Design and implement a program that has at least three different algorithms with BigXO time complexities O$($n$),$ O$($n$^2)$ and O$($log$1$n$).$ Use Java's System.nanoTime$()$ to measure the execution time of each algorithm. Generate test cases for each algorithm and record the execution times. How do they scale? Take an average $-$ run each test case n times and take the average runtime. Compare the runtime of each algorithm for different input sizes and discuss how the observed runtimes align with the expected time complexities. Don't convert the nanoseconds.

Submit by copying and pasting or uploading a txt or a word document with your reported findings include what algorithms you used, what time conversions you made, a chart$($s$)$ and$/$or graph$($s$)($you can use excel to make these$)$ with the runtimes of each algorithm with different input sizes, an analysis of the observed runtimes and their relation to BigXO time complexities, and any insight gained from the experiment. Title your report: Big O inconsis