When implementing quicksort, if the array contains lots of duplicates, it maybe better to perform a three-way partition (into elements less than, equal to,and greater than the pivot), to make smaller recursive calls. Assume three-waycomparisons, as provided by the compareTo method.a. Give an algorithm that performs a three-way in-place partition of an N-elementsubarray using only N 1 three-way comparisons. If there are d items equalto the pivot, you may use d additional Comparable swaps, above and beyond the two-way partitioning algorithm. (Hint: As i and j move toward each other,maintain five groups of elements as shown below):EQUAL SMALL UNKNOWN LARGE EQUALi jb. Prove that using the algorithm above, sorting an N-element array that containsonly d different values, takes O(dN) time.
Biol 4305 K= rate of molecular evolution due to drift (for neutral alleles) = 2Nu * 1/2N 2nu is mutation rate K=u Example Pseudogene mutation rate= 1 x 10^-9 mut/yr/bp How along ago did the ancestor btwn humans and lemurs lived 1 x 10^-9 u/bp/yr x 1000 o 1 x 10^-6 u in 1000bp/yr o ~~ In 10^6 years We have 1 u in 1000bp 150 bp differences o 150 mutations per 10 ^6 years/1 mutation/1000bp/yr or 150 million years of total divergence o 2 branches from one point(putitive ancestors)--> 150 million years of total divergence o Estimate that ~~ the ancestors lived at 75 million years ago (divide it by two from above) In Slides- Test the constancy of the molecular clock Need phylogeny and DNA sequence data for species and an out group Estimates of genetic distance Bar graph 4 fold degenerate site- no matter what change happens- it will always change the structure of the amino acids Rate of molecular change graph Flatter the line- slower the rate of change Codon position vs rate o First base- asymptote There is a point that is no longer indicative of the change Things that have been around for a LONG time - less rater of change Neutral theory- why we have those patterns of evolution Detecting Selection at molecular level Neutral theory of molecular evol Explicative theory for molecular evol Null hypothesis for empirical theory Neut