Section 10.13 Worked Example: Arrays - Minimum Value
Subgoals for Evaluating Arrays.
- Set up array from 0 to size-1
- Evaluate data type of statements against array
-
Trace statements, updating slots as you go
- Remember assignment subgoals
Subsection 10.13.1
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[0];
for (int i = 1; i < alpha.length; i++) {
if (alpha[i] < min)
min = alpha[i];
}
Subsection 10.13.2 SG1: 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
Subsection 10.13.3 SG2: Evaluate data type of statements against array
The first statement,
int min = alpha[0]
, 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.
Subsection 10.13.4 SG3: 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[0]
, 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
.”Subsection 10.13.5 Practice Pages
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