Editing Check sort/VC/Performance Analysis

''(Note: Small insignificant anomalies exist in the data due to a variety of factors. They do not introduce unacceptable errors into the results.)''

=== Check sort ===

==== Table of Performance Values ====

<pre>

1 0 0

100001 0.015 0

200001 0 0.016

300001 0.016 0

400001 0.046 0

500001 0.047 0

600001 0.062 0

700001 0.079 0

800001 0.078 0.015

900001 0.094 0

1000001 0.109 0.016

1100001 0.109 0.016

1200001 0.125 0.016

1300001 0.14 0

1400001 0.157 0.015

1500001 0.156 0.016

1600001 0.172 0.016

1700001 0.187 0

1800001 0.203 0.016

1900001 0.203 0.016

2000001 0.218 0.016

2100001 0.234 0.016

2200001 0.234 0.016

2300001 0.266 0.015

2400001 0.266 0.015

2500001 0.266 0.016

2600001 0.297 0.015

2700001 0.297 0.016

2800001 0.312 0.016

2900001 0.328 0.016

3000001 0.343 0.016

3100001 0.344 0.015

3200001 0.36 0.015

3300001 0.375 0.016

3400001 0.375 0.015

3500001 0.391 0.031

3600001 0.391 0.031

3700001 0.406 0.031

3800001 0.422 0.016

3900001 0.437 0.032

4000001 0.453 0.015

4100001 0.469 0.031

4200001 0.454 0.031

4300001 0.484 0.031

4400001 0.485 0.031

4500001 0.5 0.031

4600001 0.516 0.031

4700001 0.531 0.032

4800001 0.531 0.031

4900001 0.547 0.047

5000001 0.547 0.031

5100001 0.578 0.031

5200001 0.594 0.031

5300001 0.594 0.031

5400001 0.61 0.031

5500001 0.625 0.031

5600001 0.625 0.047

5700001 0.641 0.031

5800001 0.656 0.032

5900001 0.671 0.032

6000001 0.672 0.046

6100001 0.719 0.047

6200001 0.703 0.031

6300001 0.704 0.046

6400001 0.719 0.047

6500001 0.734 0.047

6600001 0.735 0.047

6700001 0.75 0.046

6800001 0.766 0.047

6900001 0.781 0.047

7000001 0.797 0.047

7100001 0.797 0.047

7200001 0.812 0.047

7300001 0.828 0.047

7400001 0.844 0.047

7500001 0.843 0.047

7600001 0.86 0.046

7700001 0.875 0.047

7800001 0.891 0.047

7900001 0.89 0.063

8000001 0.891 0.062

8100001 0.906 0.063

8200001 0.922 0.062

8300001 0.922 0.063

8400001 0.953 0.062

8500001 0.953 0.063

8600001 0.969 0.046

8700001 0.985 0.062

8800001 1 0.063

8900001 1 0.062

9000001 1.016 0.062

9100001 1.188 0.062

9200001 1.047 0.063

9300001 1.047 0.062

9400001 1.063 0.062

9500001 1.078 0.063

9600001 1.094 0.062

9700001 1.094 0.062

9800001 1.125 0.063

9900001 1.109 0.078

0.011481868 0.000677576 5.97%

</pre>

==== Regression Analysis ====

'''Console output - ''(constraints)'''''

RESULTS: (Check sort)

1.) Total number of items sorted:...................... 1542936

2.) Total primary array size to accomodate the sort:... 10000000

3.) Total secondary array size to accomodate the sort:. 1542936

4.) Total length of key:............................... 8 decimal digits.

5.) Total time for setup per 100,000 items:............ 1.109 seconds.

6.) Total time for sort per 100,000 items:............. 0.078 seconds.

7.) Total time for program:............................ 59.14 seconds.

Press any key to continue

==== Class Determination ====

[[Image:Checksort 14599 image001.png|400px|right]]

'''''Class''''' notated sort routines are categorized according to the [http://www.physics.csbsju.edu/stats/chi-square.html Chi Square] analysis of linear ('''L'''), parabolic {'''P'''), logarithmic ('''Ln''') and exponential ('''E''') [http://www.physics.csbsju.edu/stats/chi-square.html best fit] [[Wikipedia:Regression analysis|regression analysis]] applied to their performance data produced under a specified set of constraints. '''''Class''''' notation is used instead of [[Wikipedia:Big O notation|Big O notation]] since the advantage '''''Class''''' notation offers is to provide the values of the equation parameters obtained from [[Wikipedia:Regression analysis|regression analysis]] of the performance data such as in the case of a [[Wikipedia:Linear equation|linear equation]] best [http://www.physics.csbsju.edu/stats/chi-square.html Chi Square] fit of the value for slope (or seconds per item) in the case of a '''Class L''' (''linear equation'') category [http://www.physics.csbsju.edu/stats/chi-square.html best fit]. This additional information allows the programmer or user to select the best sort routine for his own application based upon the actual number of items which must be sorted per unit time or the time limit to sort a specific number of items. Since the Check sort performance [http://www.physics.csbsju.edu/stats/chi-square.html best fits] the '''Class L''' category the values for slope '''''m''''' and constant '''''c''''' for the [[Wikipedia:Linear equation|linear equation]] <big> '''''f(x)= m*x+c''''' </big> can be determined by a [http://www.physics.csbsju.edu/stats/chi-square.html best fit] [[Wikipedia:Linear regression|linear regression]] analysis and provided in the table below:

{| class="wikitable" style="tesxt-align:left"

|+ '''Class L'''

|-

! Routine !! Slope !! c

|-

! Setup

| 0.011481868 || 0

|-

! Sort

| 0.000677576 || 0

|}

This method of representation allows performance to be projected for any number of items or time limit. An accurate projection of sort routine performance for any [[Wikipedia:Programming language|programming language]] or [[Wikipedia:Computer|machine]] can be made using the time required to initialize an array by calculating the ratio of sort time to setup time (which in this case is <math>{0.000677576 \choose 0.011481868}</math> or 0.0597 ) or a percentage value of 5.97%. Thus on a different [[Wikipedia:Computer|machine]] providing a setup time slope value of 0.025 the projected sort time would be .025 * 0.0597 or 0.00147531 seconds per item or the ability to sort 67,782,364 items per second.

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