# Subgoals

## Section10.13Worked Example: Arrays - Minimum Value

### Subgoals for Evaluating Arrays.

1. Set up array from 0 to size-1
2. Evaluate data type of statements against array
3. Trace statements, updating slots as you go
1. Remember assignment subgoals

### Subsection10.13.1

You can watch this video or read through the content below it.
Problem: Assume that the integer array alpha has been properly declared and is full of data values. Evaluate these statements and determine the value of min. If any error occurs, give the reason.
int min = alpha;
for (int i = 1; i < alpha.length; i++) {
if (alpha[i] < min)
min = alpha[i];
}


### Subsection10.13.2SG1: Set up array from 0 to size-1

• alpha is an array of ints and has values, but we don’t know what those values are
• however, we can still diagram a representation of this array
• notice that the largest index is size - 1

### Subsection10.13.3SG2: Evaluate data type of statements against array

The first statement, int min = alpha, is valid because alpha stores integers, and 0 is a valid index. You can assign an int value to an int variable such as min.
for (int i = 1; i < alpha.length; i++) {
if (alpha[i] < min)
min = alpha[i];
}

• This loop has index i go from 0 to size - 1 (<length) by increments of 1.
• Then the value at alpha[i] is compared to min. If the value at alpha[i] is less than min, then alpha[i] is copied into min.
• All indexes into the array are valid, and all assignments are valid.

### Subsection10.13.4SG3: Trace statements, updating slots as you go

Let us trace with a sample array.
The first line of the code sample initializes min to copy the value from alpha, which in our sample is 12, and then a for-loop is used to traverse the array. The chart below uses one line to represent the memory and calculations during each iteration of the loop, starting when i has a value of zero.
We can see that each time a smaller value is located in the array, that value is stored in min.
The more general answer to the original question is: “min contains the smallest value found in the array alpha.”