06 Merge Triplets — Interview English Script (C++)
Source aligned with: docs/13_Greedy/06_Merge_Triplets.md
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1) 30-second problem restatement script
| English line | Traditional Chinese meaning (short) | Interview stage |
| Let me restate merge triplets to target. | 我先重述 Merge Triplets 題目。 | Restatement |
| We have many triplets and one target triplet. | 題目給多個 triplets 與一個 target。 | Restatement |
| Merge operation takes component-wise maximum of two triplets. | merge 操作是逐欄取最大值。 | Restatement |
| We may merge repeatedly in any order. | 可任意次、任意順序合併。 | Restatement |
| We need to know whether target can be formed exactly. | 要判斷是否能精確形成 target。 | Restatement |
| I will use greedy filtering and component coverage checks. | 我會用貪心過濾加欄位覆蓋檢查。 | Restatement |
2) Clarifying questions (5 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Do we return boolean only? | 是否只回布林值？ | Clarify |
| Is merge defined as max per coordinate only? | merge 是否僅定義為每欄取 max？ | Clarify |
| Can triplets contain values larger than target? | triplets 可能出現大於 target 的值嗎？ | Clarify |
| Are there constraints large enough to require O(n) scan? | 限制是否大到要 O(n) 掃描？ | Clarify |
| Is exact equality with target required on all three coordinates? | 三個欄位都必須精確等於 target 嗎？ | Clarify |
3) Approach discussion
Brute force (3 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Brute force explores many subsets and merge orders. | 暴力法會探索大量子集合與合併順序。 | Approach |
| Order permutations are unnecessary but still huge search space. | 合併順序雖可省但搜尋空間仍龐大。 | Approach |
| We need linear greedy reasoning. | 我們需要線性貪心推理。 | Approach |
Optimized approach (5 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Any triplet with any coordinate above target is unusable. | 任一欄超過 target 的 triplet 都不可用。 | Approach |
| Because max-merge can only keep or increase values, never decrease. | 因為 max 合併只會維持或變大，不會變小。 | Approach |
| For usable triplets, track whether each target coordinate can be matched. | 對可用 triplet，追蹤三個 target 欄位是否可被匹配。 | Approach |
| If we can match x and y and z coordinates, target is achievable. | 若 x、y、z 三欄都能命中，target 可達。 | Approach |
| This needs one pass with constant extra state. | 這只需單次掃描與常數額外狀態。 | Approach |
4) Coding-and-speaking script (line-by-line, in coding order)
| English line | Traditional Chinese meaning (short) | Interview stage |
| I initialize three flags foundX foundY foundZ as false. | 我先把 foundX、foundY、foundZ 初始化為 false。 | Coding |
| I iterate each triplet t in triplets. | 我遍歷每個 triplet t。 | Coding |
| If any t coordinate is greater than target coordinate, I skip it. | 若 t 任一欄大於 target 對應欄，直接跳過。 | Coding |
| Otherwise this triplet is safe for merging. | 否則此 triplet 可安全參與合併。 | Coding |
| If t[0] equals target[0], set foundX true. | 若 t[0]==target[0]，設 foundX=true。 | Coding |
| If t[1] equals target[1], set foundY true. | 若 t[1]==target[1]，設 foundY=true。 | Coding |
| If t[2] equals target[2], set foundZ true. | 若 t[2]==target[2]，設 foundZ=true。 | Coding |
| Return foundX and foundY and foundZ. | 回傳 foundX && foundY && foundZ。 | Coding |
| English line | Traditional Chinese meaning (short) | Interview stage |
| Let me dry-run triplets [[2,5,3],[1,8,4],[1,7,5]] and target [2,7,5]. | 我手跑 triplets=[[2,5,3],[1,8,4],[1,7,5]]、target=[2,7,5]。 | Dry-run |
| First triplet is safe and matches target x value two. | 第一組可用，命中 x=2。 | Dry-run |
| Second triplet has eight above target y seven, so skip it. | 第二組 y=8 超過目標 7，直接跳過。 | Dry-run |
| Third triplet is safe and matches target y and z values. | 第三組可用，命中 y 與 z。 | Dry-run |
| Now all three flags become true. | 此時三個旗標都為 true。 | Dry-run |
| Therefore target triplet is achievable. | 因此 target triplet 可達成。 | Dry-run |
| Final answer is true. | 最終答案是 true。 | Dry-run |
6) Edge/corner test script (at least 4 cases)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Case one: all triplets exceed target in some coordinate. | 案例一：每組都在某欄超過 target。 | Edge test |
| Case two: exact target already appears in input. | 案例二：輸入中本來就有 target。 | Edge test |
| Case three: each coordinate available but from different safe triplets. | 案例三：三欄分別由不同可用 triplet 提供。 | Edge test |
