The problem asks to check whether the sequence can be made strictly increasing. In your comment you have written to make sequence to strictly decreasing, I have taken that as a typo.
Although your given sequence can be made to strictly decreasing too with the help of pair (10,2) by interchanging the process for the left and right part of array.
Now if we keep repeating the operation then after some finite number of times(howsoever huge) we can get 7 2 4 1.000…001 1…
similarly we can make the 2 to become 1.0000…000001 and so on.
Repeat the same for the right part uptil the last element.
So we have :
1+1e(-very big number),1+1e(-very big number),…1…,1+1e(-very big number),9
Which is nearly of the form [m m m m m… >m]
This can be treated to become strictly increasing. Turn the second last element into average of 9 and 1+1e(-very big number) and so on till the first element becomes the minimum.
@cj2021 Um lets see:
for 7 and 2, you can make 7 very close to 2, greater than 2 but not equal. lets say 2.00001 2 but the sequence is still not increasing, so you need to increase 2 by an infinitesimal amount to make it greater than 2. How you do that? By increasing it with the help of a larger number than it, here it is 4. So the order becomes something like: 2.00001 2.00002 4. You can keep on repeating this to get the full sorted sequence.