CSC207.01 2014S, Class 29: Implementing Lists with Arrays ========================================================= _Overview_ * Preliminaries. * Upcoming work. * Admin. * Some notes on Quicksort. * Some notes on implementing lists with arrays. * Lab. Preliminaries ------------- ### Get ready! * Fork and clone the repository at ### Upcoming Work * Reading for Tuesday: Linked lists (forthcoming). * Today's lab writeup: Exercise 6 (implement `previous`) * Exam 2 to be distributed on Wednesday. ### Admin Some notes on Quicksort ----------------------- Big Picture * Use partition to divide the array into small and large stuff * Recurse on each half * Uses randomness and divide and conquer Partition * Randomly choose a pivot. Compare each element with that one. Anything less than or equal to the pivot goes to the left. Anything greater than the pivot goes to the right * Returns the location of the pivot after partitioning More on Partition * How might you find the median of an array, using partition? * Knowledge: How many elements are in the array * Easy technique: Sort, use element array.length/2. Expect O(nlogn) * Harder technique: Partion once * If the pivot is at the midpoint, done * If the pivot falls after the midpoint, recurse on the left * If the pivot falls before the midpoint, recurse on the right public T median(T[] values, Comparator order) { int midpoint = values.length / 2; int lb = 0; int ub = values.length; while (true) { int pivloc = partition(values, lb, ub, order); if (pivloc == midpoint) return values[midpoint]; else if (pivloc < midpoint) ub = pivloc; else lb = pivloc+1; } } // median What's the running time? n + n/2 + n/4 + n/8 + ... ~= 2n O(n) Is partition like any other algorithm? * It's a simplified version of the Dutch National Flag problem. * We can write Quicksort using DNF to partition rather than partition. Some notes on implementing lists with arrays -------------------------------------------- * Key operations: Insert, Remove, Replace, Iterate * Also need a notion of "location" * Implementing with arrays * Position: Index into the array * Iterate: Get the value at that index * Insert: Shove stuff to the right * Remove: Shove stuff to the left * Replace: Replace * Fun with Java: Use ListIterators Lab ---