thussince any changes we make at node in during this upward march takes ( time (because it affects constant number of nodes)we have the followingproposition the algorithm for removing an entry from red-black tree with entries takes (logntime and performs (lognrecolorings and at most one adjustment plus one additional trinode restructuring thusit performs at most two restructure operations in figures and we show sequence of removal operations on redblack tree we illustrate case restructurings in figure and we illustrate case recolorings at several places in figures and finallyin figure and jwe show an example of case adjustment figure sequence of removals from redblack tree(ainitial tree(bremoval of (cremoval of causing double black (handled by restructuring)(dafter restructuring (continues in figure figure sequence of removals in redblack tree (continued)(eremoval of (fremoval of