Finding the minimum key

Finding the minimum key
The procedure BINOMIAL-HEAP-MINIMUM returns a pointer to the node with the minimum key in an n-node binomial heap H. This implementation assumes that there are no keys with value ∞.

BINOMIAL-HEAP-MINIMUM(H)
1 y ← NIL
2 x ← head[H]
3 min ← ∞
4 while x ≠ NIL
5 do if key[x] < min
6 then min ← key[x]
7 y ← x
8 x ← sibling[x]
9 return y

Since a binomial heap is min-heap-ordered, the minimum key must reside in a root node. The
BINOMIAL-HEAP-MINIMUM procedure checks all roots, which number at most⌊lg n⌋ + 1,
saving the current minimum in min and a pointer to the current minimum in y.

Analysis:- 
Because there are at most ⌊lg n⌋ + 1 roots to check, the running time of BINOMIAL-HEAP MINIMUM is O(lg n).                                       operations-on-binomial-heap.php