This question is for anyone who has read Introduction to Algorithms by MIT press 3rd edition - Exercises, how to make them easier?
While it isn't necessary to do every exercise in a book, it is important to be able to do every exercise in the book. 

Similarly, while it isn't necessary to write every algorithm, it is necessary to be able to write every algorithm. 

But learning is another issue. Reading alone isn't enough to learn something. I think you already understand that. You need practice with what you've read to make sure that you have a deep and long lasting understanding of the topic. So, as you've already discovered, you need to do a lot of well chosen exercises. 

But even that isn't enough. 

You need feedback on your attempts. You need someone to look at your work and tell you where you have done the right thing and where you need improvement.

Reinforcement and feedback are the key to learning. 

I'm not sure where you will be able to find this feedback. That is the real value of taking courses - the feedback is built in. Unfortunately not every course gives enough feedback, of course. If it is just grades, it isn't enough. You need it pointed out where and why something didn't work so that you don't build bad habits. (Reinforcement without feedback can be counterproductive). 

Perhaps there is a professor who would be willing to look at your work. Perhaps you have another more advanced student available. Some people create study groups to give feedback to each other. Even an online "buddy" who can evaluate what you've tried. 

And note, also, that having the answers available isn't really sufficient feedback until you learn how to find the misconceptions that led you to the wrong answer. It is little misconceptions that can throw you off and someone giving good feedback can help you get the insight to avoid them. 

Find someone. 

As for making it easier, only reinforcement, feedback, and time will do that.