Check bracket sequence compatibility one closing mark at a time

Bracket sequence compatibility can be checked one closing mark at a time when a paper format states which opening it must match. In this original exercise, a closing mark must close the most recent opening still waiting. The record ([]) follows that rule. The record ([)] stops at its third character, even though it contains the same four kinds of marks in the same quantities.

This is a declared paper format with no numerical operation attached to its symbols. It supplies no claim about a particular application, programming language, calculator or device accepting a record. We will retain each literal sequence and trace what the chosen rules permit.

State the four-character format before checking a record

The alphabet contains an opening round mark (, its closing round mark ), an opening square mark [, and its closing square mark ]. No letters, numbers, spaces or quotation marks belong inside our literal records. When quotation marks surround an example in prose, they are presentation rather than part of its input.

Read from left to right. An opening mark adds its type to a list of unclosed openings. A closing mark requires that list to contain an opening, and its type must match the most recent entry. A successful close removes that one entry.

After the final character, the list must be empty for the complete record to be compatible. Under this authored rule, an empty input is compatible because it introduces no openings or closings. A different format could impose a minimum content requirement, but that is not part of this exercise.

Number positions starting at one. Preserve the literal characters beside their positions, so a statement such as mismatch at three refers to one identifiable place. The list records what remains open after each successful step; it is not a replacement for the original sequence.

Follow a compatible nested record

Begin with ([]) and an empty list. At position one, the opening round mark enters the list. It is the only unclosed opening. At position two, the opening square mark is added after it, making square the most recent unclosed type.

Position three contains a closing square mark. It matches the most recent square opening, so remove that entry. The round opening remains. Position four contains a closing round mark, which closes that remaining entry and returns the list to empty.

The complete four-character record passes the declared format. The inner square pair closes before the outer round pair. A note saying only that both types have partners would omit the order the trace actually checked.

You may draw the list as a row growing to the right or as a column growing upward. State which end contains the most recent entry and use that convention consistently. The drawing orientation does not change which opening was encountered last.

Stop at the wrong closing type

Now start a separate trace for ([)]. Its first two steps are the same: an opening round mark followed by an opening square mark. Immediately before position three, both openings are unclosed, with square the most recent one.

Position three is a closing round mark. It does not match that square opening. The trace therefore stops with a type mismatch at three. Record that the expected closing type was square and the supplied closing type was round.

Do not skip past the square opening to find the older round one. That would replace the stated most-recent rule with another matching method. Likewise, do not remove the square entry while recording the failed step as successful. Keep the list as it stood immediately before the mismatch.

The fourth character is a closing square mark, but its presence later in the record does not make position three acceptable. A check that merely searches forward for any matching shape would answer a different question. Our format specifies which opening the current closer must finish.

Distinguish a changed record from a new interpretation

Both ([]) and ([)] contain one opening and one closing of each type. The second can be changed into the first by exchanging the closing marks at positions three and four. That produces a new literal record whose trace succeeds.

Save the original mismatch and the changed record separately. An accepted revised sequence does not show that the unchanged original had another valid reading under the same rules. It shows that the recorded characters now meet the declared requirement.

This example gives one explicit change, not a general method for choosing the best repair. We have supplied no intended numerical expression or message that a repair must preserve. If another person intended particular content, that intention would need its own evidence before someone selected a replacement record.

Separate an unexpected closer from an unfinished record

Consider )( as another literal input. At its first character, the list is empty and a closing round mark appears. There is no unclosed opening for it to finish. Stop at position one and record an unexpected closing mark, rather than looking ahead for the opening at position two.

Now consider ([]. The opening round and opening square marks enter the list, and the closing square mark successfully removes the latter. The input then ends with the round opening still waiting. No supplied closer had the wrong type; the complete record is unfinished.

The three diagnoses identify different states. In ([)], a supplied closing type conflicts with the most recent opening. In )(, a closer arrives when no opening exists. In ([], the input ends before its remaining opening closes. Preserve the actual state instead of calling every rejected record a generic mismatch.