| Case four: one coordinate can never be matched exactly. | 案例四：某一欄永遠無法精確命中。 | Edge test |
| Case five: many duplicates with same safe values. | 案例五：大量重複且安全值相同。 | Edge test |
7) Complexity script
Short version (2 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Time complexity is O(n). | 時間複雜度是 O(n)。 | Complexity |
| Space complexity is O(1). | 空間複雜度是 O(1)。 | Complexity |
Full version (4 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| We scan each triplet exactly once. | 每個 triplet 只掃描一次。 | Complexity |
| Per triplet work is constant coordinate checks and flag updates. | 每組只做常數次欄位檢查與旗標更新。 | Complexity |
| Therefore runtime is O(n). | 因此時間是 O(n)。 | Complexity |
| We store only three booleans, so memory is O(1). | 只儲存三個布林值，空間 O(1)。 | Complexity |
8) If stuck rescue lines (10 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Let me first remove impossible triplets. | 我先排除不可能使用的 triplet。 | If stuck |
| Any coordinate above target is toxic. | 任一欄超過 target 都是有毒資料。 | If stuck |
| Max merge cannot reduce an oversized coordinate. | max 合併無法把過大的欄位降回來。 | If stuck |
| So only safe triplets should be considered. | 所以只能考慮安全 triplet。 | If stuck |
| Then I just need coordinate coverage checks. | 接著只需做欄位覆蓋檢查。 | If stuck |
| Need one safe triplet matching target x. | 需要至少一組安全 triplet 命中 target x。 | If stuck |
| Similarly for y and z. | y 與 z 也是同理。 | If stuck |
| Let me test one failing case where z cannot be matched. | 我測一個 z 永遠命不中的失敗案例。 | If stuck |
| Flags show missing z so answer is false. | 旗標顯示缺 z，所以答案 false。 | If stuck |
| Great, proof and implementation are aligned. | 很好，證明與實作一致。 | If stuck |
9) Final wrap-up lines (5 lines)
| English line | Traditional Chinese meaning (short) | Interview stage |
| I solved merge triplets with greedy filtering. | 我用貪心過濾解了 Merge Triplets。 | Wrap-up |
| Oversized triplets are discarded immediately. | 超標 triplet 會立刻丟棄。 | Wrap-up |
| Safe triplets only need to cover target coordinates. | 可用 triplet 只需覆蓋目標三欄。 | Wrap-up |
| Complexity is O(n) time and O(1) space. | 複雜度是 O(n) 時間、O(1) 空間。 | Wrap-up |
| This is concise and interview-friendly. | 這個解法簡潔且面試友善。 | Wrap-up |
10) Ultra-short cheat sheet (20 lines total)
| English line | Traditional Chinese meaning (short) | Interview stage |
| Goal: can merges form exact target triplet. | 目標：合併後能否精確得到 target。 | Cheat sheet |
| Merge uses coordinate-wise max. | merge 是逐欄取 max。 | Cheat sheet |
| Filter out triplets exceeding target in any coordinate. | 任一欄超標的 triplet 直接過濾。 | Cheat sheet |
| Oversized values can never be fixed later. | 超標值後續不可能被修正。 | Cheat sheet |
| Track foundX, foundY, foundZ. | 追蹤 foundX、foundY、foundZ。 | Cheat sheet |
| For each safe triplet, update matching flags. | 每個安全 triplet 更新命中旗標。 | Cheat sheet |
| If t[0]==target[0], foundX=true. | 若 t[0]==target[0]，foundX=true。 | Cheat sheet |
| If t[1]==target[1], foundY=true. | 若 t[1]==target[1]，foundY=true。 | Cheat sheet |
| If t[2]==target[2], foundZ=true. | 若 t[2]==target[2]，foundZ=true。 | Cheat sheet |
| Final answer is foundX&&foundY&&foundZ. | 最終答案是 foundX&&foundY&&foundZ。 | Cheat sheet |
| One pass through triplets. | 單次掃描 triplets。 | Cheat sheet |
| Time O(n). | 時間 O(n)。 | Cheat sheet |
| Space O(1). | 空間 O(1)。 | Cheat sheet |
| Common bug: not filtering oversized triplets. | 常見錯誤：沒先過濾超標 triplet。 | Cheat sheet |
| Common bug: expecting one triplet to match all coordinates. | 常見錯誤：誤以為單一 triplet 要全欄命中。 | Cheat sheet |
| Coordinates can be contributed by different triplets. | 三欄可由不同 triplet 貢獻。 | Cheat sheet |
| Exact match required for each coordinate. | 每個欄位都要精確命中。 | Cheat sheet |
| Safe triplets can be merged in any order. | 安全 triplet 合併順序不影響結論。 | Cheat sheet |
| Validate with one impossible coordinate case. | 記得驗證某欄永遠不可達案例。 | Cheat sheet |
| Keep explanation focused on monotonic max property. | 說明聚焦在 max 的單調性。 | Cheat sheet |
Quality check
- Consistency with source solution: ✅ Toxic-filter + coordinate coverage logic preserved.
- No hallucinated constraints: ✅ Merge semantics and exact-target requirement maintained.
- Language simplicity: ✅ Straightforward interview explanation tied to max monotonicity.