Finding the minimum/maximum is part of a collection of standard algorithms.

Finding the minimum/maximum is a common problem that can be phrased in a wide variety of ways. These include finding the min/max of:

There is a standard algorithm to find the min/max.

Algorithm for finding the min/max

Step 1: Store the min/max

Store something about the min/max value observed so far. Options include:

Ensure that the information stored is sufficient to:

The value(s) being stored must be unambiguous, including any special values.

Step 2: Initialize the min/max

First thing that could be the min/max

If possible, initializing the min/max to the first thing that could be the min/max reduces the chance of errors.

AP CS A Free Response that require finding a min/max often either guarantee that there are at least a certain number of elements, or explicitly indicate what should be done if there are not enough elements (ex: return null).


If it is difficult or impossible to initialize the min/max to the first thing that could be the min/max, the initialization is even more important. The initial value(s) must ensure that the first min/max identified in Step 3 is stored as the min/max.

Options include:

Some problems require that a special value be returned, or other task be performed, if no min/max can be found. The initial value(s) must ensure that it is possible to distinguish between an actual min/max and the absence of a min/max. See my erroneous solution to 2024 GridPath FR method getNextLoc for a demonstration of what not to do.

Step 3: Check each against min/max so far

Check each possible min/max against the min/max so far. Each time a smaller/larger value is found, update the min/max.

If the min/max is initialized to the first value, it may be possible to skip the first value.

In some problems, the possible min/max values are not elements in an array or ArrayList. A method might need to be called to obtain each value. The value might be calculated from elements in an array or ArrayList.

If the min/max so far is stored using more than 1 variable, each variable must be updated each time a new min/max is found.

Simple example with int[]

Method findMax returns the largest value in its parameter arr.

// precondition: arr.length > 0
public static int findMax(int[] arr)
    int max = arr[0];

    for(int i = 1; i < arr.length; i++)
        if(arr[i] > max)
            max = arr[i];
    return max;

Additional examples

Common mistakes

Common mistakes on AP CS A FR that require (or could have been avoided by) finding a min/max include:

Min/max on the AP CS A Multiple Choice

Questions on the AP CS A Multiple Choice might refer to finding the min/max. Treat each question carefully. Don’t assume that an approach doesn’t work just because it doesn’t follow the approach above. Programmers frequently encounter code written by others that may not match how we would have written the same code ourselves.

Examples: It is possible to initialize a variable that will hold a minimum value to Integer.MAX_VALUE. It is possible to handle the first value in an array in an unusual way. It is possible to find the min/max of a fixed number of values by explicitly comparing each value to each other value, though it is easy to mishandle specific cases.

Selected AP CS A FR that involve finding a min/max




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