Minimum Swaps to sort intuition + code C++ with explanation

Given an array of n distinct elements. Find the minimum number of swaps required to sort the array in strictly increasing order.

Example 1:

Input:
nums = {2, 8, 5, 4}
Output:
1
Explaination:
swap 8 with 4.
Example 2:

Input:
nums = {10, 19, 6, 3, 5}
Output:
2
Explaination:
swap 10 with 3 and swap 19 with 5.

Your Task:
You do not need to read input or print anything. Your task is to complete the function minSwaps() which takes the nums as input parameter and returns an integer denoting the minimum number of swaps required to sort the array. If the array is already sorted, return 0.

Expected Time Complexity: O(nlogn)
Expected Auxiliary Space: O(n)

[intuitive_coder]

Very nicely explained, clarity in your voice. This code is easy to understand than GFG solution. Good job!

[rishukumarsingh]

I understood the approach, but i don't get that, what lead to this approach, what is the thought process behind appraching this question in this ways, when i was solving it, i made it complicated by observing dependencies of position in terms of graph!

[arijitdey]

Very nicely explained..keep up the good work and keep coming up with such videos, and of course thanks a ton

[kaushikvelidandla]

Why is the result minimal ? That explanation is not clear. Might be better to explain using dependency graph and connected components

[sougatoghosh]

such logics are hard to build. hatsoff

[nayankhanna]

Great explanation & conceptual clarity!

[pratube]

Irony is that, this cannot be solved without sorting the array 😂

[yuvrajagarkar]

thank you for putting so much efforts, worth the time 👍

[hardcash]

in which company are you placed now and with what approx package?
(you are great motivation)

[kirankutte]

Will this appraoch work for if elements are from 0 - N-1

[shyren_more]

Thanks, but how can we claim this approach always guarantee the correct ans?
Is there some intuition behind it?

[techstuff]

How can we tackle this if duplicates are allowed?

[dhoni-]

madam i have one doubt when i have seen in solution in discussion section i am not able to understand but after watching your youtube solution i understood so why this happens i am always depending on yt videos how to overcome this i am not able to improve problem solving

[shreyamaheshwari]

Mam how do we make sure its the minimum number of sorts which we had found

[Jitendrakumar-gbcn]

I came here to see graph approach why using wrong thumbnail, but your approach is pretty much hint to the graph approach

[anshulkumarneekhara]

What is the intuition behind this approach??

[prathammittal]

do this method have a name ?
if it is pls tell the name

[kennyackerman]

You look so gorgeous btw nice explanation ❤

[systemforge]

Woah.. how to come up with ideas like this...

[aryansiroyajain]

Let me just ignore it was the best part😄