Abstract: Breadth-first and depth-first search are indispensable adventure strategies leading which many other rummage around algorithms are built. In this dissertation, we projected an loomed of integrating these two strategies in a solitary algorithm that combines the corresponding strengths of mutual. We account preliminary computational outcome using the tree width predicament as an example. This dissertation explores the configuration of red-black trees by solving an apparently straightforward crisis: grant an uphill progression of rudiments, erect, in linear time, a red-black tree that contains the rudiments in symmetric sort. Numerous tremendous red-black ranking shapes are characterized: trees of least quantity and maximum loftiness, trees with a nominal and with a maximal fraction of red nodes.