Using computer trees to derive lower bounds for selection problems

n(n-l) ••• {n-t+2)2nt leaves. This suffices to prove the Theorem, sinc;..e a binary tree with R, leaves has height at least Ilog R,1. Without loss of generality, assume all leaves of T are feasible for some input permutation. We begin by defining the problem and some basic concepts. Consider a linear ordered set of n elements, e.g., {l, ••• ,n}. We are given a permutation of the set, al, .•• ,an , called the input permutation. We wish to find elements that satisfy a given proposition,P(x1, ••• ,x t ). For example, P{xl ,x2) can be "Xl is the largest and x2 is the 2 nd largest element."