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}



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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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.

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C#

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// 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.

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PHP

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<?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
?>

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Output:

4


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Improved By : nitin mittal, MuraliSuresh



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