"""ADMM-lite solver utilities for PolicyMesh (minimal MVP).

- This module provides small helpers to perform a toy ADMM-like step and
- to compute a simple synchronization delta for cross-domain coordination.
"""

from typing import Any, Dict


def admm_lite_step(z: Dict[str, float], u: Dict[str, float], rho: float = 1.0) -> Dict[str, Dict[str, float]]:
    # Very small, deterministic update for demonstration purposes
    new_z: Dict[str, float] = {}
    new_u: Dict[str, float] = {}
    for k, val in z.items():
        # pretend we adjust z toward a neutral value 0.0 using rho
        new_z[k] = val - rho * u.get(k, 0.0)
        new_u[k] = u.get(k, 0.0)  # keep dual variable in sync (no-op placeholder)
    return {"z": new_z, "u": new_u}


def delta_sync(local_z: Dict[str, float], remote_z: Dict[str, float]) -> Dict[str, float]:
    # simple max-merge for demonstration
    merged: Dict[str, float] = dict(local_z)
    for k, v in remote_z.items():
        merged[k] = max(merged.get(k, float('-inf')), v)
    return merged