One Pager Cheat Sheet

• With Algorithm Complexity and Big O Notation, developers can measure the performance of a program, in terms of time and space complexity, to determine the most effective algorithm to use.
• Using Program 1 as an example, we can see the importance of ensuring that algorithms are designed to be as efficient as possible to maximize performance.
• We can use %timeit in a Jupyter Notebook or language interpreter to measure the performance of an algorithm.
• The program took 600 ns ± 230 ns per loop, 4 milliseconds to call customPower, and 337291 nanoseconds in total.
• The built-in pow function took 600 nanoseconds to raise 3 to the power 4, which is substantially less compared to program 2.
• The execution time for Python, Javascript, and Java was 308 ns, 7 ms, and 1555964 ns, respectively.
• The efficient choice of algorithms can greatly improve user experience, and this is shown by Program 2 being twice as fast as Program 1, taking only 308 nanoseconds.
• Big(O) Notation measures the time complexity of an algorithm based on the relationship between the number of inputs and the steps it takes to process them.
• The best complexity metric given is O(log(n)), as it takes logarithmic time in proportion to the input data.
• The execution of a program with Constant Complexity remains the same, regardless of the input size.
• The display_first_cube function has a constant algorithm complexity which does not scale with input.
• Thenum_of_inputson the x-axis and thestepson the y-axis plot out a straight line when graphed.
• A function or algorithm with linear complexity will require an equal increase in the number of steps required for execution as the number of units in its input increases.
• The display_all_cubes function has linear complexity and its execution time increases proportionally with the number of items in the items list.
• The complexity of a function increases quadratically as the input size increases.
• The display_all_products function in the code iterates through n items in a n x n loop and outputs a graph showing the quadratic equation.
• The space complexity of an algorithm can be determined by calculating the memory needed to store its inputs, expressed in terms of Big(O) Notation.
• The space complexity of the display_first_cube is O(1) (constant), while that of the display_all_cubes is O(n).
• The complexity of an algorithm can be defined as its worst case scenario, which is optimized for the least ideal situation.
• Sorting an array with consecutive elements is a best case scenario, requiring O(n) operations.
• Measuring algorithm performance in terms of time taken and space consumed can be done through Big(O) notation.
• No, O(n) time complexity does not necessarily mean that the algorithm will use n nested loops.