feat(islands): add StudyDeck component and markdown decks for algorithms

islands/decks/binary-search.md

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+## Binary Search
+
+Halve a **monotonic** search space each step → O(log n).
+
+---
+
+## Recognition
+
+- Sorted input + "find / insert position"
+- "Minimize the maximum" / "first value where condition flips"
+- Answer itself is numeric and checkable → binary search **on the answer**
+
+---
+
+## Template
+
+```js
+function search(nums, target) {
+  let lo = 0;
+  let hi = nums.length - 1;
+  while (lo <= hi) {
+    const mid = lo + ((hi - lo) >> 1);
+    if (nums[mid] === target) return mid;
+    if (nums[mid] < target) lo = mid + 1;
+    else hi = mid - 1;
+  }
+  return -1; // lo is the insert position
+}
+```
+
+---
+
+## First-true boundary
+
+```js
+// smallest index where ok(i) is true; ok is false...false true...true
+let lo = 0;
+let hi = n; // exclusive; n means "never true"
+while (lo < hi) {
+  const mid = lo + ((hi - lo) >> 1);
+  if (ok(mid)) hi = mid;
+  else lo = mid + 1;
+}
+return lo;
+```
+
+Most "hard" binary searches are this shape in disguise.
+
+---
+
+## Pitfalls
+
+- Off-by-one: pick `lo <= hi` **or** `lo < hi` and stay consistent
+- `mid = lo + ((hi - lo) >> 1)` avoids overflow and floats
+- No progress → infinite loop: every branch must shrink the range
+
+---
+
+## Recall
+
+- What property must the search space have? (not "sorted" — *monotonic*)
+- Where does `lo` land when the target is absent?
+- When do you search the answer space instead of the array?