Random Level similar to Flow Free Game in C# ?

Greeting !

I need some advice. I'm developing a game similar to Flow Free wherein the gameboard is composed of a grid and colored dots, and the user has to connect the same colored dots together without overlapping other lines, and using up ALL the free spaces in the board.

My question is about level-creation. I wish to make the levels generated randomly (and should at least be able to solve itself so that it can give players hints) and I am in a stump as to what algorithm to use in C# . Any suggestions?



Note: image shows the objective of Flow Free, and it is the same objective of what I am developing.

Thanks for your help.