Sort Part to Make Entire Array Sorted

Given an unsorted array arr[0..n-1] of size n, find the minimum length subarray arr[s..e] such that sorting this subarray makes the whole array sorted.

 

Examples:
1) If the input array is [10, 12, 20, 30, 25, 40, 32, 31, 35, 50, 60], your program should be able to find that the subarray lies between the indexes 3 and 8.

2) If the input array is [0, 1, 15, 25, 6, 7, 30, 40, 50], your program should be able to find that the subarray lies between the indexes 2 and 5.

Solution:
1) Find the candidate unsorted subarray 
a) Scan from left to right and find the first element which is greater than the next element. Let s be the index of such an element. In the above example 1, s is 3 (index of 30).
b) Scan from right to left and find the first element (first in right to left order) which is smaller than the next element (next in right to left order). Let e be the index of such an element. In the above example 1, e is 7 (index of 31).

2) Check whether sorting the candidate unsorted subarray makes the complete array sorted or not. If not, then include more elements in the subarray.
a) Find the minimum and maximum values in arr[s..e]. Let minimum and maximum values be min and max. minand max for [30, 25, 40, 32, 31] are 25 and 40 respectively.
b) Find the first element (if there is any) in arr[0..s-1] which is greater than min, change s to index of this element. There is no such element in above example 1.
c) Find the last element (if there is any) in arr[e+1..n-1] which is smaller than max, change e to index of this element. In the above example 1, e is changed to 8 (index of 35)

3) Print s and e.

 

Lets take an example:

int a[]={1,3,4,6,10,6,16,12,13,15,16,19,20,22,25}

Now if i will put this in to the graph (X-coordinate -> array index and Y-coordinate -> array's value) then the graph will look like as below: 

Now if we see the graph there are two places where dip happens one is after 10 and another after 16. Now in the zig zag portion if we see the min value is 6 and max val is 16. So the portion which we should sort to make the whole array sorted is between (6,16). Please refer to the below image:

Now we can easily divide the array in to three part. And middle part the one which we want to sort so that the whole array will be sorted.

 

Reference:

http://www.geeksforgeeks.org/minimum-length-unsorted-subarray-sorting-which-makes-the-complete-array-sorted/

http://stackoverflow.com/questions/15855594/min-n-m-so-that-whole-array-will-be-sorted/15855670