Binary Search
Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.
Beginne mit diesem mentalen Modell
Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.
So funktioniert es – ohne unnötigen Jargon
Compare target with the middle element.
If target is smaller, continue in the left half; if larger, continue in the right half.
Lies den Algorithmus als Folge von Entscheidungen
Set left and right bounds.
Compute mid without leaving the range.
Move exactly one bound after each comparison until found or left > right.
Searching 23 in [3, 8, 12, 23, 31, 44] checks the middle, then keeps only the half where 23 can still exist.
function binarySearch(items, target) {
let left = 0;
let right = items.length - 1;
while (left <= right) {
const mid = left + Math.floor((right - left) / 2);
if (items[mid] === target) return mid;
if (items[mid] < target) left = mid + 1;
else right = mid - 1;
}
return -1;
}Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.
O(log n)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Gut geeignet
- Match the algorithm to the structure and preprocessing state of the data.
Was typischerweise schiefgeht
- Using it on unsorted data.
- Off-by-one errors and infinite loops.
- Not defining whether boundaries are inclusive or half-open.
Struktur einer professionellen Antwort
Say the invariant: if the target exists, it is inside the current search interval. Then explain how each comparison preserves that invariant while halving the interval.
What problem does Binary Search solve?
Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.
Was sollte ich zur Komplexität erwähnen?
Its typical cost here is O(log n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
Was ist der häufigste Fehler?
Using it on unsorted data.