Linear Search. Sorting Algorithms. linear search code. Sorting in Ascending Order Selection Sort. Selection sort algorithm

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1 Linear Search Additional CPSC1620 topics Searching, Sorting, Big(O) template functions, classes The idea of a linear search is to walk through the entire list until the value is found. The list does not have to have its members in any order. If the item to find is not located some type of indicator needs to be returned. 2 linear search code // Searches an integer array for a given element (the target) // Array elements ranging from 0 to size - 1 are // searched for an element equal to target. // Pre: The target and array are defined. // Post: Returns the subscript of target if found; otherwise, returns -1. int linsearch (const int items[ ], int itemtofind, int size) for (int i = 0, i < size, i++) if (items[i] = = itemtofind) return i; // not the itemtofind but its position. // All elements were tested without success. return -1; // end linsearch Sorting Algorithms Least efficient (but still really good) bubble sort insertion sort selection sort More efficient heap sort shaker sort merge sort Most efficient quick sort (recursive algorithm) Many web sites offer sorting demonstrations of the above and others. 3 4 Sorting in Ascending Order Selection Sort locate the largest value in the array Then switch positions of this value and the one in position [n-1] Start from beginning again and look for the largest, not including the last position, swapping it with item in position [n-2], etc. Continue this process n times. Selection sort algorithm selection sort after first pass: after second pass: after third pass:

2 findindexofmax function // n is number of items need to check int findindexofmax(int arr[ ], int n) maxindex = 0; for(int k=1; k<n; k++) if(arr[maxindex] < arr[k]) maxindex = k; return maxindex; 7 selsort function // Sorts an array (ascending order) using selection sort algorithm // Uses exchange and findindexofmin // Sorts the data in array items (items[0] through items[n-1]). // Pre: items is defined and n <= declared size of actual argument array. // Post: The values in items[0] through items [n-1] are in increasing order. void selsort(int items[ ], int n) int maxsub; for (int i = 0; i < n; i++) // Find index of smallest element in unsorted section of items. maxsub = findindexofmax(items, n-i); // Exchange items at position minsub and i exchange(items[maxsub], items[n i 1]); void exchange (double& a1, double& a2) double temp; temp = a1; a1 = a2; a2 = temp; 8 Bubble Sort bubble sort after first pass: after second pass: after third pass: Insertion sort insertion sort after first pass: after second pass: after third pass: QuickSort Is tougher to explain. We first go through a partitioning phase now 9 is in its proper place. Now we take the left half not including the 9 and partition again Now we partition the right half like we did the first half we keep doing it until the list is sorted. (Arie will demonstrate another example with more numbers to sort) Binary Search Before a binary search can be done the list must already be in order. Binary searches are extraordinarily more efficient than linear searches (but work had to be done to sort first). Pick the half way point in the list. If the number at the half way positions == numbertofind we are done and report back the position. If the numbertofind < that number set the upper limit of the list as the midpoint 1 If it is greater set the lower limit of the list to midpoint +1 Repeat process

3 binary search int binarysearch(int list[ ], int size, int itemtofind) int firstposn = 0; int lastposn = size 1; int midposn; bool found = false; while(firstposn <= lastposn &&!found) midposn = (firstposn + lastposn)/2; if(list[midposn]==itemtofind) found = true; else if(itemtofind < list[midposn]) lastposn = midposn 1; else firstposn = midposn + 1; if (found) return midposn; // note: we are passing back the position of the itemtofind else return -1; // we could not find itemtofind 13 efficiency of algorithms A measuring stick to do quantitative analysis on algorithms. Done on sorting and searching Most algorithms have BigO published 14 efficiency is directly proportional to the number of elementary machine operations Compares Exchanges One loop Example: for (k=1; k<=n; k++) Has efficiency O(n) //this is good nested loops Product of the loop counter is the efficiency n * n = n 2 is O(N 2 ) //not efficient for large n Example: for (k=1; k<=n; ++k) for (j=1; j<=n; ++j) Efficiencies of Sorts bubble O(n 2 ) // poor for large n but very good for small n insertion O(n 2 ) selection O(n 2 ) quick O(nlog n) // excellent for large n binary search O(log n) // lightning speed for large n

