[RyPope]

Stacked on #25.

Problem

Correct solutions were marked wrong in two ways, and the list meant to hide bad test data was hiding one of them:

1. Problems with several valid answers were judged against one. About 75 problems say "return any valid answer" (course orders, Gray codes, reorganised strings, balanced BSTs, CIDR covers, …), and "in any order" only applied to the outer list. For example find-the-difference-of-two-arrays rejected [[3,7],[101,8,9]].
2. Invalid test inputs slipped through. The generated dataset has inputs that break their problem's constraints. A case was excluded only when both the Java and C++ references failed it, and C++ often doesn't crash on out-of-bounds input.

Judging

• New comparison modes: any_order_deep (order free at every level), each_any_order (fixed slots, unordered contents), and checker:<slug>. judge() now receives the case's inputs from all four callers.
• 75 answer checkers in judging/checkers/. Each validates an answer against the inputs, and uses the recorded answer only for optimal values such as a minimum length.
  • Unit tests: every checker accepts the statement's example and a different valid answer, and rejects invalid ones.
  • make check-checkers: every checker accepts the dataset's recorded answer on every non-excluded case (75/75).
• Curated modes: judging/answer_modes.py holds the problems whose any-order rule isn't stated in the usual words.
• Runner: Java submissions now import java.text. The reference for minimize-rounding-error-to-meet-target failed to compile on every case, and so would any user's DecimalFormat.

Excluded test cases

validate_cases now excludes a case in any of these situations:

• every trusted reference (passing ≥50% of the suite) fails it, as before;
• one confident reference (≥90%) fails it;
• all references fail exactly the same cases and at least 3 cases survive;
• its recorded answer fails the problem's checker.

It also reports two lists for a person to act on:

• order-only differences: these need a compare mode;
• exclusions resting only on agreeing references: a person should confirm these.

--from-sources builds an unfiltered database first, so make validate-cases regenerates from scratch. Before, it validated the already-filtered data and could never rediscover existing exclusions.

Result

• Before: 1,314 cases in 220 problems. After: 2,086 cases in 308 problems, out of about 275k.
• No longer excluded: 135 cases in 13 problems, because they were correct answers the old judge rejected. For example, all 42 in find-the-difference-of-two-arrays.
• Checked by hand: the 9 problems where only reference agreement drove exclusions. They are regions-cut-by-slashes, recover-a-tree-from-preorder-traversal, count-of-integers, count-unhappy-friends, mean-of-array-after-removing-some-elements and four checker problems. In every one, the inputs really break the constraints: non-square grids, 4-child binary-tree nodes, 31-digit numbers where 22 are allowed, and similar.

Verification

• Tests and lint: make lint passes, and make test passes (backend 373, web 17, runner 62).
• Full rebuild: make validate-cases regenerated the list in 46 minutes with three runners.
• On a live stack after re-import: make smoke passes. For course-schedule-ii, a different valid order ([0,2,1,3] against [0,1,2,3]) is Accepted and an invalid order gets Wrong Answer.
• Independent review: a fresh reviewer read the whole judging change. I fixed its findings, including float tolerance in unordered comparison and non-canonical CIDR blocks, and added the review report for agreement-only exclusions.

Follow-ups (not in this PR)

• Expected-answer display: the Run panel still shows the recorded answer as "expected" when a different valid answer passes. A short note there would avoid confusion.
• find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree: its target parameter is a node reference, which the harness can't represent in C++.
• Transient failures: a reference that fails transiently under load (seen once for Java) scores 0, so it can't wrongly exclude cases. Timeouts are still treated as failures.