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Subgoals

Section 10.18 Worked Example: Arrays - Find 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

Subsection 10.18.1

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, and that the variable target is an int with a value in it. Evaluate these statements and determine the value of loc. If any error occurs, give the reason.
int loc = -1;
boolean found = false;
for (int i = 0; i < alpha.length && !found; i++) {
    if (alpha[i] == target)   {
    loc = i;  found = true;
    }
}

Subsection 10.18.2 SG1: Set up array from 0 to size-1

Figure 10.18.1.
  • 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 10.18.3 SG2: Evaluate data type of statements against array

References to the array are in the loop and selection statements:
for (int i = 0; i < alpha.length && !found; i++) {
   if (alpha[i] == target)        {
      loc = i;  found = true;
   }
}
  • 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 the int value of target.
  • If the value at alpha[i] is equal to target, then the value i is copied into loc.
  • All indexes into the array are valid, and all assignments are valid.

Subsection 10.18.4 SG3: Trace statements, updating slots as you go

Let us trace with a sample array and assume the value of target is 15.
Figure 10.18.2.
The first statement, int loc = -1; gives loc a value that is not a valid index for any array.
Then a for-loop is used to traverse the array and compare each element to target. The chart below uses one line to represent the memory and comparisons during each iteration of the loop, starting when i has a value of zero.
Figure 10.18.3.
When we find the target value in the array, we store the index (location) of where it is in the array.
Some questions to consider:
  1. What would happen if the target value is not in the array? Then the selection statement is never true, and loc is never changed from its initial value of -1.
  2. Why is -1 a good initial value for loc? It is not a valid index for any array. You or another programmer using this algorithm could check the value of loc to make a decision (selection!) for how the program will behave when the target value is found or not found at a valid array index.
  3. What would happen if there were 2 occurrences of the target value in the array? The loop does not end when the target value is found, so additional occurences would overwrite the value of loc with the last occurence.
The more general answer to the original question is: “loc contains the index of the last occurrence of target in the array alpha or -1 if target is not in the array.”

Subsection 10.18.5 Practice Pages

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