In Division Nim, the heap cannot be divided into equal halves. Factor Division Nim relaxes this constraint by allowing a heap of 2n matches to be divided into two heaps of n matches if n has a common prime factor with the player’s turn number. The turns are numbered consecutively starting from zero. Give a complete game tree for Factor Division Nim with seven matches and assign the values ‘win’, ‘loss’, and ‘draw’ to the nodes.

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Heap Sort

A Heap is a type of data structure that is built on trees. It's a binary tree that's virtually complete. Except for the very bottom level, all levels of the tree must be filled in a heap. The last (bottom) level should be filled from left to right. The heap data structure is used for the efficient implementation of priority queues.Heap can be of two types: