Editing Binomial heap
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 25: | Line 25: | ||
==Merging== | ==Merging== | ||
− | Let two binomial heaps be denoted <math>A</math> and <math>B</math>, with sizes <math>n</math> and <math>m</math>, respectively. Let <math>A_k</math> denote <math>A</math>'s power-of-two tree of size <math>2^k</math>, if it has one, and <math>B_k</math> denote likewise a power-of-two tree of <math>B</math>. We want to create a new binomial | + | Let two binomial heaps be denoted <math>A</math> and <math>B</math>, with sizes <math>n</math> and <math>m</math>, respectively. Let <math>A_k</math> denote <math>A</math>'s power-of-two tree of size <math>2^k</math>, if it has one, and <math>B_k</math> denote likewise a power-of-two tree of <math>B</math>. We want to create a new binomial tree <math>S</math> that contains all the nodes from either <math>A</math> or <math>B</math> and has size <math>m+n</math>. After this operation, <math>A</math> and <math>B</math> will no longer exist as binomial heaps. |
(In theory, we could create a new binomial heap <math>S</math> that contained all the elements from both <math>A</math> and <math>B</math> ''without'' also destroying <math>A</math> and <math>B</math>. However, this would require copying over all the data from both heaps, which would take linear time (in the sum of their sizes). This would then be no more efficient than simply using the [[binary heap]]s. For this reason, we assume we usually do not want to do this.) | (In theory, we could create a new binomial heap <math>S</math> that contained all the elements from both <math>A</math> and <math>B</math> ''without'' also destroying <math>A</math> and <math>B</math>. However, this would require copying over all the data from both heaps, which would take linear time (in the sum of their sizes). This would then be no more efficient than simply using the [[binary heap]]s. For this reason, we assume we usually do not want to do this.) |