Lecture Activity

Today we talked about statement counts and time complexity. We analyzed the following during lecture:

• The first try of the Driver.java file from 2/13 has a statement count of 14 (1 + 2*6 + 1) and a time complexity of O(1).
• The first catch of the Driver.java file from 2/13 has a statement count of 2 and a time complexity of O(1).
• The second try of the Driver.java file from 2/13 has a statement count of 1 + 3*n and a time complexity of O(n) where n is the number of pairs of data lines in the input file.
• The second catch of the Driver.java file from 2/13 has a statement count of 2 and a time complexity of O(1).
• The constructor of the Numbers.java file from 2/15 has a statement count of 1 + n and a time complexity of O(n) where n is the size of the numbers array.
• The initialize method of the Numbers.java file from 2/15 has a statement count of n and a time complexity of O(n) where n is the size of the numbers array.
• The print method of the Numbers.java file from 2/15 has a statement count of n and a time complexity of O(n) where n is the size of the numbers array.
• The getNumbers method of the Numbers.java file from 2/15 has a statement count of 1 and a time complexity of O(1).
• The swap method of the Sort.java file from 2/15 has a statement count of 3 and a time complexity of O(1).
• The findMin method of the Sort.java file from 2/15 has a statement count of 2 + 2k in the worst case and a statement count of 2 + k in the best case and a time complexity of O(k) where k is finish - start.
• The selectionSort method of the Sort.java file from 2/15 has a worst case statement count of 6n + n² and a time complexity of O(n²).

A Useful Summation Equality

_{i=1 to n}Σ i = (1 + 2 + ... + n ) = n(n+1)/2