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Maximum number of partitions that can be sorted individually to make sorted in C++
We are given with an array of N numbers with elements lying in range 0 and N-1. The elements are unsorted. The goal is to find the maximum number of partitions of the array which can be sorted individually and then can be concatenated to make a whole sorted array of length N.
Each partition is chosen such that elements in it are unsorted. For N numbers ranging between 0 and N-1, sorted elements are at index equal to the value. Arr[i] = i.
We will solve this by comparing each element by maximum value found so far on its left. When reached at the correct position of maximum, (maximum == i ). All elements to its left are less so can make a separate partition. All to its right are greater. Now do the same procedure for the rest of the right elements and divide them into partitions.
Let’s understand with examples.
Input − Arr[]={ 0,3,2,1,4,5 }
Output − Maximum number of partitions − 3
Explanation − Starting from 0, Let max=0 Arr[0]
Between index 0 and 3. 3 is maximum. When reached at index i=3 ( maxx==i). So first partition is [0,3,2,1]
For index 4, maximum is 4. Index i=4 ( maxx==i). So second partition is [4]
For index 5, maximum is 5. Index i=5 ( maxx==i). So second partition is [5]
Total 3 partitions [0,3,2,1][4][5]. Sort each and concatenate.
Input − Arr[]={ 5,4,3,2,1,0 }
Output − Maximum number of partitions − 1
Explanation − Starting from 0, Let max=0 Arr[0]
Between index 0 and 5. 5 is maximum. When reached at index i=5 ( maxx==i). So only partition is [5,4,3,2,1,0]
Approach used in the below program is as follows
We take an integer array Num[] initialized with numbers in range 0 to N.
Function partitions(int arr[], int n ) takes an array and its length as parameters and returns the count of maximum partitions that can be individually sorted to make the whole array sorted.
Initial partition count is 0. Initial maximum value is in maxx as arr[0].
For all elements starting from the leftmost element. Find if it's greater than maxx.
If arr[i]>maxx is true. Update maxx.
If the current maxx and index is the same. ( maxx==i ) then all elements upto i are part of one partition. Increment count.
Do this for the rest of the elements on the right till end.
Return the result as count.
Example
#include <bits/stdc++.h>
using namespace std;
int partitions(int arr[], int n){
int count = 0;
int maxx = arr[0];
for (int i = 0; i < n; ++i) {
if(arr[i] > maxx)
maxx=arr[i];
if (maxx == i)
count++;
}
return count;
}
int main(){
int Num[] = { 2,1,0,4,5,3 };
int len = 6;
cout <<"Maximum partitions that can be sorted: "<<partitions(Num, len);
return 0;
}Output
If we run the above code it will generate the following output −
Maximum partitions that can be sorted: 18
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