4 Template functions To find the max of 3 integers, 3 doubles or 3 chars would require three different maximum functions. We can write one template function that will do all three. template <typename T> T maximum(t val1, T val2, T val3) T tempmax = val1; if(val2 > tempmax) tempmax = val2; if(val3 > tempmax) tempmax = val3; return tempmax; int main() int int1 = 4; int int2 = 1; int int3 = 7; int max = maximum(int1,int2,int3); double f1 = 2.5; double f2 = 1.4; double f3 = -5.6 double max2 = maximum(f1,f2,f3); char c1 = A ; char c2 = J ; char c2 = * ; char max3 = maximum(c1,c2,c3) //T is the type of the data to be tested by the function maximum //int is substituted for T throughout, as is double, as is char So far we have used simple data types: int, double, bool, char. We have used structure data types like: arrays, structs. We have also used classes: eg. <string>, <cctype>, <fstream>, <iostream>, etc. These classes have been written by someone else. We will now attempt to write our own classes. Here s how we can think of an Automobile class. What does an Automobile have? model (VW, Toyota, Chevrolet, Chrysler, Ford, etc.) type (sedan, station wagon, SUV, convertible, etc.) engine (4-cyl, 6-cyl, 8-cyl, etc.) color (red, white, brown, etc.) transmission type (standard, automatic, combination) current speed current gear What can an Automobile do? accelerate (speed up, slow down) turn: left, right start or shut off shift gears if standard (1 st, 2 nd, 3 rd, 4 th, reverse) shift gears if automatic (drive, overdrive, reverse) find the current gear find the current speed Think of the Automobile as the class Think of what it has as an attribute or data member model, type, engine, color, transmission, etc. Think of what it can do as a method or function accelerate, turn, start, turn off, etc. 21 Some methods are accessor while others are modifiers eg. getting the speed is an accessor, as is getting the current gear. They get values of an object without changing them. eg. setting the speed or shutting the car off are modifying methods. They change the value of the data members Once we have a class established we can declare objects of that type. (Just like a struct). This is same as declaring struct variables, in fact C++ structs are identical to classes except in one way. More on this later. eg. Automobile mycar, wifecar, kidcar; mycar.model( Ford ); set my car to be a Ford wifecar.accelerate(50); get wife's car going to 50km/hr kidcar.shutoff( ); - turn off my kid's car s engine Object oriented programming comes from creating objects. mycar is an object of the Automobile class. mycar has all the characteristics and properties of the class. wifecar can perform all the methods/functions that the class has provided. It has a current gear. It can start. It can accelerate. 22 class Die public: private: ; Die::Die() Die(); int gettop(); void roll(); int sides; int top; sides = 6; top = 1; Die class class Die public: private: ; Die::Die() Die(); int gettop(); void roll(); int sides; int top; sides = 6; top = 1; int Die::getTop() return top; Die class int main() Die d1, d2; d1.roll(); d2.roll(); cout << Your roll was: << d1.gettop() + d2.gettop() << endl; return 0; void Die::roll() top = rand() % sides +1;

5 Final Exam Tuesday, June 25, :00am 11:50am Room: B543 Emphasis on: Chapter 5: Repetition and Loop Structures Chapter 3: Files streams, input and output, <iostream> functions Chapter 6a: Library functions, user defined functions with value parameters. Chapter 6b: User defined functions with reference parameters Chapter 7: string data type and string functions, enum type Chapter 8: Arrays (1 and 2 dimensional) c-strings (character arrays) Chapter 9: structs Additional: searching, sorting, bigo, template functions, Die class write program fragments (ie. not necessarily whole programs) program tracing given a function, what does it do, or what is it s output? write out a whole C++ program 25 5