# 2.8.6 - M-Way Search Tree

m: Tree's Degree

主要用於external search及sort，因為通常資料量很大的時候，無法一次全部置於Memory中進行搜尋，需藉助外部儲存記憶體來保存Data(通常使用樹狀結構來保存)，再分批載入Memory中search。

![](/files/-LHqUrJc1frbSUY25L1E)

Tree的高度 = Disk I/O次數，若要降低樹的高度最有效的作法就是加大樹的Degree。

若一m-way search tree高度為h，求其最多節點數、最多資料數。

$$m^{0}+m^{1}+m^{1}+...+m^{h-2}+m^{h-1}=\frac{m^h-1}{m-1}個節點\ \frac{m^h-1}{m-1}\*(m-1)=m^{h}-1筆資料$$ 


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