/**
 * @file src/tableau/mip-utils.ts
 * @description Mixed-integer programming utility functions
 *
 * Provides helper functions for MIP solving:
 * - Checking integrality of current solution
 * - Variable selection for branching (most fractional, etc.)
 * - Fractional volume computation
 *
 * Functions are designed to be bound to a Tableau instance via `this`.
 */
import type Tableau from "./tableau";
import type { VariableValue } from "./types";
/**
 * Count how many integer variables currently have integral values.
 */
export declare function countIntegerValues(this: Tableau): number;
/**
 * Check if all integer variables have integral values.
 * Returns true if the current solution is integral.
 */
export declare function isIntegral(this: Tableau): boolean;
/**
 * Compute a measure of how fractional the current solution is.
 * Used for evaluating the quality of cutting planes.
 */
export declare function computeFractionalVolume(this: Tableau, ignoreIntegerValues?: boolean): number;
/**
 * Select the integer variable with the most fractional value.
 * Standard branching strategy - picks the variable closest to 0.5 fractionality.
 */
export declare function getMostFractionalVar(this: Tableau): VariableValue;
/**
 * Select the fractional integer variable with the lowest cost coefficient.
 * Alternative branching strategy that considers objective function impact.
 */
export declare function getFractionalVarWithLowestCost(this: Tableau): VariableValue;