--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/julia/dp.jl	Fri Feb 24 23:31:00 2023 +0100
@@ -0,0 +1,114 @@
+
+function largest_plus(a::AbstractMatrix{Bool})::Int
+    is_still_plus(i, j, n) = (i+n) <= size(a, 1) && (i-n) >= 1 && (j+n) <= size(a, 2) && (j-n) >= 1 && a[i,j] && a[i+n,j] && a[i-n,j] && a[i,j+n] && a[i,j-n]
+    is_plus_center(i, j) = is_still_plus(i, j, 1)
+
+    initial_centers = [(i, j) for i = 2:size(a, 1)-1 for j = 2:size(a, 2)-1 if is_plus_center(i, j)]
+
+    centers = initial_centers
+    for n = 2:size(a, 1)
+        new_centers = [(i, j) for (i, j) = centers if is_still_plus(i, j, n)]
+        if isempty(new_centers)
+            return n-1
+        end
+        centers = new_centers
+    end
+    -1
+end
+
+"""
+ACDB is interleaving of AB and CD
+ 
+ADEBCF is interleaving of ABC and DEF
+ 
+ACBCD is interleaving of ABC and CD
+ 
+ACDABC is interleaving of ABC and ACD
+"""
+function string_is_interleaving(a::AbstractString, b::AbstractString, c::AbstractString)::Bool
+    if length(a) == 0 && length(b) == 0 && length(c) == 0
+        true
+    else
+        if !isempty(a) && a[begin] == c[begin]
+            if length(a) == 1 && length(b) == 0
+                length(c) == 1
+            else
+                string_is_interleaving(a[2:end], b, c[2:end])
+            end
+        elseif !isempty(b) && b[begin] == c[begin]
+            if length(b) == 1 && length(a) == 0
+                length(c) == 1
+            else
+                string_is_interleaving(a, b[2:end], c[2:end])
+            end
+        else
+            false
+        end
+    end
+end
+
+function partition_3(s::AbstractSet{T}, s1=nothing, s2=nothing, s3=nothing, n=length(s)) where {T<:Integer}
+    if isnothing(s1) || isnothing(s2) || isnothing(s3)
+        s1, s2, s3 = Set{T}(), Set{T}(), Set{T}()
+    end
+    if length(s1) > 0 && length(s2) > 0 && length(s3) > 0 && length(s1)+length(s2)+length(s3) == n && sum(s1) == sum(s2) && sum(s2) == sum(s3)
+        return (true, (s1, s2, s3))
+    elseif isempty(s)
+        return (false, (s1,s2,s3))
+    end
+
+    e = pop!(s)
+
+    push!(s1, e)
+    ok, sets = partition_3(s, s1, s2, s3, n)
+    if ok
+        return ok, sets
+    end
+
+    pop!(s1, e)
+    push!(s2, e)
+    ok, sets = partition_3(s, s1, s2, s3, n)
+    if ok
+        return ok, sets
+    end
+
+    pop!(s2, e)
+    push!(s3, e)
+    ok, sets = partition_3(s, s1, s2, s3, n)
+    if ok
+        return ok, sets
+    end
+
+    pop!(s3, e)
+    push!(s, e)
+
+    return false, (s1, s2, s3)
+end
+
+function total_possible_solutions(coefficients::AbstractVector{<:Integer}, rhs::Integer)::Int
+    if isempty(coefficients)
+        return rhs == 0 ? 1 : 0
+    end
+    c = 0
+    for v = 0:rhs
+        c += total_possible_solutions((@view coefficients[2:end]), rhs-coefficients[begin]*v)
+    end
+    c
+end
+
+function number_of_pattern_times(hs::AbstractString, pat::AbstractString)::Int
+    if isempty(pat) || isempty(hs)
+        0
+    else
+        if length(pat) == 1
+            c = hs[begin] == pat[begin] ? 1 : 0
+            c + number_of_pattern_times((@view hs[2:end]), pat)
+        else
+            if hs[begin] == pat[begin]
+                number_of_pattern_times((@view hs[2:end]), (@view pat[2:end])) + number_of_pattern_times((@view hs[2:end]), pat)
+            else
+                number_of_pattern_times((@view hs[2:end]), pat)
+            end
+        end
+    end
+end