Operations

Union

Union(H₁, H₂)
$\;\;\;\;\;$H = new heap whose root list contains roots from H₁ and H₂
$\;\;\;\;\;$n(H) = n(H₁) + n(H₂)
$\;\;\;\;\;$min(H) = min(H₁)
$\;\;\;\;\;$if (min(H₁) = NIL) or (min(H₂) $\neq$ NIL and min(H₂) <min(H₁))
$\;\;\;\;\;$then min(H) = min(H₂)

Analysis:

t(H) = t(H1) + t(H2)
m(H) = m(H1) + m(H2)

$$\begin{eqnarray*}\hat{c_i} & = & c_i + \Phi(H) - (\Phi(H_1) + \Phi(H_2)) \\ & ... ... 2m(H_1) + t(H_2) + 2m(H_2)] \\ & = & O(1) + 0 \\ & = & O(1) \end{eqnarray*}$$