Appending a closing round mark to ([] would create the complete record ([]). Keep that as a changed input if you choose to make it. The original three-character record remains incomplete under the rule we used to inspect it.

Allow completed groups to sit beside one another

Our rule does not require one outer pair to surround the entire record. For ()[], the first round pair opens and closes, returning the list to empty at position two. The square pair then opens and closes, returning it to empty again at position four.

Similarly, ([])[] completes its nested round-and-square group at position four. A new square group begins at five and closes at six. Both groups meet the same local closing rule, and no opening remains after the final character.

An empty list in the middle of a trace therefore need not signal an error or the end of the input. Continue through the actual remaining characters. Acceptance concerns the complete record, including whether a later closer appears without a corresponding active opening.

Check a deeper example without changing the rule

Use ([[]]) for a six-character nested record. Its first three characters open a round group, a square group and another square group. The most recent opening is the second square one, although the two square symbols have the same visible shape.

The closing square at four removes the entry created at three. The closing square at five removes the one created at two. Finally, the closing round mark at six removes the opening from position one. All six characters are accounted for and the list finishes empty.

Recording opening positions beside their types makes this trace easier to inspect. Two identical square marks still entered at different times. Removing one entry per successful closing preserves that distinction without inventing different meanings for the two symbols.

Keep this inspection within its declared scope. A compatible bracket-only sequence has no arithmetic value here. We have not defined addition, a function call or the meaning of any enclosed content. Correct structure under this paper rule cannot establish that a different format or actual system would accept the same characters.

Read the two folder accounts

The Business Source BSN17239 account names end-tab folders and 100 per box. Its two images show a complete plain folder. No delivered quantity, material or filing-performance result is verified here.

The Pendaflex 421013BLA account describes black/gray assorted-tab folders. Its single image shows that form. The account gives 100/box and package quantity 500 each; their relationship is unresolved here. The image establishes no delivered quantity or material finding.

Leave other uses of parentheses with their own questions

The gap-rule grouping FAQ compares two defined numerical groupings and calculates their different results. Our paper format assigns no operation or value to an accepted bracket record. Structural acceptance cannot choose which numerical grouping someone intended.

The calculator error-message guide uses applicable model manuals to distinguish actual input and calculation errors. Its controls and allowed commands remain model-specific. This invented format supplies no key sequence or claim about a calculator validating these bracket records.

Keep an optional order separate from the format check

If you separately consider an order on republeq.com and want to ask about USDT, identify the exact offer and intended quantity before discussing payment. The characters and positions in this paper format are invented inputs, not product prices, token amounts or instructions to transfer funds. A compatible record establishes no available payment method or commitment by a seller. Read the choices and conditions actually presented for the intended transaction, and ask the responsible support contact to clarify essential information before deciding whether to proceed. If a cryptocurrency option is offered, establish the specified asset and network, the requested amount, any stated validity period and the reference associating payment with that order. Do not infer a destination from an illustration, a previous transaction or a message about another proposed purchase. Resolve any necessary item or supplied-contents question separately from the payment discussion. Ask about applicable delivery, cancellation, return and refund conditions, including the denomination of an approved refund and relevant deductions. Keep each answer attached to the offer and quantity it concerns. A changed basket may require reviewing the resulting transaction information again. If an instruction has expired, obtain current information before making a transaction decision. This article promises no present USDT availability, conversion result, fee level, processing time, refund amount or delivery outcome. You can trace every record without placing an order. Preserve any eventual acknowledgement and payment record separately from the worksheet. A successful character trace cannot confirm that a transaction was authorized, completed or reconciled. If the transaction status is uncertain, resolve it through the responsible merchant before considering another payment.

Retain the literal record and its first unresolved step

For ([]) the list empties after four successful characters. For ([)], retain the mismatch at three, the expected square closer and the still-open round-and-square entries. For ([], retain the round opening left at the end. Each finding belongs to its own literal sequence.

A useful record includes the alphabet, the most-recent opening rule, the input and its trace. Keep any revised sequence under a separate label. Bracket sequence compatibility then describes the stated paper format and the actual characters inspected, while leaving numerical meaning and real-system acceptance as separate questions.