sequenceDiagram
    participant S as Solver
    participant M as MarkerMerger
    participant P as Package

    S->>M: merge_override_packages(override_packages)
    activate M
    M->>M: Group packages by identity
    M->>M: Check if markers are same across overrides
    alt Markers are same
        M->>M: Apply performance shortcut
        M->>M: Union override markers once
    else Markers differ
        M->>M: Apply general algorithm
        M->>M: Iteratively merge markers
    end
    M->>P: Update package dependencies
    M-->>S: Return merged packages
    deactivate M

classDiagram
    class Package {
        +requires: List[Dependency]
        +add_dependency(dep)
    }

    class TransitivePackageInfo {
        +depth: int
        +groups: Set
        +markers: Dict
    }

    class BaseMarker {
        +intersect(other)
        +union(other)
        +without_extras()
    }

    class Solver {
        -_provider: Provider
        +_solve_in_compatibility_mode(overrides)
        +_solve()
    }

    Package -- TransitivePackageInfo
    TransitivePackageInfo -- BaseMarker
    Solver -- Package

    note for TransitivePackageInfo "Stores package metadata and markers"
    note for BaseMarker "Handles marker operations with improved performance"

graph TD
    A[Start] --> B[Collect all packages and overrides]
    B --> C{Are markers same\nfor all overrides?}
    C -->|Yes| D[Use performance shortcut]
    C -->|No| E[Use general algorithm]
    D --> F[Union override markers]
    F --> G[Intersect with package markers]
    E --> H[Iteratively merge markers]
    H --> I[Union with existing markers]
    G --> J[Update package dependencies]
    I --> J
    J --> K[End]