June 2018 Update

Task/Percolation-Bond-percolation/Julia/percolation-bond-percolation.julia

@@ -0,0 +1,93 @@
+using Distributions
+
+struct Grid
+    cells::BitArray{2}
+    hwall::BitArray{2}
+    vwall::BitArray{2}
+end
+function Grid(p::AbstractFloat, m::Integer=10, n::Integer=10)
+    cells = fill(false, m, n)
+    hwall = rand(Bernoulli(p), m + 1, n)
+    vwall = rand(Bernoulli(p), m, n + 1)
+    vwall[:, 1] = true
+    vwall[:, end] = true
+    return Grid(cells, hwall, vwall)
+end
+
+function Base.show(io::IO, g::Grid)
+    H = (" .", " _")
+    V = (":", "|")
+    C = (" ", "#")
+    ind = findfirst(g.cells[end, :] .& .!g.hwall[end, :])
+    percolated = !iszero(ind)
+    println(io, "$(size(g.cells, 1))×$(size(g.cells, 2)) $(percolated ? "Percolated" : "Not percolated") grid")
+    for r in 1:size(g.cells, 1)
+        println(io, "    ", join(H[w+1] for w in g.hwall[r, :]))
+        println(io, " $(r % 10)) ", join(V[w+1] * C[c+1] for (w, c) in zip(g.vwall[r, :], g.cells[r, :])))
+    end
+    println(io, "    ", join(H[w+1] for w in g.hwall[end, :]))
+    if percolated
+        println(io, " !)  ", "  " ^ (ind - 1), '#')
+    end
+end
+
+function floodfill!(m::Integer, n::Integer, cells::AbstractMatrix{<:Integer},
+                    hwall::AbstractMatrix{<:Integer}, vwall::AbstractMatrix{<:Integer})
+    # fill cells
+    cells[m, n] = true
+    percolated = false
+    # bottom
+    if m < size(cells, 1) && !hwall[m+1, n] && !cells[m+1, n]
+        percolated = percolated || floodfill!(m + 1, n, cells, hwall, vwall)
+    # The Bottom
+    elseif m == size(cells, 1) && !hwall[m+1, n]
+        return true
+    end
+    # left
+    if n > 1 && !vwall[m, n] && !cells[m, n-1]
+        percolated = percolated || floodfill!(m, n - 1, cells, hwall, vwall)
+    end
+    # right
+    if n < size(cells, 2) && !vwall[m, n+1] && !cells[m, n+1]
+        percolated = percolated || floodfill!(m, n + 1, cells, hwall, vwall)
+    end
+    # top
+    if m > 1 && !hwall[m, n] && !cells[m-1, n]
+        percolated = percolated || floodfill!(m - 1, n, cells, hwall, vwall)
+    end
+    return percolated
+end
+function pourontop!(g::Grid)
+    m, n = 1, 1
+    percolated = false
+    while !percolated && n ≤ size(g.cells, 2)
+        percolated = !g.hwall[m, n] && floodfill!(m, n, g.cells, g.hwall, g.vwall)
+        n += 1
+    end
+    return percolated
+end
+
+function main(probs, nrep::Integer=1000)
+    sampleprinted = false
+    pcount = zeros(Int, size(probs))
+    for (i, p) in enumerate(probs), _ in 1:nrep
+        g = Grid(p)
+        percolated = pourontop!(g)
+        if percolated
+            pcount[i] += 1
+            if !sampleprinted
+                println(g)
+                sampleprinted = true
+            end
+        end
+    end
+    return pcount ./ nrep
+end
+
+probs = collect(10:-1:0) ./ 10
+percprobs = main(probs)
+
+println("Fraction of 1000 tries that percolate through:")
+for (pr, pp) in zip(probs, percprobs)
+    @printf("\tp = %.3f ⇒ freq. = %5.3f\n", pr, pp)
+end