Matrix-chain cost planning
The same matrix product can take different amounts of arithmetic. ChainArbor connects dimension fixtures to an AI project discussion so you can inspect the cost recurrence before implementing a multiplication strategy.
def chain_cost(dimensions):
if type(dimensions) not in (list, tuple) or not 2 <= len(dimensions) <= 13:
raise ValueError("one through twelve matrices")
if any(type(d) is not int or not 1 <= d <= 1000 for d in dimensions):
raise ValueError("dimensions 1 through 1000")
n = len(dimensions)-1
cost = [[0]*n for _ in range(n)]
for width in range(2, n+1):
for left in range(n-width+1):
right = left+width-1
cost[left][right] = min(
cost[left][k]+cost[k+1][right]+
dimensions[left]*dimensions[k+1]*dimensions[right+1]
for k in range(left,right))
return cost[0][n-1]| Project | Test one matrix and different parenthesizations, rejecting dimensions outside 1 through 1000 without multiplying any matrix entries. |
|---|---|
| Review before applying | Compare actual behavior with the expected result. If a check fails, investigate it before applying more changes. |
| Connection | Base URL, credentials and a reachable server. |
def chain_cost(dimensions):
if type(dimensions) not in (list, tuple) or not 2 <= len(dimensions) <= 13:
raise ValueError("one through twelve matrices")
if any(type(d) is not int or not 1 <= d <= 1000 for d in dimensions):
raise ValueError("dimensions 1 through 1000")
n = len(dimensions)-1
cost = [[0]*n for _ in range(n)]
for width in range(2, n+1):
for left in range(n-width+1):
right = left+width-1
cost[left][right] = min(
cost[left][k]+cost[k+1][right]+
dimensions[left]*dimensions[k+1]*dimensions[right+1]
for k in range(left,right))
return cost[0][n-1]Separate a computed plan from the work it represents
ChainArbor gives computational planning work a Windows coding workspace where you can discuss assumptions with a connected model. Begin by identifying what a planning function actually returns and who consumes it. A cost estimate, an execution order and an executed operation are different outputs, and a useful change request makes that distinction explicit.
Matrix-chain cost planning is the supplied example task. You could ask the assistant to review dimension validation and the reported arithmetic cost before extending the surrounding application. Include the caller and its expectations so a proposed edit does not accidentally present a minimum cost as though it were a multiplication schedule or completed matrix result.
Use the conversation to expose those interface decisions, then inspect the resulting source changes. Check small dimension sequences with independently established costs, including the single-matrix case, and run the project's own tests. If you later request an execution plan, treat its representation and verification as additional requirements rather than assume they follow from a cost calculation.
For unfiltered AI model choice, connect a supported OpenAI-compatible or Anthropic service that offers the model you want. Credentials, tool support and context limits depend on that setup. The workspace does not override provider restrictions; it helps keep proposed planning changes connected to source and acceptance criteria you can review.
Questions that clarify planning-code scope
What should I ask for if I need an execution order?
Request an explicit representation of the order and describe how the caller will use it. A function that reports minimum arithmetic cost may not produce that representation. Include verification examples for both the plan and its reported cost.
Why test a chain containing just one matrix?
It defines the base behavior when no multiplication is needed. Include that case alongside a small multi-matrix example so the assistant's proposal is checked against both the boundary and the planning logic used for longer chains.
Can the workspace verify actual numerical matrix results?
Use your project's numerical tools and tests for those results. The coding workspace supports discussion and review of proposed changes; a correct cost fixture does not establish that a separate multiplication implementation produces correct values.
How do I prevent a cost refactor from expanding its interface?
State the current return type and required caller behavior in the request. Review the diff for new outputs or changed units. If a richer plan is wanted, define it as a deliberate follow-up rather than an incidental refactor.
ChainArbor · Updated 2026-10-25