Correct Code Framework: Case Briefing #002

Case Briefing

Before you solve the case

The missing partner investigation

Before you write code, prove why the current number needs evidence from an earlier frame.

Case File #002 exists because Two Sum introduces the first real Recorder problem. The active candidate cannot prove the answer alone; it needs a preserved complement.

Solve Two Sum teaches why professionals use a HashMap here: it records prior values so the current candidate can close the case in constant time.

Primary lesson: A Recorder is lawful only when previous evidence is required to validate the active candidate. For Two Sum, the Recorder preserves value → index evidence before the answer appears.

Two Sum evidence board showing one candidate searching for its complement — The current suspect needs a missing partner from the evidence locker.

Read the Witness Statement

How to Analyze Two Sum

The Correct Code Framework treats the problem statement as an evidence locker. Two Sum is not solved by pattern memory. It is solved by asking what evidence must be remembered.

1. Extract the contract: The answer must return two indices, not the values themselves.

2. Map the environment: The input is an unsorted integer array and a target sum.

3. Derive the invariant: The active candidate needs a complement where candidate + complement == target.

4. Prove the Recorder: Since the complement may have appeared earlier, prior values must be preserved as value → index.

Formal Translation / CCF Translation

Translate the contract into Recorder-backed movement

Formal Translation

Iterate through numbers from left to right. For each index i, compute needed = target - numbers[i]. If needed already exists in the Recorder, return [recorder[needed], i]. Otherwise record numbers[i] → i and continue.

CCF Translation

The Answer Space requires two indices. The Problem Space is an unsorted indexed array and a stable target. The Invariant is complement equality. The Recorder is a HashMap from value to index. The Scanner advances one index at a time while the Recorder preserves prior evidence.

Elimination Map, Wrong Path Analysis, and Transfer

Formal Translation

For each candidate, compute its complement and query a value-to-index map containing only earlier elements.

CCF Translation

The Scanner brings present evidence; the Recorder preserves prior evidence. Candidate Qualification occurs when the current suspect finds its required complement in an earlier Frame.

Elimination Map

Route	Ruling	Why
Nested pair scan	Lawful but inefficient	It repeatedly reopens prior evidence and costs quadratic work.
Set only	Insufficient	It can preserve existence but loses the indices required by the Answer Space.
Sort and use boundaries	Risky here	Sorting changes original positions unless additional index evidence is preserved.
HashMap Recorder	Survives	It preserves exactly the prior value-to-index evidence the active candidate needs.

Wrong Path Analysis

Brute force is correct, not unlawful. The professional upgrade is the HashMap Recorder because it stops reopening every earlier Frame and preserves the complement evidence needed by the current candidate.

Evidence Commitment

The current number does not close the case by itself. Commit the answer only when its complement is already present in the Recorder. That prior entry proves a different, earlier element exists. Lookup happens before recording so the current element cannot testify as its own partner.

Correctness Ruling

Every prior value is recorded with its index. For the active value, complement = target - current. If that complement exists, its stored index and the current index form a valid pair. Lookup-before-recording prevents index reuse; otherwise the current value is preserved for future candidates.

Common Mistakes

Recording before lookup, which may let the active element match itself.
Rejecting brute force as incorrect when it is lawful but inefficient.
Returning values when the Answer Space requires indices.
Confusing duplicate values with duplicate indices; values may match while positions remain distinct.

Transfer Question

Change the environment

What changes if the array is sorted? What must the Recorder or Answer Space preserve if the case asks for every qualifying pair instead of one?

Run the Investigation

Two Sum Simulator

Watch the Scanner inspect one candidate at a time. The Recorder keeps earlier values so the current candidate can ask whether its complement has already been seen.

Evidence array Target sum

Problem Statement Reference

Given an array of integers numbers and an integer target, return the indices of the two numbers such that they add up to target. Each input has exactly one solution, and the same element may not be used twice. Return the two indices once the matching pair is discovered.

Closing Report

✓ Case Closed

You solved Case File #002 by proving the Recorder.

You read the problem statement like evidence, identified that one candidate cannot close the case alone, and derived the HashMap Recorder before writing the implementation.

Answer Space — return two indices.
Problem Space — unsorted integer array numbers and integer target.
Invariant — candidate + complement == target.
Operation — compute complement, lookup, then record.
Recorder — HashMap value → index preserves prior evidence.
Scanner — linear forward scan, one active candidate at a time.
Finalizer — return [recorder[complement], i] when the complement is found.

The Recorder followed the evidence. It was not chosen by preference.