Frequency Array (Counting by Index)

A frequency array uses the array's indices as bins. To count how often each value appears, increment counts[arr[i]] for every element. The result: counts[v] is the frequency of value v.

This works when values are small, non-negative integers — like grades 0-100, dice rolls 1-6, or letter indices 0-25. For arbitrary values, use parallel lists or an ArrayList of objects instead.

On the AP exam, this pattern is the most elegant way to handle "count how many of each" questions.

Basic frequency count

public int[] frequencies(int[] arr, int maxValue) {
    int[] counts = new int[maxValue + 1];
    for (int v : arr) {
        counts[v]++;
    }
    return counts;
}

The counter array's length is maxValue + 1 so the highest value has a valid index.

Mode (most frequent value)

int mode = 0;
for (int v = 1; v < counts.length; v++) {
    if (counts[v] > counts[mode]) {
        mode = v;
    }
}

The mode is the index — not the count. The count is the value at that index.

Counting characters

int[] charCounts = new int[26];
for (int i = 0; i < s.length(); i++) {
    char c = s.charAt(i);
    charCounts[c - 'a']++;
}

Subtracting 'a' maps each lowercase letter to index 0-25.