# Maximize partitions that if sorted individually makes the whole Array sorted

Given an array **arr[]**. The task is to divide **arr[] **into the maximum number of partitions, such that, those partitions if sorted individually make the whole array sorted.

**Examples:**

Input:arr[] = { 28, 9, 18, 32, 60, 50, 75, 70 }Output:4Explanation:Following are the partitions in which the array is divided.

If we divide arr[] into four partitions {28, 9, 18}, {32}, { 60, 50}, and {75, 70}, sort them and concatenate.

Sorting all of them indivudually makes the whole array sorted.

Hence, 4 is the answer.

Input:arr[] = { 2, 1, 0, 3, 4, 5 }Output:4

**Approach: **This problem is implementation-based. Follow the steps below to solve the given problem.

- Create a
**maximum array**that calculates the maximum element to the left till that index of the array. - Create a
**minimum array**that calculates the minimum element to the right till that index of the array. - Iterate through the array, each time all elements to the
**leftMax[]**are smaller (or equal) to all elements to the**rightMax[]**, that means there is a new chunk, so increment the**count**by**1**. - Return
**count+1**as the final answer.

Below is the implementation of the above approach.

## C++

`// C++ program for above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find maximum partitions.` `int` `maxPartitions(vector<` `int` `>& arr)` `{` ` ` `int` `N = arr.size();` ` ` `// To keep track of max` ` ` `// and min elements at every index` ` ` `vector<` `int` `> leftMax(arr.size());` ` ` `vector<` `int` `> rightMin(arr.size());` ` ` `leftMax[0] = arr[0];` ` ` `for` `(` `int` `i = 1; i < N; i++) {` ` ` `leftMax[i] = max(leftMax[i - 1],` ` ` `arr[i]);` ` ` `}` ` ` `rightMin[N - 1] = arr[N - 1];` ` ` `for` `(` `int` `i = N - 2; i >= 0; i--) {` ` ` `rightMin[i] = min(rightMin[i + 1],` ` ` `arr[i]);` ` ` `}` ` ` `int` `count = 0;` ` ` `for` `(` `int` `i = 0; i < N - 1; i++) {` ` ` `if` `(leftMax[i] <= rightMin[i + 1]) {` ` ` `count++;` ` ` `}` ` ` `}` ` ` `// Return count + 1 as the final answer` ` ` `return` `count + 1;` `}` `// Driver code` `int` `main()` `{` ` ` `vector<` `int` `> arr{ 10, 0, 21, 32, 68 };` ` ` `cout << maxPartitions(arr);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the above approach` `import` `java.util.*;` `public` `class` `GFG {` ` ` `// Function to find maximum partitions.` ` ` `static` `int` `maxPartitions(` `int` `[] arr)` ` ` `{` ` ` `int` `N = arr.length;` ` ` `// To keep track of max` ` ` `// and min elements at every index` ` ` `int` `[] leftMax = ` `new` `int` `[arr.length];` ` ` `int` `[] rightMin = ` `new` `int` `[arr.length];` ` ` `leftMax[` `0` `] = arr[` `0` `];` ` ` `for` `(` `int` `i = ` `1` `; i < N; i++) {` ` ` `leftMax[i] = Math.max(leftMax[i - ` `1` `], arr[i]);` ` ` `}` ` ` `rightMin[N - ` `1` `] = arr[N - ` `1` `];` ` ` `for` `(` `int` `i = N - ` `2` `; i >= ` `0` `; i--) {` ` ` `rightMin[i] = Math.min(rightMin[i + ` `1` `], arr[i]);` ` ` `}` ` ` `int` `count = ` `0` `;` ` ` `for` `(` `int` `i = ` `0` `; i < N - ` `1` `; i++) {` ` ` `if` `(leftMax[i] <= rightMin[i + ` `1` `]) {` ` ` `count++;` ` ` `}` ` ` `}` ` ` `// Return count + 1 as the final answer` ` ` `return` `count + ` `1` `;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `[] arr = { ` `10` `, ` `0` `, ` `21` `, ` `32` `, ` `68` `};` ` ` `System.out.println(maxPartitions(arr));` ` ` `}` `}` `// This code is contributed by Samim Hossain Mondal.` |

