using PyPlot
using NtToolBox

p = 0.1;

n = 512;

x = (rand(n) .> p) + 1;

h = [sum(x .== 1); sum(x .== 2)]
h = h/sum(h)

print("Empirical p = $(h[1])")

e = - sum(h.*log2([max(e,1e-20) for e in h]))
print("Entropy = $e")

h = [.1, .15, .4, .15, .2];

m = length(h)
T=Array{Any,1}(zeros(m)); # create an empty tree

#we use the symbols i = 0,1,2,3,4 (as strings) with the associated probabilities h(i)

for i in 1:m
    T[i] = (h[i],string(i))
end

while length(T) > 1

    sort!(T) #sort according to the first values of the tuples (the probabilities)
    t = tuple(T[1:2]...)
    q = T[1][1] + T[2][1]
    T = [T[3:end]; [(q,t)]]
end

function trim(T)
    T0 = T[2]
    if typeof(T0) == String
        return T0
    else
        return (trim(T0[1]),trim(T0[2]))
    end
end
T = trim(T[1]);

plot_hufftree(T);

codes = Dict()

function huffman_gencode(T,codes,c)
    if typeof(T) == String #test if T is a leaf
        codes[T] = c
    else
        huffman_gencode(T[1],codes, string(c, "0"))
        huffman_gencode(T[2],codes, string(c, "1"))
    end
end

huffman_gencode(T,codes,"") ;

for e in keys(codes)
    println(string("Code of token ", e, ": ", codes[e]))
end

n = 1024;

x = rand_discr(h, m=n);

include("NtSolutions/coding_2_entropic/exo1.jl")

## Insert your code here.

e = - sum(h.*log2([max(e,1e-20) for e in h]))
println("Entropy bound = $(n*e)")
println("Huffman code  = $(length(y))") 

x1 = [];

T0 = T
for e in y
    if e == '0'
            T0 = T0[1]
    else
            T0 = T0[2]
    end
    if typeof(T0) == String
        append!(x1,T0)
        T0 = T
    end
end
    

err = norm(x-map(x->parse(Int, x), x1))
print("Error (should be zero) : $err")

t = .12;

h = [t, 1-t];

n = 4096*2
x = (rand(n) .> t) + 1;

q = 3;

m = 2;

n1 = Int(ceil(n/q)*q);

x1 = zeros(n1)
x1[1:length(x)] = x
x1[length(x)+1:end] = 1
x1 = x1 - 1
x2 = []

mult = [m^j for j in 0:q-1]
for i in 1:q:n1-1
    append!(x2,sum(x1[i:i+q-1].*mult)+1)
end

H = h
for i in 1:q-1
    Hold = H
    H = []
    for j in 1:length(h)
        append!(H,[e*h[j] for e in Hold])
    end
end

H = h
for i in 1:q-1
    H = kron(H, h)
end

include("NtSolutions/coding_2_entropic/exo2.jl");

## Insert your code here.