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------------------------------------------------ Count the best-case number of addition operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely.

**Preconditions:**
\[ X = \{x_1, x_2, x_3, x_4, x_5\} \subseteq \{10, 20, 30, 40, 50, 60, 70, 80\}, \]
where \( x_1 < x_2 < x_3 < x_4 < x_5 \).

```
t ← 0
i ← 1
while t < 101 do
t ← t + x_i
i ← i + 1
```

How many addition operations are performed in the best-case scenario?

Answer :

For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.

Given that,

The following pseudocode snippet performs the maximum number of + operations. Assume that the probability of each potential piece of data is equal. Preconditions: X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}, where x1 < x2 < x3 < x4 < x5. t ← 0 i ← 1 while t < 101 do t ← t + xi i ← i + 1

We know that,

Here,

X = {x₁, x₂, x₃, x₄, x₅} ⊆ {10, 20, 30, 40, 50, 60, 70, 80}

By doing the iteration method

Iteration process till 4th iteration we get 6

Therefore, For the best cases there will be 6+operations, The number of operations are best cases 6 and the worst cases are 10.

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