Finding Θ for an algorithm

Question

I have the below pseudocode that takes a given unsorted array of length size and finds the range by finding the max and min values in the array. I'm just learning about the various time efficiency methods, but I think the below code is Θ(n), as a longer array adds a fixed number of actions (3).

For example, ignoring the actual assignments to max and min (as the unsorted array is arbitrary and these assignments are unknown in advance), an array of length 2 would only require 5 actions total (including the final range calculation). An array of length 4 only uses 9 actions total, again adding the final range calculation. An array of length 12 uses 25 actions.

This all points me to Θ(n), as it is a linear relationship. Is this correct?

Pseudocode:

// Traverse each element of the array, storing the max and min values
// Assuming int size exists that is size of array a[]
// Assuming array is a[]

min = a[0];
max = a[0];

for(i = 0; i < size; i++) {
    if(min > a[i]) {         // If current min is greater than val,
        min = a[i];        // replace min with val
    }

    if(max < a[i]) {         // If current max is smaller than val,
        max = a[i];        // replace max with val
    }
}

range = max – min;             // range is largest value minus smallest

Answer 1

You're right. It's O(n).

An easy way to tell in simple code (like the one above) is to see how many for() loops are nested, if any. For every "normal" loop (from i = 0 -> n), you add a factor of n. [Edit2]: That is, if you have code like this:

array a[n]; //Array with n elements.
for(int i = 0; i < n; ++i){ //Happens n times.
    for(int j = 0; j < n; ++j){ //Happens n*n times.
        //something //Happens n*n times.
    }
}
//Overall complexity is O(n^2)

Whereas

array a[n]; //Array with n elements.
for(int i = 0; i < n; ++i){ //Happens n times.
    //something //Happens n times.
}
for(int j = 0; j < n; ++j){ //Happens n times.
    //something //Happens n times.
}
//Overall complexity is O(2n) = O(n)

This is pretty rudimentary, but useful if someone has not taken an Algorithm course.

The procedures within your for() loop are irrelevant in a complexity question.

[Edit]: This assumes that size actually means the size of array a.