书上说 BDT 的叶节点数是和!...它是怎么来的!?

Book says number of leaf nodes for a BDT to be n!... How is it n!?

书中的文字:"Let us define the external path length of a tree as the sum of the lengths of paths from the root to each of the leaf nodes. Then the average time complexity of a sorting algorithm based on comparisons is equal to the external path length of the binary decision tree corresponding to this algorithm divided by the number of leaf nodes, which is n!"。叶子节点的个数n! ?

(与Sorting的average case lower bound有关)

此声明似乎假定所有元素都是唯一的(无重复)。 n 个唯一元素的排列(排序)数为 n!,因此在决策树中,每个叶子代表唯一元素的特定排序,因此有 n!叶子,其中只有一个代表排序顺序。