Please note that you have to typeset your assignment using either MTEX or Microsoft Word, and produce a PDF file for submission. Hand-written assignment (or photo of it) will not be graded. You need to submit an electronic version (in PDF form) on the HW03-LastName- You should name your file using the format FirstName. 1. (30 pts) Fig. 1 illustrates a red-black tree, where a rectangle represents a black data-bearing node, a circle represents a red data-bearing node, and the nil nodes are not shown. In your work, you have to use the same notations 40 20 80 10 30 60 100 50 70 90 120 13 Figure 1: A red-black tree. (5 pts) Draw the resulting red-black tree after inserting 0 from the red-black tree in Fig (5 pts) Draw the resulting red-black tree after inserting 140 into the red-black tree in Fig (5 pts) Draw the resulting red-black tree after deleting 20 from the red-black tree in Fig (5 pts) Draw the resulting red-black tree after deleting 120 from the red-black tree in Fig (5 pts) Which property or properties (give the property number) may be violated when inserting (5 pts) Which property or properties (give the property number) may be violated when deleting 1. You only have to draw the portion of the tree that is affected 1. You only have to draw the portion of the tree that is affected 1. You only have to draw the portion of the tree that is affected 1. You only have to draw the portion of the tree that is affected a new node into a red-black tree? Describe the violation before the fix-up. a node into a red-black tree? Describe the violation before the fix-up