docs(docs): add and expand algorithm documentation

docs/(algorithms)/greedy.mdx

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+---
+title: Greedy Algorithms
+---
+
+# Greedy Algorithms
+
+## The idea
+
+At each step, take the best move *right now*. Never look back.
+
+Grokking's example: the classroom problem.
+You want the most classes in one room. Which do you pick?
+**Always pick the class that ends first.** It leaves the most room for the rest.
+
+Greedy works only when the local best is *provably* the global best.
+When it works, it beats DP — no memo table, no lookback, often O(n).
+
+## The picture
+
+```mermaid
+gantt
+    dateFormat HH:mm
+    axisFormat %H:%M
+    section Pick ✓
+    Art (ends first)     :done, 09:00, 45m
+    Math (ends next)     :done, 10:00, 60m
+    Music                :done, 11:00, 60m
+    section Skip ✗
+    English (overlaps Art)  :crit, 09:30, 60m
+    CS (overlaps Math)      :crit, 10:30, 60m
+```
+
+Pick by earliest end time. Skip anything that overlaps a pick.
+
+## Kadane's — DP squeezed to one variable (LC 53 — Maximum Subarray)
+
+The greedy question at each element:
+"Do I extend the running sum, or start fresh here?"
+If the running sum is negative, it only hurts. Drop it.
+
+```python
+def max_sub_array(nums: list[int]) -> int:
+    best = current = nums[0]
+
+    for n in nums[1:]:
+        current = max(n, current + n)   # extend or restart
+        best = max(best, current)
+    return best
+```
+
+```mermaid
+flowchart LR
+    A["-2"] --> B["1<br/>restart"] --> C["-2<br/>extend"] --> D["4<br/>restart"] --> E["3<br/>extend"] --> F["5<br/>extend"] --> G["6<br/>extend ← best"]
+
+    style G fill:#2e7d32,color:#fff
+```
+
+## Jump Game (LC 55) — track the farthest reach
+
+One pass. Keep the farthest index you can touch.
+If your position ever passes the reach, you are stuck.
+
+```python
+def can_jump(nums: list[int]) -> bool:
+    reach = 0
+    for i, n in enumerate(nums):
+        if i > reach:
+            return False                 # stuck
+        reach = max(reach, i + n)
+    return True
+```
+
+## How to justify greedy in an interview
+
+Use an **exchange argument**: "If an optimal answer made a different choice here, I could swap in my greedy choice without making it worse."
+Say this out loud. It is the difference between guessing and proving.
+
+## Complexity
+
+| | Time | Space |
+|---|---|---|
+| One-pass greedy (Kadane, Jump) | O(n) | O(1) |
+| Sort-then-commit (intervals) | O(n log n) | O(1) |
+
+## Close-out ritual
+
+Before you submit, say out loud:
+1. Time and space complexity.
+2. One edge case trace: all-negative array, single element, or zero at index 0.
+
+## Plan problems
+
+**A-set:** LC 53 · 55 · 45 · 134
+**B-set:** LC 122 · 918 · 763
+**Feeds into topic 24 (Intervals):** LC 57 · 56 · 435 · 253