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CS 112 - Fall 2012, Lab 03 Haohan Zhu CS 112 - Fall 2012, Lab 03 5/30/2016 Random Class Boston University Slideshow Title Goes Here http://docs.oracle.com/javase/7/docs/api/java/util/Random.ht ml Create an object for Random() Random r = new Random(); Use method .nextInt(n) to generate a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value n (exclusive) 2 CS 112 - Fall 2012, Lab 03 5/30/2016 Evaluation by Time Boston University Slideshow Title Goes Here http://docs.oracle.com/javase/7/docs/api/java/lang/System.ht ml System.nanoTime(); System.currentTimeMillis(); 3 CS 112 - Fall 2012, Lab 03 5/30/2016 Practice: Inversion Boston University Slideshow Title Goes Here Let int A[] be an array of distinct integers. There are len = A.length distinct integers. If i<j and A[i]>A[j], then the pair (i, j) is called an inversion of A. There exists many such pairs in A. Compute how many inversions in A. 4 CS 112 - Fall 2012, Lab 03 5/30/2016 Practice: Inversion Boston University Slideshow Title Goes Here Intuitive method: O(n^2) 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 5 CS 112 - Fall 2012, Lab 03 5/30/2016 Practice: Inversion Boston University Slideshow Title Goes Here Maximal number of inversions ? Find an efficient algorithm When the array is partly sorted, to determine how many inversions are caused by a number, we do not need to compare every pair of numbers. For instance, in array {1,3,5,7,2,4,6,8}, consider the number of inversions caused by 2. 6 CS 112 - Fall 2012, Lab 03 5/30/2016 Practice: Inversion Boston University Slideshow Title Goes Here Use the process similar to merge sort 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 1 3 2 5 7 4 6 8 7