[2%, 2%, 2%, 2%] Consider the two missing parts for the decrease key operation in F-heap.

DecreaseKey(H, x, k){
  if k > x.key return "error"
  x.key = k
  y = x.p   // note: x.p represents the parent node of x

  if y != NIL and (1) {
    CUT(H, x, y)
    CASCADING-CUT(H, y)
  }
  if x.key < H.min.key
      H.min = x
}

CUT(H, x, y){
  x.p = (2)
  x.mark = FALSE
}

CASCADING-CUT(H, y){
  z = y.p
  if z != NIL
    if y.mark == FALSE
        y.mark = TRUE
    else {
        CUT(H, y, z)
        CASCADING-CUT(H, z)
    }
}

(i) Which of the following for (1) is true? (A) $x.key < y.key$ (B) $x.key > y.key$ (C) $x.key \ge y.key$ (D) $x.key \le y.key$

(ii) Which of the followings is true for (2)? (A) NIL (B) $y$ (C) $x$ (D) None of the above

(iii) What is the amortized time complexity of function DecreaseKey? (A) $O(1)$ (B) $O(n)$ (C) $O(\lg n)$ (D) $O(\lg n^2)$

(iv) What is the time complexity of inserting node into F-heap? (A) $O(1)$ (B) $O(n)$ (C) $O(\lg n)$ (D) $O(\lg n^2)$