Index algebra

Index algebra is a skill you practice on paper. Three workhorses:

Min/max with the index. Track the position, not the value, when the answer needs a location:

int best = 0;
for (int i = 1; i < arr.length; i++) {
    if (arr[i] > arr[best]) { best = i; }
}
return best;   // index of max (first on ties)

Left/right neighbors. "Every element bigger than both neighbors":

for (int i = 1; i < arr.length - 1; i++) {
    if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) { count++; }
}

The bounds exclude index 0 and the last index — they have only one neighbor. Off-by-one here changes the answer silently.

Rotation. Shift everything right by 1, last wraps to front:

int[] out = new int[arr.length];
for (int i = 0; i < arr.length; i++) {
    out[(i + 1) % arr.length] = arr[i];
}

Or the in-place copy form most students find clearer:

for (int i = 0; i < arr.length - 1; i++) {
    out[i + 1] = arr[i];
}
out[0] = arr[arr.length - 1];

Single-element and empty arrays are the two inputs that break careless rotations — run them in your head first. Note arr.length - 1 in the loop bound: with arr.length, out[i + 1] walks off the end.