R: Create a variable that uses value from previous row in a for loop

I am trying to create a variable that takes on a value for a variable (z) when two rows differ on another variable (x). So if row numbers 1 and 2 differs for x (starting on row #2), I would like z to take the value of 1, otherwise 0.

I have tried with different if and if-else sentences based on this question (For Loop that References the Previous Row in R), but it does not give me the desired results.

df <-
  data.frame(
    x = c(1, 1, 2, 0, 0, 0, 0, 1, 1, 2),
    y = c(1, 1, 2, 0, 0, 0, 0, 1, 1, 2),
    z = c(0, 1, 2, 0, 0, 0, 0, 1, 1, 2)
  )

for (i in 2:length(df)) {
  df$z <- ifelse(df$x[i] != df$x[i - 1], 1, 0)
}


for (i in 2:length(df)) {
  if (df$x[i] != df$x[i - 1]) {
    df$z == 1
  } else{
    df$z == 0
  }
}

My expected results are:

df_expected <-
  data.frame(
    x = c(1, 1, 2, 0, 0, 0, 0, 1, 1, 2),
    y = c(1, 1, 2, 0, 0, 0, 0, 1, 1, 2),
    z = c(NA, 1, 1, 1, 0, 0, 0, 1, 0, 1)
  )

Thanks a lot in advance!