N = 10
M = 10000
means = rep(0, M)
for (i_rep in 1:M){
  dat <- runif(N)
  means[i_rep] <- mean(dat)
}
hist(means, xlab = "Estmatedmeans", probability = T, 
  breaks = 30, xlim = c(0,1))
x.temp = seq(0, 1, length.out = 1000)
dens <- dnorm(x.temp, mean = 0.5, sd = (1/sqrt(12*N)))
lines(x.temp, dens, col = "red", lwd = 3)
legend("topright","theoretical desiity",lwd =3, col = "red")

X = 10
Y = 1
sumXY = X + Y

summation <- function(X,Y){
  sumXY = X + Y
  return(sumXY)
}
summation(X=1, Y=10)
summation(X=5, Y=2)

CLT_example <- function(N, M){
  means = rep(0, M)
  for (i_rep in 1:M){
    dat <- runif(N)
    means[i_rep] <- mean(dat)
  }
  hist(means, xlab = "Estmated means", probability = T, 
   breaks = 30, xlim =c(0,1))
  x.temp = seq(0, 1, length.out = 1000)
  dens <- dnorm(x.temp, mean = 0.5, sd = (1/sqrt(12*N)))
  lines(x.temp, dens, col = "red", lwd = 3)
  legend("topright","theoretical desiity",lwd =3, col = "red")
}

x0 = 1e5
y0 = 10
z0 = 0
dt = 0.01
T = 10000
alpha = 1e-5
beta = 0.1
x = y = z = rep(0,T)
x[1] = x0
y[1] = y0
z[1] = z0
for(t in 1:(T-1)){
  x[t+1] = x[t] - (alpha*x[t]*y[t])*dt
  y[t+1] = y[t] + (alpha*x[t]*y[t]-beta*y[t])*dt 
  z[t+1] = z[t] + (beta*y[t])*dt
}
plot(x=1:T, x, type = "l", col = 2, lwd = 3, ylim = c(0,x0),
  xlab = "Time", ylab = "Number of people")
lines(x=1:T, y, col = 3, lwd = 3)
lines(x=1:T, z, col = 4, lwd = 3)
legend("right", c("not infected", "infected","no longer infected"), col=2:4,lwd=3)

# creating example vectors
students = paste("s", 1:20, sep = "")
suite = rep(c("s","h","c","d"),13)
ns = sort(rep(1:13,4))
cards  = paste(suite, ns, sep="")

# samples
rand_select = sample(1:10, 2)
rand_perm = sample(1:10)
with_replacemnt = sample(0:1, 10, replace = T)
temp = sample(1:5, 5, replace = T)

# concrete example

# random selection
pointed <- sample(students,2)

# random permutation
randID= sample(1:20)
h1 = students[randID[1:10]]
h2 = students[randID[11:20]]

h1order = sample(h1)
h2order = sample(h2)

shuffled = sample(cards)
cardPlay = data.frame(p1 = shuffled[1:5], p2 = shuffled[6:10], p3 = shuffled[11:15])

# with replacement

# for loop 
num = 1:5
chr = c("a","b","c","d","e")
for (i in num){
  print(i)
}
for (i in chr){
  print(i)
}
for (i in num){
  print(chr[i])
}

p1 = p2 = p3 = rep("joker",5)
Ncard = 5
Nplayer = 3
cardSeq = seq(1, Ncard*Nplayer, Nplayer)
cardN = 0
for (i_card in cardSeq){
  cardN = cardN + 1
  p1[cardN] = shuffled[i_card]
  p2[cardN] = shuffled[i_card+1]
  p3[cardN] = shuffled[i_card+2]
}

p1 = shuffled[seq(1,15,3)]
p2 = shuffled[seq(2,15,3)]
p3 = shuffled[seq(3,15,3)]

players = matrix("joker",nrow = Ncard, ncol = Nplayer)
colnames(players) <- c("p1","p2","p3")
cardN = 0
for (i_card in 1:Ncard){
  for (i_player in 1:Nplayer){
    cardN = cardN + 1
    players[i_card, i_player] = shuffled[cardN]
  }
}

players$p1 = shuffled[seq(1,15,3)]
players$p2 = shuffled[seq(2,15,3)]
players$p3 = shuffled[seq(3,15,3)]



p1WinC = p2WinC = tie = 0
Nplay = 10
for (i_play in 1:Nplay){
  p1 = sample(1:6,1)
  p2 = sample(1:6,1)
  if (p1 > p2){
    p1WinC = p1WinC + 1
  } else {
    if (p2 > p1){
      p2WinC = p2WinC + 1
    } else {
      tie = tie + 1 
    }
  }
}

result = sample(c(0,1,2),10, replace=T, prob = c(2/12,5/12,5/12))

win_thres = 5
p1WinC = p2WinC = tie = 0

while(max(c(p1WinC, p2WinC)) < win_thres){
  p1 = sample(1:6,1)
  p2 = sample(1:6,1)
  if (p1 > p2){
    p1WinC = p1WinC + 1
  } else {
    if (p2 > p1){
      p2WinC = p2WinC + 1
    }
  }
}
if (p1WinC>p2WinC){
  print("player 1 won")
} else {
    print("player 2 won")
}


win_thres = 5
p1WinC = p2WinC = tie = 0

repeat{
  p1 = sample(1:6,1)
  p2 = sample(1:6,1)
  if (p1 > p2){
    p1WinC = p1WinC + 1
  } else {
    if (p2 > p1){
      p2WinC = p2WinC + 1
    }
  }
  if(max(c(p1WinC, p2WinC)) >= win_thres){
    if (p1WinC>p2WinC){
      print("player 1 won")
    } else {
      print("player 2 won")
    }
    break
  }
}


vec = sample(1:15)
len_vec = length(vec)
#vec = 1:15
for (loop1 in 1:(len_vec-1)){
  for (loop2 in 2:(len_vec - loop1 + 1)){
    if (vec[loop2] < vec[(loop2 - 1)]){
      temp_num = vec[loop2]
      vec[loop2] = vec[(loop2-1)]
      vec[(loop2-1)] = temp_num
    }
  }
  print(paste("result after loop1 = ", loop1))
  print(vec)
}

vec = sample(1:15)
len_vec = length(vec)
#vec = 1:15
for (loop1 in 1:(len_vec-1)){
  if (all(1:15 == vec)) {
    print("sorted")
    print(vec)
    break
  }
  for (loop2 in 2:(len_vec - loop1 + 1)){
    if (vec[loop2] < vec[(loop2 - 1)]){
      temp_num = vec[loop2]
      vec[loop2] = vec[(loop2-1)]
      vec[(loop2-1)] = temp_num
    }
  }
  print(paste("result after loop1 = ", loop1))
  print(vec)
}