COS 126 Conditionals, Loops, Arrays |
Programming Assignment |
% java Bits 0 % java Bits 8 0 4 % java Bits 1 % java Bits 16 1 5 % java Bits 2 % java Bits 1000 2 10 % java Bits 4 % java Bits -23 3 Illegal input
Remark: This computes the number of bits in the binary representation of N, which also equals 1 + floor(log_{2} N) when N is positive. This quantity arises in information theory and the analysis of algorithms.
% java Ordered 10 17 49 true % java Ordered 49 17 10 true % java Ordered 10 49 17 false
Write a program RGBtoCMYK.java that converts RGB to CMYK. Read three integers red, green, and blue from the command line, and print the input red, green, and blue, then print the equivalent CMYK values using these formulas:
Hint. Math.max(x, y) returns the maximum of x and y.
% java RGBtoCMYK 75 0 130 // indigo red = 75 green = 0 blue = 130 cyan = 0.423076923076923 magenta = 1.0 yellow = 0.0 black = 0.4901960784313726
If all three red, green, and blue values are 0, the resulting color is black. Here is what your program should do:
% java RGBtoCMYK 0 0 0 // black red = 0 green = 0 blue = 0 cyan = 0.0 magenta = 0.0 yellow = 0.0 black = 1.0
% java Time 50 Start time: 12:00pm End time: 12:50pm % java Time 100 Start time: 12:00pm End time: 1:40pm % java Time 720 Start time: 12:00pm End time: 12:00am
% java Checkerboard 4 % java Checkerboard 5 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
% java RandomWalker 10 % java RandomWalker 20 (0, -1) (0, 1) (0, 0) (-1, 1) (0, 1) (-1, 2) (0, 2) (0, 2) (-1, 2) (1, 2) (-2, 2) (1, 3) (-2, 1) (0, 3) (-1, 1) (-1, 3) (-2, 1) (-2, 3) (-3, 1) (-3, 3) squared distance = 10 (-3, 2) (-4, 2) (-4, 1) (-3, 1) (-3, 0) (-4, 0) (-4, -1) (-3, -1) (-3, -2) (-3, -3) squared distance = 18
% java RandomWalkers 100 10000 % java RandomWalkers 400 2000 mean squared distance = 101.446 mean squared distance = 383.12 % java RandomWalkers 100 10000 % java RandomWalkers 800 5000 mean squared distance = 99.1674 mean squared distance = 811.8264 % java RandomWalkers 200 1000 % java RandomWalkers 1600 100000 mean squared distance = 195.75 mean squared distance = 1600.13064
As N increases, we expect the random walker to end up farther and farther away from the origin. But how much farther? Use RandomWalkers to formulate a hypothesis as to how the mean squared distance grows as a function of N. Use T = 100,000 trials to get a sufficiently accurate estimate.
Remark: this process is a discrete version of a natural phenomenon known as Brownian motion. It serves as a scientific model for an astonishing range of physical processes from the dispersion of ink flowing in water, to the formation of polymer chains in chemistry, to cascades of neurons firing in the brain.
Remark: the central limit theorem, a key result in probability and statistics, asserts that the shape of the resulting histogram tends to the ubiquitous bell curve (Gaussian distribution) if the number of dice and rolls is large.
% java TenDice 1000 10: 11: 12: 13: 14: 15: 16: 17: 18: * 19: **** 20: 21: *** 22: ****** 23: ******** 24: **************** 25: ************* 26: ********** 27: ********************************* 28: **************************************** 29: ********************************* 30: *************************************************** 31: ***************************************************************** 32: ******************************************************** 33: ************************************************************************************** 34: *********************************************************** 35: ********************************************************************* 36: *********************************************************************************** 37: ************************************************************** 38: ***************************************************************** 39: *************************************** 40: ***************************************************** 41: ************************************ 42: **************************** 43: ************************ 44: ************************ 45: ********* 46: *********** 47: ******* 48: *** 49: ** 50: 51: 52: * 53: 54: 55: 56: 57: 58: 59: 60:
Program style and format. Now that your program is working, go back and look at the program itself. Is your header complete? Did you comment appropriately? Did you use descriptive variable names? Did you avoid unexplained, hard-wired constants? Are there any redundant conditions? Follow the guidelines in the Reviewing your Programs section of the Checklist.
Submission. Submit the files Bits.java, Time.java, Ordered.java, RGBtoCMYK.java, Checkerboard.java, RandomWalker.java, RandomWalkers.java, TenDice.java, and a fully completed copy of the readme.txt file for this week. Challenge for the bored. Implement Time.java with no if statements!