1. Recursion Method calls itself iteratively until a base case is met and usually containing the following: if-else for base case with return value increment/decrement to advance closer to base case recursive call with changed value upon each successive call

2. Recursion public void recursiveMethod(int number) { if(number == 0) {// base case return; } else { System.out.println(number); // iteration # recursiveMethod(--number); // value change return; } What is the output of recursiveMethod(6)?

3. Recursion public void recursiveMethod(int number) { if(number == 0) { // base case return; } else { System.out.println(number); // iteration # recursiveMethod(--number); // value change return; } Terminal Window 654321654321

4. Recursion public void recursiveMethod(int number) { if(number == 0) {// base case return; } else { System.out.println(number); // iteration # recursiveMethod(--number); // value change System.out.println(number); // after decrement return; } Now … output of recursiveMethod(6)?

5. Recursion public void recursiveMethod(int number) { if(number == 0) { // base case return; } else { System.out.println(number); // iteration # recursiveMethod(--number); // value change System.out.println(number); // after decrement return; } Terminal Window 654321012345654321012345

6. Recursion Write a recursive method factorial(int num) that returns 5! = 5*4*3*2*1 = 120

7. Recursion Write a recursive method factorial(int num) that returns 5! = 5*4*3*2*1 = 120 public int factorial(int num) { if(num == 1) { return 1; } else { return(num*factorial(num-1)); }

8. Sorting A process that puts elements of a list into a certain order satisfying the following: The resulting list is a permutation or reordering of the original list comprised of the same number of elements All resulting elements (in reference with each other) are in increasing/decreasing numerical or alphabetical order unsortedArray = {8, 4, 6, 1, 9, 3, 2, 5, 7} sortedArray = {1, 2, 3, 4, 5, 6, 7, 8, 9}

9. Sorting Algorithms Many existing sorting algorithms exist: Selection and Insertion Sorts –low overhead with use –efficient on small amounts of data –inefficient on large data sets –Insertion sort faster with fewer comparisons and better for mostly sorted lists –Selection sort uses fewer writes Bubble Sort –simple to understand and use –highly inefficient Merge Sort –practical and may be more efficient –high overhead with small amounts of data –poor performance on almost sorted lists

10. Selection Sort FIND SMALLEST Repeatedly finds the smallest element to put into the first position at the beginning pass thru list from start to end store first index i as the min index of smallest value compare each element value[j] to value[min] if value[min] > value[j], change to new min = j at end of pass, swap value[i] and value[min] 1 pass thru results with smallest value in start index i repeat iteration for next smallest until complete int[ ] array = {6, 4, 7, 3} Write the method selectionSort(int[ ] array)...

11. Selection Sort public void selectionSort(int[] array) { // start with first position at beginning for(int i = 0; i < array.length; i++) { int min = i; // store 1st smallest for(int j = i; j<array.length; j++) { if(array[min] > array[j]) { // compare min = j; // new min found } int tmp = array[i]; // swap position array[i] = array[min]; // with the smallest array[min] = tmp; // 1 pass results with smallest in position i }

12. Insertion Sort FIND THE PLACE Repeatedly takes successive elements and finds the proper place by inserting into the sorted list pass thru list from 2nd element at index i to end store value[i] as the insert value to find proper place for start index j at same location as index i compare each element value[j-1] to insert value while value[j-1] > insert, keep shifting value[j-1] to value[j] at end of pass, put insert value into proper place at value[j] results with original insert value at index i in proper place repeat iteration for next element to place until complete int[ ] array = {6, 4, 7, 3} Write the method insertionSort(int[ ] array)...

13. Insertion Sort public void insertionSort(int[] array) { // start with second element at index i for(int i = 1; i < array.length; i++) { int insert = array[i]; // store value to insert int j = i; // start j same as I // while position is not found, keep comparing while((j > 0) && (array[j-1] > insert)) { array[j] = array[j-1]; { // shift value right j--; // look at next left } array[j] = insert; // put value in place // 1 pass results with original insert value // at index i in its proper place }

14. Bubble Sort FIND LARGEST Repeatedly finds the largest element to put into the last position at the end pass thru list from start to end compare adjacent elements [j] and [j+1] swap if value[j] > value[j+1] 1 pass thru results with largest in last position repeat iteration for next largest until complete int[ ] array = {6, 4, 7, 3} Write the method bubbleSort(int[ ] array)...

15. Bubble Sort public void bubbleSort(int[] array) { // start with last position at end for(int i=(array.length-1); i > 0; i--) { for(int j=0; j<i; j++) { if(array[j] > array[j+1]) { // compare int tmp = array[j]; array[j] = array[j+1]; // swap array[j+1] = tmp; } } // 1 pass results with largest in position i } Could this be improved to terminate if elements are all in order (i.e. no swaps occur on a pass)?

16. Bubble Sort public void bubbleSort2(int[ ] array) { int j = 0; boolean swapped = true; while (swapped) { swapped = false; j++; for (int i = 0; i < array.length - j; i++) { if (array[i] > array[i + 1]) { int tmp = array[i]; array[i] = array[i + 1]; array[i + 1] = tmp; swapped = true; } Note: swapped signals the end of sorting...