An amidakuji (i.e., ladder lotteries, or Ghost Legs) consists of n vertical lines (lines for short) and some horizontal bars (bars for short), where lines have their labels, and each bar connects two lines. By regarding each bar as the exchange of the labels of a pair of lines, an amidakuji (i.e., the network of the lines and bars) represents a permutation. Amidakuji's also correspond to sorting networks, in which bars are regarded as comparators. An amidakuji corresponds to a primitive sorting network if every bar connects two consecutive lines. A rhombus tiling is a tiling of rhombuses of unit edge length without gap or overlap. In this talk, we begin with the relation between Amidakujis and rhombus tilings. Then, we move to the enumeration by the reverse search and ZDDs (Zero-Suppressed Binary Decision Diagrams).