In analyzing the time complexity of Algorithm Select, we obtain the recurrence $T(n)=T(|$~$\frac{n}{5}$~$|)+$

$T(\frac{7}{10}n+3)+(6|$~$\frac{n}{5}$~$|+(n-1))$ from which we deduce $T(n)=O(n).$

Suppose that we have an algorithm for finding the $k$ th smallest element whose time complexity is

$T(n)=T(c_{1}n)+T(c_{2}n)+n,$ where $c_1+c_2<mn\; id="EditorElement\_917018">1</mn><mi\; id="EditorElement\_917020">T</mi><mi\; id="EditorElement\_917024">(</mi><mi\; id="EditorElement\_917023">n</mi><mi\; id="EditorElement\_917025">)</mi><mn\; id="EditorElement\_917028">0</mn>$ and Determine $T(n).$