recursion recbinarysearch(values, , middle item recbinarysearch(values, , middle item recbinarysearch(values, , false log levels middle item recbinarysearch(values, , false figure the recursive call tree for the binary search algorithm (topwhen searching for value in the given sequence (bottomtowers of hanoi the towers of hanoi puzzleinvented by the french mathematician edouard lucas in consists of board with three vertical poles and stack of disks the diameter of the disks increases as we progress from the top to bottomcreating tower structure the illustration in figure shows the boardthe three towersand five disks any number of disks can be used with the puzzlebut we use five for ease of illustration pole pole pole figure the towers of hanoi puzzle with five disks the objective is to move all of the disks from the starting pole to one of the other two poles to create new tower there arehowevertwo restrictions( only one disk can be moved at timeand ( larger disk can never be placed on top of smaller disk