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

islands/decks/prefix-sum.md

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+## Prefix Sum
+
+Precompute cumulative totals once → any range sum in **O(1)**.
+
+---
+
+## Recognition
+
+- Many range-sum queries over a static array
+- "Count subarrays with sum k" (negatives allowed — window won't work)
+- "Product/sum of everything except me" → prefix from both directions
+
+---
+
+## Template — range query (LC 303)
+
+```js
+// prefix[i] = sum of nums[0..i-1], prefix[0] = 0
+const prefix = [0];
+for (const x of nums) prefix.push(prefix[prefix.length - 1] + x);
+
+// sum of nums[l..r] inclusive:
+const rangeSum = (l, r) => prefix[r + 1] - prefix[l];
+```
+
+The leading 0 removes every edge case at `l = 0`.
+
+---
+
+## Template — prefix + hashmap (LC 560)
+
+```js
+function subarraySum(nums, k) {
+  const count = new Map([[0, 1]]); // empty prefix
+  let sum = 0;
+  let total = 0;
+  for (const x of nums) {
+    sum += x;
+    total += count.get(sum - k) ?? 0; // earlier prefix to cut off
+    count.set(sum, (count.get(sum) ?? 0) + 1);
+  }
+  return total;
+}
+```
+
+sum(l..r) = prefix[r] − prefix[l−1] — so look up `sum - k`.
+
+---
+
+## Pitfalls
+
+- Forgetting the seed `(0, 1)` misses subarrays starting at index 0
+- Count **before** inserting the current prefix (a subarray has length ≥ 1)
+- Sliding window fails here when values can be negative
+
+---
+
+## Recall
+
+- Why does LC 560 need a hashmap instead of a window?
+- LC 238 Product Except Self: how do prefix and suffix passes combine?
+- LC 525 Contiguous Array: what do you turn 0s into, and why?
+
+---
+
+## Drill
+
+- 303 Range Sum Query · 1480 Running Sum
+- 238 Product of Array Except Self
+- 560 Subarray Sum Equals K
+- 525 Contiguous Array · 974 Subarray Sums Divisible by K