Compare Supplied Through and Split Fare Paths Without Guessing Ticket Validity — Free
A fare list is a network, not a sum of every price on the page. Find the least-cost complete chain of entered forward quotes while leaving train and ticket compatibility explicitly unverified.
The proof surface
Adding quoted reservation fees is not minimizing a chain of compatible entered fare edges. Ticket validity and same-train compatibility remain human checks.
InputQuote code | from stop index | to stop index | quoted fare dollars; destination stop index (origin is 0)
Rare deviceAdding quoted reservation fees is not minimizing a chain of compatible entered fare edges. Ticket validity and same-train compatibility remain human checks.
Output artifactMinimum complete entered fare-path total plus complete labeled working
Cost$0 local core · no account, card, paid key or subscription · filing proposal has no checkout
Sample, not your facts: Invented records: Through Cedar | 0 | 3 | 47.80; Maple first leg | 0 | 1 | 12.40; Oak longer leg | 1 | 3 | 28.60; Pine middle leg | 1 | 2 | 11.20; Birch final leg | 2 | 3 | 14.30. Destination stop index (origin is 0) = 3; expected Minimum complete entered fare-path total: 37.9 $ minimum entered path fare. These are not quotations, verified observations or personal evidence.
Before using the fare-splice ticket
Index one chosen route from origin zero to the destination setting. In the invented four-stop legend, Cedar Junction is zero, Maple Halt one, Oak Exchange two and Harbor Terminal three; these names and fares are fictional. A quote covers a forward interval between two indices. Connecting quote endpoints creates a mathematical fare path only, not permission to split tickets on a train. No timetable, stop pattern, ticket availability, minimum connection, passenger right, discount, currency conversion or booking fee is checked. Prices must already be comparable dollar amounts, and a responsible booking provider must confirm the actual combination before purchase.
Why the flat version breaks
All quote prices are added as if all are purchased
Through and segment quotes are alternatives. Adding every row answers no coherent fare question. The path model selects a complete endpoint chain and totals only its edges. It still keeps unchosen quotes in view so the reader can understand the comparison and correct a missing or mistyped source price.
A missing edge is filled to make a cheap path
A graph gap is missing evidence, not a zero-cost segment. The app rejects an unreachable destination rather than inventing a fare or a transfer. A supplied zero quote is valid only as a numerical input; actual availability and restrictions remain external checks. Do not convert the error into a booking plan by adding fictional edges to real quotes.
The cheapest arithmetic path is called valid travel
Ticket splitting can depend on actual stopping patterns and fare conditions, and separate tickets may have different practical consequences. This page knows none of them. The selected chain is a model candidate, not a verified bargain or guaranteed journey. Check it with the responsible booking provider before payment, and retain the boundary in any shared or exported result.
How to work the fare-splice ticket
Build a coherent indexed route and quote set
Give each quote a unique neutral code and enter its from/to indices and comparable fare. Indices are whole numbers with zero at origin and a larger to-index no greater than the destination. Backtracking and circular paths are outside this forward-route model. Multiple quote records may connect the same pair; their different source conditions remain your responsibility. Do not add a quote merely because a route interval exists: a missing edge stays missing.
Set the destination without inventing connections
The setting is a whole index from one to 200. It defines the destination, not the number of tickets to buy. Up to 200 quotes are accepted. Every endpoint must lie within the modeled route. A set with no complete origin-to-destination chain gets a specific input error while preserving the quote list. The tool never repairs a gap with a free edge or chooses a station outside the supplied route.
Minimize cents over the forward quote graph
At each stop, compare the best known total cost of reaching it plus each outgoing quote, using integer cents. Because every edge moves forward, the graph is acyclic and can be evaluated in stop order. Track all least-cost path counts. For display, tied totals prefer fewer quote edges, then the lexicographically earlier input-index sequence. Those are transparent representation rules, not a claim about convenience or ticket protection. Mark the displayed chosen edges while keeping every entered quote visible.
Verify the candidate path before any booking
Read the selected quote codes, endpoint chain, cost and tie count. Confirm each split is valid on the actual chosen train and under the provider’s conditions; verify fees, time windows and whether separate tickets change rights or protection. A mathematically cheaper path is not a verified travel saving. Ask an appropriate booking provider to check the combination. The article demo remains unlimited, and the optional filing prototype exports this modeled working rather than a purchase recommendation.
What the fare-splice ticket keeps distinct
Question
Before
Check this working
All quote prices are added as if all are purchased
Through and segment quotes are alternatives. Adding every row answers no coherent fare question. The path model selects a complete endpoint chain and totals only its edges. It still keeps unchosen quotes in view so the reader can understand the comparison and correct a missing or mistyped source price.
Set the destination without inventing connections
A missing edge is filled to make a cheap path
A graph gap is missing evidence, not a zero-cost segment. The app rejects an unreachable destination rather than inventing a fare or a transfer. A supplied zero quote is valid only as a numerical input; actual availability and restrictions remain external checks. Do not convert the error into a booking plan by adding fictional edges to real quotes.
