Print Longest Decreasing Segment
As said above adding an extra Array does not change the space complexity to n^2. 


Another thing is you do not need that extra Array also. All you need is 3 or 4 variables. 
You can store the previous beginIndex and length of and the currentBeginIndex and length and if it crosses the previous maxLength then store the max as the crrentMax else continue with the iteration. 


Let me know if you want some code sample.