## Python

`# Python program for above approach` `# Function to find maximum partitions.` `def` `maxPartitions(arr):` ` ` `N ` `=` `len` `(arr)` ` ` `# To keep track of max` ` ` `# and min elements at every index` ` ` `leftMax ` `=` `[]` ` ` `rightMin ` `=` `[]` ` ` `leftMax.append(arr[` `0` `])` ` ` `for` `i ` `in` `range` `(` `1` `, N):` ` ` `leftMax.append(` `max` `(leftMax[i ` `-` `1` `], arr[i]))` ` ` `rightMin.append(arr[N ` `-` `1` `])` ` ` `for` `i ` `in` `range` `(` `1` `, N):` ` ` `rightMin.append(` `min` `(rightMin[i ` `-` `1` `], arr[N ` `-` `i ` `-` `1` `]))` ` ` `rightMin.reverse()` ` ` `count ` `=` `0` ` ` `for` `i ` `in` `range` `(` `0` `, N ` `-` `1` `):` ` ` `if` `(leftMax[i] <` `=` `rightMin[i ` `+` `1` `]):` ` ` `count ` `=` `count ` `+` `1` ` ` `# Return count + 1 as the final answer` ` ` `return` `count ` `+` `1` `# Driver code` `arr ` `=` `[` `10` `, ` `0` `, ` `21` `, ` `32` `, ` `68` `]` `print` `(maxPartitions(arr))` `# This code is contributed by Samim Hossain Mondal.` |

## C#

`// C# program for above approach` `using` `System;` `class` `GFG {` ` ` `// Function to find maximum partitions.` ` ` `static` `int` `maxPartitions(` `int` `[] arr)` ` ` `{` ` ` `int` `N = arr.Length;` ` ` `// To keep track of max` ` ` `// and min elements at every index` ` ` `int` `[] leftMax = ` `new` `int` `[arr.Length];` ` ` `int` `[] rightMin = ` `new` `int` `[arr.Length];` ` ` `leftMax[0] = arr[0];` ` ` `for` `(` `int` `i = 1; i < N; i++) {` ` ` `leftMax[i] = Math.Max(leftMax[i - 1], arr[i]);` ` ` `}` ` ` `rightMin[N - 1] = arr[N - 1];` ` ` `for` `(` `int` `i = N - 2; i >= 0; i--) {` ` ` `rightMin[i] = Math.Min(rightMin[i + 1], arr[i]);` ` ` `}` ` ` `int` `count = 0;` ` ` `for` `(` `int` `i = 0; i < N - 1; i++) {` ` ` `if` `(leftMax[i] <= rightMin[i + 1]) {` ` ` `count++;` ` ` `}` ` ` `}` ` ` `// Return count + 1 as the final answer` ` ` `return` `count + 1;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[] arr = { 10, 0, 21, 32, 68 };` ` ` `Console.WriteLine(maxPartitions(arr));` ` ` `}` `}` `// This code is contributed by ukasp.` |

## Javascript

`<script>` ` ` `// JavaScript code for the above approach ` ` ` `// Function to find maximum partitions.` ` ` `function` `maxPartitions(arr)` ` ` `{` ` ` `let N = arr.length;` ` ` `// To keep track of max` ` ` `// and min elements at every index` ` ` `let leftMax = ` `new` `Array(arr.length);` ` ` `let rightMin = ` `new` `Array(arr.length);` ` ` `leftMax[0] = arr[0];` ` ` `for` `(let i = 1; i < N; i++) {` ` ` `leftMax[i] = Math.max(leftMax[i - 1],` ` ` `arr[i]);` ` ` `}` ` ` `rightMin[N - 1] = arr[N - 1];` ` ` `for` `(let i = N - 2; i >= 0; i--) {` ` ` `rightMin[i] = Math.min(rightMin[i + 1],` ` ` `arr[i]);` ` ` `}` ` ` `let count = 0;` ` ` `for` `(let i = 0; i < N - 1; i++) {` ` ` `if` `(leftMax[i] <= rightMin[i + 1]) {` ` ` `count++;` ` ` `}` ` ` `}` ` ` `// Return count + 1 as the final answer` ` ` `return` `count + 1;` ` ` `}` ` ` `// Driver code` ` ` `let arr = [10, 0, 21, 32, 68];` ` ` `document.write(maxPartitions(arr));` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

4

* Time Complexity:* O(N)

*O(N)*

**Auxiliary Space:**