Minimize cents over the forward quote graph
The cheapest arithmetic path is called valid travel
Ticket splitting can depend on actual stopping patterns and fare conditions, and separate tickets may have different practical consequences. This page knows none of them. The selected chain is a model candidate, not a verified bargain or guaranteed journey. Check it with the responsible booking provider before payment, and retain the boundary in any shared or exported result.
Verify the candidate path before any booking
The fare-splice ticket replaces this named manual reconciliation, not source verification or the responsible human's decision.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Entered-fare graph only: no live prices, ticket-validity check, timetable, connection guarantee or passenger-rights advice. Confirm every selected quote, split condition, train stop and fee with the responsible booking provider before purchasing travel.
Data note: This fare-splice ticket calculates in the tab from Quote code | from stop index | to stop index | quoted fare dollars. No input-collection endpoint, AI request or file upload is built into it. Drafts may be saved locally; explicit input-state links and optional external formatting can disclose the records. Use non-sensitive codes and clear the draft when finished.
Go deeper: the companion app files the same reading as a till receipt with a tear-off foot
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the fare-splice ticket reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
Keep the complete fare-splice ticket answer free; optional filing proposes its boundary-preserving print, row-and-summary CSV and five local reading summaries. The $4 one-time prototype is not for sale; another calculation remains free in the article demo.
Entered-fare graph only: no live prices, ticket-validity check, timetable, connection guarantee or passenger-rights advice. Confirm every selected quote, split condition, train stop and fee with the responsible booking provider before purchasing travel.
What this is built on
Declared local method: At each stop, compare the best known total cost of reaching it plus each outgoing quote, using integer cents. Because every edge moves forward, the graph is acyclic and can be evaluated in stop order. Track all least-cost path counts. For display, tied totals prefer fewer quote edges, then the lexicographically earlier input-index sequence. Those are transparent representation rules, not a claim about convenience or ticket protection. Mark the displayed chosen edges while keeping every entered quote visible.
Every sample code, measurement, date, price, fingerprint and scenario is invented. Artifact checks do not verify reader data, policies, actual files, tickets, votes or health/accessibility outcomes.
Google’s official Gemini pricing page, fetched 2026-10-01, lists AI Studio access in its Free section, limited model access and free input/output tokens. Free-tier content may be used to improve products. Optional external formatting may require an account; limits/access can change. Manual local entry needs none. Do not send sensitive records.
Before: a list of fares looked like prices to add or a bargain to assume. After: a complete least-cost quote chain is inspectable while ticket compatibility remains an explicit human check.
Three worked readings, with different inputs
Sample A — typical inputs
Through Cedar | 0 | 3 | 47.80
Maple first leg | 0 | 1 | 12.40
Oak longer leg | 1 | 3 | 28.60
Pine middle leg | 1 | 2 | 11.20
Birch final leg | 2 | 3 | 14.30
Setting: Destination stop index (origin is 0) = 3. Expected summary: 37.9 $ minimum entered path fare.
The through quote costs 47.80. Splitting at stop one costs 12.40 + 28.60 = 41.00. The three-edge path costs 12.40 + 11.20 + 14.30 = 37.90, the minimum of the entered complete paths. That difference is conditional on all those ticket combinations actually being valid and available; the app has not checked train stops, fare restrictions, connections or booking fees.
Sample B — changed plan
Harbor through | 0 | 3 | 32.15
Orchard first segment | 0 | 2 | 24.20
Spruce end segment | 2 | 3 | 12.10
Setting: Destination stop index (origin is 0) = 3. Expected summary: 32.15 $ minimum entered path fare.
The entered split path totals 36.30, so the through quote is lower at 32.15. Splitting is not inherently cheaper. Only quotes supplied here participate; no missing ticket is assigned a zero fare and no live provider is queried. A cheaper unentered option could exist, while an entered quote could be unavailable by the time a traveler books.
Sample C — boundary convention
East zero segment | 0 | 1 | 0
West continuation | 1 | 3 | 18.25
North direct quote | 0 | 3 | 18.25
Setting: Destination stop index (origin is 0) = 3. Expected summary: 18.25 $ minimum entered path fare.
Two complete entered paths tie at 18.25. The displayed example path uses the direct quote because the tie convention prefers fewer quote edges; the optimal-path count still reports both. The zero segment is a supplied fare, not an inferred free missing connection. Equal fares do not imply equal conditions or passenger protections, which must be checked outside this model.
Optional AI formatting, never the calculation
Manual entry completes this fare-splice ticket for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a fare-splice ticket. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string", "string"]}], "setting": "string"}. The columns are Quote code | from stop index | to stop index | quoted fare dollars; the setting is Destination stop index (origin is 0). Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.