k-Subset Sum Optimization API

API ID 13201

High-speed analytical C++ engine to solve the subset sum problem with exact cardinality constraint (k-Subset Sum). Instantly processes massive instances with giant integers of up to 1000 bits in a constant time of 3 seconds with absolute zero error. Perfect for logistics payload optimization, indexed portfolio balancing, and manufacturing stock-cutting waste reduction.

API Documentation

Endpoints

Request

"a" (Array of Strings): The input set of numbers. It supports arbitrary-precision integers with no limits on digits (e.g., 10, 100, or 1000+ digits per number) and no size limitations on the array (e.g., 10, 100, or 1000+ elements). Both positive and negative integers are supported. Note on Decimals: If your dataset includes decimal numbers, you must scale them into integers before sending the request. For example, multiply all numbers by 1,000 if you have up to 3 decimal places, or by 100,000 for up to 5 decimal places, and scale your target accordingly.

"target" (String): The target sum you want to approximate or achieve. Just like the array elements, it must be sent as a string to support arbitrary-precision numbers (up to 1000+ digits) without losing decimal precision or encountering bits overflow.

"nelem" (Integer): The exact number of elements (cardinality) required in the resulting subset.

"timeoutinmiliseconds" (Integer): The execution time limit in milliseconds (e.g., 3000 for 3 seconds). If the timeout is reached before completing the exhaustive search, the engine will safely halt and return the best solutions discovered up to that millisecond.

The API returns a JSON object containing two optimal subsets: "less": The subset of elements whose sum is closest to, and less than or equal to, the target. "greater": The subset of elements whose sum is closest to, and greater than or equal to, the target.

The response also includes the execution time taken by the high-speed C++ engine.

Endpoint ID: 26939
POST https://zylalabs.com/api/13201/k-subset+sum+optimization+api/26939/find+the+elements+with+sum+closest+to+a+target
INPUT PARAMETERS

Find the elements with sum closest to a target — Endpoint Features

Object Description
Request Body Required Json

Free test requests remaining: 3 of 3.


INPUT PARAMETERS

API EXAMPLE RESPONSE
JSON
{"less":{"a":["8","50"],"e":0,"error":"0","sum":"58"},"greater":{"a":["8","50"],"e":0,"error":"0","sum":"58"},"execution_miliseconds":0,"status":"success"}
Find the elements with sum closest to a target — CODE SNIPPETS

curl --location --request POST 'https://zylalabs.com/api/13201/k-subset+sum+optimization+api/26939/find+the+elements+with+sum+closest+to+a+target' --header 'Authorization: Bearer YOUR_API_KEY' 

--data-raw '{
	"a": [ "1", "2", "4", "8", "50" ],
	"target": "58",
	"nelem": 2,
	"timeoutinmiliseconds": 3000
}'

    

API Access Key & Authentication

After signing up, every developer is assigned a personal API access key, a unique combination of letters and digits provided to access to our API endpoint. To authenticate with the k-Subset Sum Optimization API simply include your bearer token in the Authorization header.

Headers
Header Description
Authorization Required Should be Bearer access_key. See "Your API Access Key" above when you are subscribed.

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Overview

High-Speed Arbitrary-Precision k-Subset Sum Optimizer

This API calculates the exact or closest subsets of integers that sum to a specific target value under strict cardinality constraints (k elements). The underlying engine is implemented in C++ and uses pruning algorithms and parallel processing to handle large datasets.
 
Technical Features
  • Arbitrary Precision: Supports integer inputs of arbitrary length (10, 100, 1000+ digits) without bit overflow, bypassing standard primitive data type limits.
  • Dataset Scale: Processes arrays containing thousands of elements.
  • Multi-Threaded Execution: Computes subset combinations in parallel with configurable timeout constraints.
  • Dual-Bound Output: Returns two distinct subsets simultaneously: the closest exact or approximate match bounded below the target, and the closest match bounded above the target.
Data Format Requirements
To maintain numeric precision and avoid floating-point truncation across different programming languages, all numeric inputs (array elements and target values) must be formatted and transmitted as text strings.
 
Handling Decimals
This engine operates exclusively on integers. To process datasets with floating-point decimals, scale the input array and the target value by a power of 10 (e.g., multiply by 1,000 for 3 decimal places) to convert all values into whole numbers before submission.
 
Applicable Domains
  • Logistics: Payload balancing and container packing optimization.
  • Finance: Index-tracking portfolio rebalancing and exact risk-exposure matching.
  • Manufacturing: Cutting-stock optimization for material waste reduction.

k-Subset Sum Optimization API FAQs

The API returns a JSON object containing two optimal subsets: "less" and "greater." Each subset includes an array of strings representing the elements that sum closest to, but less than or equal to, and greater than or equal to the target, respectively.

The key fields in the response include "less" and "greater," each containing an array "a" of selected elements, "e" for the number of elements, "error" for any processing errors, and "sum" for the total of the subset. Additionally, "execution_miliseconds" indicates the processing time.

The response data is structured as a JSON object with two main sections: "less" and "greater." Each section contains the subset of elements, their count, any errors encountered, the sum of the elements, and the execution time, allowing for easy parsing and utilization.

The endpoint accepts four parameters: "a" (array of strings for input numbers), "target" (string for the target sum), "nelem" (integer for the required number of elements), and "timeoutinmiliseconds" (integer for execution time limit). Each parameter customizes the request for specific needs.

Users can customize their requests by adjusting the "target" value to specify the desired sum, setting "nelem" to define the exact number of elements in the subset, and using "timeoutinmiliseconds" to control the maximum execution time, ensuring tailored results.

Typical use cases include logistics for payload balancing, finance for portfolio rebalancing, and manufacturing for optimizing cutting stock to reduce waste. The API efficiently handles large datasets, making it suitable for complex optimization problems in these domains.

Data accuracy is maintained through the use of arbitrary precision for integer inputs, ensuring no overflow occurs. The C++ engine employs advanced pruning algorithms and parallel processing, which enhances the reliability of the results returned by the API.

If the API cannot find a valid subset that meets the criteria, it will return the best solutions discovered up to the timeout. Users should check the "error" field in the response to understand any issues and utilize the "less" and "greater" subsets for the closest matches available.

The API can process both positive and negative integers of arbitrary precision, allowing for inputs with 10, 100, or even 1000+ digits. This capability ensures that users can work with very large numbers without encountering overflow issues.

If the execution time exceeds the specified "timeoutinmiliseconds," the API will halt processing and return the best solutions found up to that point. Users can check the "error" field to understand if a timeout occurred and utilize the available "less" and "greater" subsets.

The API operates exclusively on integers. To use decimal numbers, users must scale their inputs by a power of 10 to convert them into whole numbers before submission, ensuring compatibility with the API's requirements.

The "nelem" parameter specifies the exact number of elements required in the resulting subset. This allows users to tailor their requests to meet specific cardinality constraints, ensuring the output aligns with their optimization needs.

The API utilizes a high-speed C++ engine that employs advanced pruning algorithms and multi-threaded execution. This design enables it to process large datasets quickly, achieving results in a constant time of approximately 3 seconds.

Users should check the "error" field in the response to identify any issues encountered during processing. This field provides insights into what went wrong, allowing users to adjust their input parameters or data accordingly.

The "execution_miliseconds" field indicates the time taken by the API to process the request. This metric helps users assess performance and efficiency, especially when working with large datasets or tight time constraints.

The "less" subset provides elements that sum closest to but do not exceed the target, useful for scenarios like budget constraints. The "greater" subset offers elements that meet or exceed the target, ideal for maximizing resource allocation in logistics and finance.

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