```
T(n)
├── T(n/4)
│ ├── T(n/16)
│ │ ├── ...
│ │
│ ├── T(n/16)
│ │ ├── ...
│ │
│ ├── T(n/16)
│ │ ├── ...
│ │
│ └── T(n/16)
│ ├── ...
│
├── T(n/4)
│ ├── ...
│
├── T(n/4)
│ ├── ...
│
└── T(n/4)
├── ...
```
In each level of the recursion tree, there are four subproblems of size \(n/4\), and the cost at each level is \(n\).
Now, let's find the pattern:
- Level 1: \(n\)
- Level 2: \(4 \cdot \frac{n}{4} = n\)
- Level 3: \(4^2 \cdot \frac{n}{4^2} = n\)
- ...
The total number of levels in the recursion tree is \(\log_4 n\). Therefore, the total cost is the product of the number of levels and the cost at each level:
\[
T(n) = \underbrace{n}_{\text{level 1}} + \underbrace{n}_{\text{level 2}} + \underbrace{n}_{\text{level 3}} + \ldots + \underbrace{n}_{\text{level }\log_4 n} = n \cdot \log_4 n
\]
So, the explicit formula for \(T(n)\) is \(T(n) = n \cdot \log_4 n\).