Update 17.4.md

docs/Chap17/17.4.md

@@ -8,13 +8,27 @@ By theorems 11.6-11.8, the expected cost of performing insertions and searches i
 
 > Show that if $\alpha_{i - 1} \ge 1 / 2$ and the $i$th operation on a dynamic table is $\text{TABLE-DELETE}$, then the amortized cost of the operation with respect to the potential function $\text{(17.6)}$ is bounded above by a constant.
 
-$$
-\begin{aligned}
-\hat c_i & = c_i + \Phi_i - \Phi_{i - 1} \\\\
-         & = 1 + (2 \cdot num_i - size_i) - (2 \cdot (num_i + 1) - size_i) \\\\
-         & = -1.
-\end{aligned}
-$$
+- **Case 1:** When $\alpha_i \ge 1 / 2$
+
+    $$
+    \begin{aligned}
+    \hat c_i & = c_i + \Phi_i - \Phi_{i - 1} \\\\
+             & = 1 + (2 \cdot num_i - size_i) - (2 \cdot (num_i + 1) - size_i) \\\\
+             & = -1.
+    \end{aligned}
+    $$
+
+- **Case 2:** When $\alpha_i < 1 / 2$ and $\alpha_i \ge 1 / 4$
+
+    $$
+    \begin{aligned}
+    \hat c_i & = c_i + \Phi_i - \Phi_{i - 1} \\\\
+             & =  1 + (\frac{1}{2} size_i - num_i) - (2 \cdot (num_i + 1) - size_i) \\\\
+             & = -1 + (\frac{3}{2} size_i - 3 \cdot num_i) \\\\
+             & = -1 + 3 \quad \text{(since } size_i - 1 = 2 \cdot num_i - 1) \\\\
+             & = 2.
+    \end{aligned}
+    $$
 
 ## 17.4-3