Algorithms with-java-advanced-1.0

Searching and sorting arrays combinatorial samples Algorithms with Java

Contents ,[object Object],[object Object],[object Object],[object Object]

What is “algorithm”? ,[object Object],[object Object],[object Object]

More about algorithms ,[object Object],[object Object],[object Object]

Similarities with Maths ,[object Object],[object Object],[object Object],[object Object]

Complexity of algorithms ,[object Object],[object Object],[object Object],[object Object],[object Object]

Examples of complexity ,[object Object],[object Object],[object Object],[object Object],[object Object]

How to ,[object Object],[object Object],[object Object],[object Object],[object Object]

Sorting ,[object Object],[object Object],[object Object],[object Object]

Different methodologies ,[object Object],[object Object],[object Object],[object Object],[object Object]

Bubble sort ,[object Object],[object Object],[object Object]

Bubble sort: steps ,[object Object],[object Object],[object Object],[object Object]

Bubble sort – Example ,[object Object],public static void bubble(int[] array) { for(int i = 0; i < array.length; i++) { for(int j = 0; j < array.length-1; j++) { if(array[j] > array[j+1]) { int tmp = array[j]; array[j] = array[j+1]; array[j+1] = tmp; } } } }

Insertion sort ,[object Object],[object Object],[object Object],[object Object]

Insertion sort: steps ,[object Object],[object Object],[object Object]

Insertion sort - Example ,[object Object],for(int i = 1; i < array.length; i++) { // take current element and position int current = array[i]; int dec = i; while(dec > 0 && current < array[dec-1]) { array[dec] = array[dec-1]; dec = dec-1; } array[dec] = current; }

Quick sort ,[object Object],[object Object],[object Object]

Quick sort: steps ,[object Object],[object Object],[object Object],[object Object]

Quick sort - Example ,[object Object],call quick_sort(low, high); left = 0; right = n; mid = a[(left+right)/2]; while left <= right: while a[left] < mid -> left++; while a[right] > mid -> right--; if left <= right: swap(left, right); left++; right--; quicksort(low, right); quicksort(left, high);

Searching ,[object Object],[object Object],[object Object]

Binary search ,[object Object],[object Object],[object Object]

Binary search: steps ,[object Object],[object Object],[object Object],[object Object],[object Object]

Binary search - Example ,[object Object],public static int binarySearch(int[] array, int low, int high, int number) { if (low < high) { int middle = (low + high) / 2; if (number < array[middle]) { return binarySearch(array, low, middle, number); } else if (number > array[middle]) { return binarySearch(array, middle+1, high, number); } else { return middle; // real result } } return -1; // element not found }

Combinatorial ,[object Object],[object Object],[object Object],[object Object],[object Object]

Combinatorial (2) ,[object Object],[object Object],[object Object]

Permutation ,[object Object],[object Object],[object Object]

Permutations (2) ,[object Object],for i=n to 0: if a[i] > a[i-1]: for j=i to n: find min(a[j]) > a[i-1]; swap(a[i-1], a[j]); sort(a[i], n);

Summary ,[object Object],[object Object],[object Object],[object Object]

Exercises ,[object Object],[object Object],[object Object],[object Object]

Exercises ,[object Object],[object Object]

Exercises (6) ,[object Object],[object Object],[object Object],[object Object]

Homework ,[object Object],[object Object],[object Object],[object Object]

Homework (2) ,[object Object],a) b) c) d) 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 7 11 14 16 4 8 12 15 2 5 9 13 1 3 6 10 1 8 9 16 2 7 10 15 3 6 11 14 4 5 12 13 1 12 11 10 2 13 16 9 3 14 15 8 4 5 6 7

Homework (3) ,[object Object],[object Object],13 1 3 2 2 2 4 3 3 3 2 4 4 4 3 1 2 3 3 4 3 1 3 3 1 4 3 3 3 1 1

Algorithms with-java-advanced-1.0

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