2. (10%) In a Fibonacci heap, when the decrease operation tries to mark a node for the second time,it cuts the node and marks its parent. Suppose we change the rule and only cuts a node when thedecrease operation tries to mark it for the third time. (In other words, a node can be marked twicewithout getting cut.) Draw the structure of the smallest tree of root degree 5. Briefly explain whyno smaller tree of root degree 5 is possible.
2. (10%) In a Fibonacci heap, when the decrease operation tries to mark a node for the second time,it cuts the node and marks its parent. Suppose we change the rule and only cuts a node when thedecrease operation tries to mark it for the third time. (In other words, a node can be marked twicewithout getting cut.) Draw the structure of the smallest tree of root degree 5. Briefly explain whyno smaller tree of root degree 5 is possible.
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