"Algorithm" simulates throwing dice

Simulates the roll of a dice. The following code calculates the exact probability distribution of the sum of each of the two dice:

int SIDES = 6;double[] dist = new Double[2*sides+1];for (int i = 1; I <= SIDES; i++) for     (int j = 1; I <= SIDES; J + +)        Dist[i+j] + = 1.0;for (int k = 2; k <= 2*sides; k++)    dist[k]/= 36.0;

The value of dist[i] is the probability that the sum of two dice is I. Simulate n-roll dice with an experiment and calculate two 1 to

The sum of random integers between 6 records the frequency at which each value appears to verify their probability. n How big will it be to guarantee you

The empirical data and accurate data to match the degree of three digits after the decimal point?

Experiment Code:

1  Packagecom.beyond.algs4.experiment;2 3 ImportJava.math.BigDecimal;4 5 ImportCom.beyond.algs4.lib.StdRandom;6 7 8  Public classSides {9 Ten     Private Static intSIDES = 6; One      A     Private Double[] dist =New Double[2*sides + 1]; -      -      Public Double[] Getdist () { the         returnDist; -     } -  -      Public voidSetdist (Double[] Dist) { +          This. Dist =Dist; -     } +  A      Public voidprobability () { at          for(inti = 1; I <= SIDES; i++) { -             for(intj = 1; J <= SIDES; J + +) { -Dist[i + j] + = 1.0; -            }  -         } -          for(intK = 2; K <= 2*sides; k++) { inDist[k]/= 36.0; -         } to     } +      -      Public voidprint () { the          for(inti = 0; i < dist.length; i++) { * System.out.println ( $String.Format ("Probability of [%d] is:%f", I, dist[i]));Panax Notoginseng         } -     } the      +      Public Static classEmulator { A         Private intN = 100; the          +         Private Double[] dist =New Double[2*sides + 1]; -          $          Public intGetn () { $             returnN; -         } -  the          Public voidSETN (intN) { -N =N;Wuyi         } the  -          Public Double[] Getdist () { Wu             returnDist; -         } About  $          Public voidSetdist (Double[] Dist) { -              This. Dist =Dist; -         } -  A          Public voidEmulator () { +              for(inti = 0; i < N; i++) { the                 intA = Stdrandom.uniform (1, 7); -                 intb = Stdrandom.uniform (1, 7); $Dist[a + b] + = 1.0; the             } the              for(intK = 2; K <= 2*sides; k++) { theDIST[K]/=N; the             } -         }         in          the          Public intN (Sides Sides) { the              for(inti = 1; I <= 100; i++) { About                  This. SETN (NewDouble (Math.pow (ten, I)). Intvalue () * This. N); the                  This. Emulator (); the                 BooleanAPPR =true; the                  for(intK = 2; K <= 2*sides; k++) { +                     Doubles = This. Getdist () [K]; -BigDecimal bs =NewBigDecimal (s); the                     DoubleS1 = Bs.setscale (2, Bigdecimal.round_down). Doublevalue ();Bayi                     Doublet =sides.getdist () [K]; theBigDecimal BT =NewBigDecimal (t); the                     DoubleT1 = Bt.setscale (2, Bigdecimal.round_down). Doublevalue (); -                     if(S1! =T1) { -APPR =false; the                          Break; the                     } the                 } the                 if(appr) { -                     return  This. GETN ();  the                 } the             } the             return0;94         } the          the          Public voidprint () { the              for(inti = 0; i < dist.length; i++) {98 System.out.println ( AboutString.Format ("Probability of [%d] is:%f", I, dist[i])); -             }101         }102         103         104     } the     106      Public Static voidMain (string[] args) {107Sides Sides =NewSides ();108 sides.probability ();109  theEmulator e =NewEmulator ();111         intN =E.N (sides); theSystem.out.println (String.Format ("The N is:%d", N));113System.out.println ("Actual:"); the sides.print (); theSYSTEM.OUT.PRINTLN ("Experiment:"); the e.print ();117     }118 119}

Experimental results:

1The N is:1000000002 Actual:3probability of [0] is:0.0000004probability of [1] is:0.0000005probability of [2] is:0.0277786probability of [3] is:0.0555567probability of [4] is:0.0833338probability of [5] is:0.1111119probability of [6] is:0.138889Tenprobability of [7] is:0.166667 Oneprobability of [8] is:0.138889 Aprobability of [9] is:0.111111 -Probability of [ten] is:0.083333 -Probability of [one] is:0.055556 theProbability of [] is:0.027778 - Experiment: -probability of [0] is:0.000000 -probability of [1] is:0.000000 +probability of [2] is:0.027754 -probability of [3] is:0.055544 +probability of [4] is:0.083374 Aprobability of [5] is:0.111130 atprobability of [6] is:0.138897 -probability of [7] is:0.166751 -probability of [8] is:0.138832 -probability of [9] is:0.111088 -Probability of [ten] is:0.083306 -Probability of [one] is:0.055517 inProbability of [] is:0.027807

Results Analysis:
Run multiple times, the n value is typically 100000000, and there are other values that are unstable.

Additional notes:

1. With n=100 as the initial value, the loop executes the probability of simulating n times, and if the anastomosis is not satisfied then n is incremented by 10 times times until the appropriate n value is found. (need to be improved with while (find))

2. The realization of "three digits after the decimal point" adopts the method of three-bit round_down after decimal point, which needs to be improved

3. The n value is not a stable result of 100000000 for each run, it can be executed randomly multiple times to analyze the distribution of n values.

Resources:

Algorithm fourth edition She Luyun algorithms Fourth Edition [US] Robert Sedgewick, Kevin Wayne

http://algs4.cs.princeton.edu/home/

SOURCE Download Link:

Http://pan.baidu.com/s/1c0jO8DU

"Algorithm" simulates throwing dice