What Algorithm i should use???

newb here...

currently doing a thesis. my thesis is a game.. a board game...

now my problem is what algorithm should i use when generating a path to

the start point and to end point. the objective is the path must be random when generating in each level also it adds 1*level of block.

what algorithm should I use??? now im currently studying the Breadth first search algorithm and depth first search algorithm. is this the right algos?

tnx

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