{"uid":"cap_h0KC3yTnnvzkkcOS9NBSB","slug":"0-1-knapsack-solver-exact-dp-capacity-planning-047ab47c","name":"0/1 Knapsack Solver — Exact DP Capacity Planning","description":"0/1 knapsack solver — exact work-bounded capacity planning and portfolio selection for maximum value, with deterministic ties and reproducible DP evidence.","url":"https://decision-solver.use.x402atlas.com/knapsack","method":"POST","headers":{},"bodySchema":null,"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.005","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.005/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.005","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_VPxKAkVHSUQH7Iu0wJaXn","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.005","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves the 0/1 knapsack problem exactly using dynamic programming, selecting items to maximize total value within a weight/capacity constraint with deterministic tie-breaking and reproducible evidence.","exampleAgentPrompt":"I have 8 projects with different costs and estimated ROI values, and my total budget is $50,000 — use the 0/1 knapsack solver to tell me exactly which projects to fund to maximize total return without going over budget.","exampleUseCases":[{"title":"Sprint backlog capacity planning","prompt":"I have 12 user stories with story point estimates and business value scores, and my sprint capacity is 40 points — which stories should I include to maximize total business value without exceeding capacity?"},{"title":"Investment portfolio selection under budget","prompt":"I have a list of 10 potential investments, each with a cost and an expected return, and I can only spend $100,000 total — find the exact combination that maximizes my expected return."},{"title":"Cargo loading for maximum profit","prompt":"I'm loading a truck that can carry at most 2,000 kg, and I have 15 shipment options each with a weight and a revenue value — which shipments should I take to maximize total revenue?"}],"resultDescription":"Returns the exact optimal subset of items selected, their combined value and weight, a deterministic selection when ties exist, and reproducible dynamic programming evidence (typically the DP table or traceback path) confirming the solution.","failureModes":["Items list is empty or malformed — returns validation error","Capacity value is zero or negative — returns error or trivially empty selection","Very large item counts or capacities may exceed work bounds and return a bounded-work error","Weights or values contain non-numeric or negative entries — returns input validation error","Missing required fields in request body — returns 400-level error"],"whenToPreferThis":"Choose this endpoint when you need an exact optimal solution to a 0/1 knapsack problem (each item selected at most once) with full DP evidence and deterministic tie-breaking. Prefer it over heuristic bin-packing when correctness and reproducibility matter more than speed at large scale. Use it for budget/capacity planning, portfolio selection, or any scenario where you must maximize value under a hard capacity constraint and need a provably optimal, auditable answer.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T00:32:14.116Z","isFirstParty":false}