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2. Heap (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Heap_(mathematics)

   Theorem: A semiheap with a biunitary element e may be considered an involuted semigroup with operation given by ab = [a, e, b] and involution by a –1 = [e, a, e]. [1]: 76 When the above construction is applied to a heap, the result is in fact a group. [1]: 143 Note that the identity e of the group can be chosen to be any element of the heap.

3. Worksheet - Wikipedia

   en.wikipedia.org/wiki/Worksheet

   The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.

4. Pairing heap - Wikipedia

   en.wikipedia.org/wiki/Pairing_heap

   A pairing heap is either an empty heap, or a pairing tree consisting of a root element and a possibly empty list of pairing trees. The heap ordering property requires that parent of any node is no greater than the node itself. The following description assumes a purely functional heap that does not support the decrease-key operation.

5. Skew heap - Wikipedia

   en.wikipedia.org/wiki/Skew_heap

   A skew heap (or self-adjusting heap) is a heap data structure implemented as a binary tree. Skew heaps are advantageous because of their ability to merge more quickly than binary heaps. In contrast with binary heaps, there are no structural constraints, so there is no guarantee that the height of the tree is logarithmic. Only two conditions ...

6. Heap's algorithm - Wikipedia

   en.wikipedia.org/wiki/Heap's_algorithm

   A map of the 24 permutations and the 23 swaps used in Heap's algorithm permuting the four letters A (amber), B (blue), C (cyan) and D (dark red) Wheel diagram of all permutations of length = generated by Heap's algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).

7. Binary heap - Wikipedia

   en.wikipedia.org/wiki/Binary_heap

   and we want to add the number 15 to the heap. We first place the 15 in the position marked by the X. However, the heap property is violated since 15 > 8, so we need to swap the 15 and the 8. So, we have the heap looking as follows after the first swap: However the heap property is still violated since 15 > 11, so we need to swap again: