options(repr.plot.width=3.5, repr.plot.height=3.5)
options(warn=-1) # turns off warnings, to turn on: "options(warn=0)"

library(Matrix)
library(stringr)
library(ape)

# Importing the libraries
for (f in list.files(path="nt_toolbox/toolbox_general/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_general/", f, sep=""))
}
for (f in list.files(path="nt_toolbox/toolbox_signal/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_signal/", f, sep=""))
}

p = 0.1

n = 512

x = ceiling(runif(n, 0, 1) > p ) +1

h = c(sum(x==1), sum(x==2))
h = h/sum(h)

print(paste("Empirical p =" , h[1]))

e = - sum(h*log2(c(max(h[1],1e-20), max(h[2],1e-20))))
print(paste("Entropy = ", e))

h = c(.1, .15, .4, .15, .2)

m = length(h)
T = list(list())

#we use the symbols i = 1,2,3,4,5 (as strings) with the associated probabilities h(i)

for (i in (1:m))
{
    T[[i]] = list(toString(i), h[i])
    
 }


while (length(T)>=2)
{
    T = T[order(sapply(T,'[[',2))]
    q = as.numeric(T[[1]][2])+as.numeric(T[[2]][2])
    t = T[1:2]
    T = T[-(1:2)]
    T[[length(T)+1]] = list(t,q)
}

trim = function(T)
{
    T0 = T[[1]][1]
    if (typeof(T0[[1]][1]) == 'character')
    {
        return (T0)
    }
    else
    {
        return (list(trim(T0[[1]][1]),trim(T0[[1]][2])))
    }
}

K = list()
K[[1]] = list(trim(T)[[1]][[1]][1],trim(T)[[2]])
T = K 

# flatten list
x2 = paste0(lapply(T, function(y) paste0("(", paste0(y, collapse = ","), ")")), collapse = ",")

# remove unwanted characters
x2 = gsub('\"|c|list| ', "", x2)
x2 = paste0("(", x2, ");")

# remove brackets from single term list object
x3 = str_replace_all(x2, "\\([a-z]*\\)", function(x) gsub("^\\(|\\)$", "", x))

# plot
plot(read.tree(text = x3), color="blue")

codes = list()
c = compute_huffcode(h)
for (i in (1:length(h)))
{
    codes[[toString(i)]] = c[i]
}

for (e in (1:length(codes)))
{
    print(paste("Code of token", e, "=", codes[[toString(e)]]))
}

n = 1024

rand_discr = function (p, m)
{
      #  rand_discr - discrete random generator 
        
      #    y = rand_discr(p, n);
        
     #    y is a random vector of length n drawn from 
     #     a variable X such that
     #        p(i) = Prob( X=i )
    p = p/sum(p)
    n = length(p)
    coin = runif(m, 0, 1)
    cumprob = c(0,cumsum(p))
    sample = matrix(0, nrow=1, ncol=m)

    for (j in (1:n))
    {
        ind = c((coin > cumprob[j]) & (coin <= cumprob[j+1]))
        sample[ind] = j
    }
    return (sample)
}

x = rand_discr(h, n)

source("nt_solutions/coding_2_entropic/exo1.R")

## Insert your code here.

e = - sum(h*log2(c(max(h[1],1e-20),max(h[2],1e-20),max(h[3],1e-20),max(h[4],1e-20),max(h[5],1e-20))))
print(paste("Entropy bound = ", n*e))
print(paste("Huffman code = ", nchar(y)))

x1 = c()

T0 = K
for (e in strsplit(y,split=''))
{
    if (e == '0')
    {
        T0 = T0[[1]]
    } 
    else
    {
        T0 = T0[[1]][[2]]
    }
    if (typeof(T0) == 'character')
    {
        i = i+1
        x1 = c(x1,T0)
        T0 = T
    }
}

err = norm(x - as.double(x1))
print(paste("Error (should be zero) : ", err))

t = .12

h = c(t, 1-t)

n = 4096 * 2
x = (runif(n, 0, 1) >t) +1

q = 3

m = 2

n1 = (floor(n/q)+1)*q

x1 = matrix(0, nrow=1, ncol=n1)
x1[1:length(x)] = x
x1[length(x):length(x1)] = 1
x1 = x1 - 1
x2 = c()

for (i in seq(1,n1,by=q))
{
    mult = m**c(1:q-1)
    x2 = c(x2, sum(x1[i:(i+q)]*mult))
}

H = h
for (i in (1:(q-1)))
{
    Hold = H
    H = c()
    for (j in (1:length(h)))
    {
        H = c(H, h[j]*Hold)
    }
}


H = h
for (i in (1:(q-1)))
{
    H = kronecker(H,h)
}
H

source("nt_solutions/coding_2_entropic/exo2.R")

## Insert your code here.