Arrays and Iteration

Find Maximum

Scan the array once, keeping the largest value seen so far. The replay highlights when a candidate replaces the running maximum.

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `array-find-max`.
cross-language comparison This SQL DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.sql
Replay: real traced execution (multi-file project)
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CREATE TABLE arr(idx INTEGER PRIMARY KEY, val INTEGER);
INSERT INTO arr(idx, val) VALUES
  (0, 3), (1, 1), (2, 4), (3, 1), (4, 5), (5, 9), (6, 2), (7, 6);
WITH RECURSIVE scan(idx, best) AS (
  SELECT 0, (SELECT val FROM arr WHERE idx = 0)
  UNION ALL
  SELECT idx + 1,
         MAX(best, (SELECT val FROM arr WHERE idx = scan.idx + 1))
  FROM scan
  WHERE idx + 1 < (SELECT COUNT(*) FROM arr)
)
SELECT best FROM scan ORDER BY idx DESC LIMIT 1;

  1. arr ← [3, 1, 4, 1, 5, 9, 2, 6], best ← 3

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    values this step[3, 1, 4, 1, 5, 9, 2, 6]arr3best

  2. replaced ← no

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    values this stepnoreplaced1i1arr[i]3best

  3. best ← 4, replaced ← yes

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    values this step3 → 4bestyesreplaced2i4arr[i]

  4. replaced ← no

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    values this stepnoreplaced3i1arr[i]4best

  5. best ← 5, replaced ← yes

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    values this step4 → 5bestyesreplaced4i5arr[i]

  6. best ← 9, replaced ← yes

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    values this step5 → 9bestyesreplaced5i9arr[i]

  7. replaced ← no

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    values this stepnoreplaced6i2arr[i]9best

  8. replaced ← no

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    values this stepnoreplaced7i6arr[i]9best

  9. stdout ← 9

    6WITH RECURSIVE scan(idx, best) AS (7  SELECT 0, (SELECT val FROM arr WHERE idx = 0)8  UNION ALL
    values this step9stdout9best

Complexity

  • Time: O(n)
  • Space: O(1)

Implementation notes

  • Keep the explicit control flow. Library shortcuts would hide the state changes this lesson is meant to replay.
  • The final output is intentionally small and deterministic for cross-language comparison.