, max_so_far = 0; 
        for (int i = 0; i < n; ++i)  
        { 
      
            // Find maximum in prefix arr[0..i] 
            max_so_far = Math.Max(max_so_far, arr[i]); 
      
            // If maximum so far is equal to index, 
            // we can make a new partition ending at 
            // index i. 
            if (max_so_far == i) 
                ans++; 
        } 
        return ans; 
    } 
      
    // Driver code 
    public static void Main ()  
    { 
        int []arr = { 1, 0, 2, 3, 4 }; 
        int n = arr.Length; 
        Console.Write (maxPartitions(arr, n)); 
              
    } 
}  
  
// This code is contributed by nitin mittal. 

PHP

<?php 
// PHP program to find Maximum 
// number of partitions such  
// that we can get a sorted array. 
  
// Function to find maximum partitions. 
function maxPartitions($arr, $n) 
{ 
    $ans = 0;  
    $max_so_far = 0; 
    for ($i = 0; $i < $n; ++$i) { 
  
        // Find maximum in prefix arr[0..i] 
        $max_so_far = max($max_so_far, $arr[$i]); 
  
        // If maximum so far is equal to index, 
        // we can make a new partition ending at 
        // index i. 
        if ($max_so_far == $i) 
            $ans++; 
    } 
    return $ans; 
} 
  
// Driver code 
{ 
    $arr = array(1, 0, 2, 3, 4); 
    $n = sizeof($arr) / sizeof($arr[0]); 
    echo maxPartitions($arr, $n); 
    return 0; 
} 
  
// This code is contributed by nitin mittal 
?> 

Output:

My Personal Notes

Recommended Posts:

Sagar Shukla

Intern at GeeksforGeeks

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : nitin mittal, MuraliSuresh

Writing code in comment? Please use ide.geeksforgeeks.org, generate link and share the link here.