In-Place Shifting and Pair Counting

In-place shifting moves elements left or right within the same array — usually to insert or delete without allocating new memory. Pair counting tallies pairs (i, j) that share some property.

Shifting requires direction-aware loops: shift right uses a backward loop; shift left uses a forward loop. Pair counting uses nested loops with j > i to avoid double counting.

On the AP exam, shifting appears in array-modification FRQs; pair counting appears in "how many pairs" or "common-difference" problems.

Shift right (insert space)

// Shift positions [start..end-1] right by 1
for (int i = end; i > start; i--) {
    arr[i] = arr[i - 1];
}
arr[start] = newValue;

Backward iteration prevents overwriting unread values.

Shift left (delete)

// Shift positions [start+1..end] left by 1 (effectively remove arr[start])
for (int i = start; i < end; i++) {
    arr[i] = arr[i + 1];
}

Forward iteration; the last position becomes a duplicate or sentinel.

Counting matching pairs

public int pairsSummingTo(int[] arr, int target) {
    int count = 0;
    for (int i = 0; i < arr.length; i++) {
        for (int j = i + 1; j < arr.length; j++) {
            if (arr[i] + arr[j] == target) count++;
        }
    }
    return count;
}

Starting inner loop at j = i + 1 ensures each pair counted exactly once.