Binary Search
Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.
ابدأ بهذا النموذج الذهني
Binary search finds a target in a sorted search space by repeatedly discarding half of the remaining range.
كيف يعمل، بلا مصطلحات زائدة
Compare target with the middle element.
If target is smaller, continue in the left half; if larger, continue in the right half.
اقرأ الخوارزمية كسلسلة من القرارات
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;
}لا تحفظ الصياغة. تتبع الحالة التي تتغير في كل سطر واربطها بالثابت الموضح أعلاه.
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Do not quote this complexity mechanically.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.
مناسب لـ
- Match the algorithm to the structure and preprocessing state of the data.
ما الذي يسوء عادةً
- Using it on unsorted data.
- Off-by-one errors and infinite loops.
- Not defining whether boundaries are inclusive or half-open.
صيغة إجابة احترافية
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.
ماذا يجب أن أذكر عن التعقيد؟
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.
ما الخطأ الأكثر شيوعاً؟
Using it on unsorted data.