How to resolve the algorithm Galton box animation step by step in the Zig programming language

Published on 12 May 2024 09:40 PM
#Zig

How to resolve the algorithm Galton box animation step by step in the Zig programming language

Table of Contents

Problem Statement

A   Galton device   Sir Francis Galton's device   is also known as a   bean machine,   a   Galton Board,   or a   quincunx.

In a Galton box, there are a set of pins arranged in a triangular pattern.   A number of balls are dropped so that they fall in line with the top pin, deflecting to the left or the right of the pin.   The ball continues to fall to the left or right of lower pins before arriving at one of the collection points between and to the sides of the bottom row of pins. Eventually the balls are collected into bins at the bottom   (as shown in the image),   the ball column heights in the bins approximate a   bell curve.   Overlaying   Pascal's triangle   onto the pins shows the number of different paths that can be taken to get to each bin.

Generate an animated simulation of a Galton device.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Galton box animation step by step in the Zig programming language

Source code in the zig programming language

const std = @import("std");
const rand = std.rand;
const time = std.time;

const PEG_LINES = 20;
const BALLS = 10;

fn boardSize(comptime peg_lines: u16) u16 {
    var i: u16 = 0;
    var size: u16 = 0;
    inline while (i <= peg_lines) : (i += 1) {
        size += i + 1;
    }
    return size;
}

const BOARD_SIZE = boardSize(PEG_LINES);

fn stepBoard(board: *[BOARD_SIZE]u1, count: *[PEG_LINES + 1]u8) void {
    var prng = rand.DefaultPrng.init(@bitCast(time.timestamp()));

    var p: u8 = 0;
    var sum: u16 = 0;
    while (p <= PEG_LINES) : (p += 1) {
        const pegs = PEG_LINES - p;
        var i: u16 = 0;
        while (i < pegs + 1) : (i += 1) {
            if (pegs != PEG_LINES and board[BOARD_SIZE - 1 - sum - i] == 1) {
                if (prng.random().boolean()) {
                    board.*[BOARD_SIZE - 1 - sum - i + pegs + 1] = 1;
                } else {
                    board.*[BOARD_SIZE - 1 - sum - i + pegs + 2] = 1;
                }
            } else if (pegs == PEG_LINES and board[BOARD_SIZE - 1 - sum - i] == 1) {
                count.*[pegs - i] += 1;
            }
            board.*[BOARD_SIZE - 1 - sum - i] = 0;
        }
        sum += pegs + 1;
    }
}

fn printBoard(board: *[BOARD_SIZE]u1, count: *[PEG_LINES + 1]u8) !void {
    const stdout = std.io.getStdOut();
    _ = try stdout.write("\x1B[2J\x1B[1;1H");
    var pegs: u16 = 0;
    var sum: u16 = 0;
    while (pegs <= PEG_LINES) : (pegs += 1) {
        var i: u16 = 0;
        while (i < (PEG_LINES - pegs)) : (i += 1) _ = try stdout.write(" ");
        i = 0;
        while (i < pegs + 1) : (i += 1) {
            const spot = if (board[i + sum] == 1) "o" else " ";
            _ = try stdout.write(spot);
            if (i != pegs) _ = try stdout.write("*");
        }
        sum += pegs + 1;
        _ = try stdout.write("\n");
    }
    for (count) |n| {
        const num_char = [2]u8{'0' + n, ' '};
        _ = try stdout.write(&num_char);
    }
    _ = try stdout.write("\n");
}

pub fn main() !void {
    var board: [BOARD_SIZE]u1 = [_]u1{0} ** BOARD_SIZE;
    var bottom_count: [PEG_LINES+1]u8 = [_]u8{0} ** (PEG_LINES + 1);

    var i: u16 = 0;
    while (i < PEG_LINES + BALLS + 1) : (i += 1) {
        if (i < BALLS) board[0] = 1;

        try printBoard(&board, &bottom_count);
        stepBoard(&board, &bottom_count);
        time.sleep(150000000);
    }
}

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