Question

5. Consider the following binary search trees. Try to color them as valid red-black trees. If not possible, please explain. Consider the dummy leaf nodes as well.

Answer 1

To become a Red-Black trees fonowing a considitions must be hold. 1 Every node is either red or black 4) The Proof and leaves (Nil's) are black w of node is red, then its parent ist black Oh if a node is red then its both children must be black. in) Number of black nodes from any node to nil node should be the same.

A is a Binary Search free. To coloro 8 this free first we insert one by one node that might not viointo the rule of BSLT so, we have 3 nodes. oceuring as Redna ceuring as Red node] Enter 1 st node. I new node ® Color The root must be black now, insert and mode 0 [not violating any Insert sind node, B , so need r 3rd not violante rue r 390 o chose 1 ® colore color > nii nil This is not free because Rule EV a Red - Black it violating

D Rednode 8. Black male • dummy note nil nil نه |: insert B any rule (mot violating and node insest aww y ( not wolnting rule) 3rd node ® ® . insout 4rth mode (viointing 19 rue, so need change) woro ® Color insent th, e viointing rule, so need change) node color, ® ® ingest 17 rule, so nead change 6th node & violading color inset th node Ang. This is final Red Black DOOR