"""Spike (homemaker-py-2g7.4): Otten/Stockmeyer shape-curve DP vs nm_search.

Motivation (DESIGN.md §37, plan point 2): the inner loop answers "does some
equal-offset ratio assignment clear the size/width/proportion FAIL_THRESHOLD
for every leaf" by an 80-200 eval Nelder-Mead search per topology. The
classic slicing-floorplan result answers the size/width/proportion family of
this question EXACTLY in one bottom-up pass: each leaf's feasible (width,
height) region is bounded by an area hyperbola (``quality_size``), a min-width
line (``quality_width``), and an aspect-ratio wedge (``quality_proportion``) --
all three are FAIL_THRESHOLD-inversions of the Gaussian/clipped-Gaussian
factors in ``fitness.py`` (see ``leaf_constraints`` below). These per-leaf
regions compose bottom-up through the slicing tree: a node's cut ALWAYS sums
its two children's contributions into the node's own "w" (edge0+edge2)
dimension, with "h" (edge1+edge3) the shared/cross dimension -- a fixed
convention of ``geometry.py``'s division formula, no per-node ambiguity.
The only variable is which of a CHILD's own (w, h) plays which role, an
EXACT function of that child's ``rotation`` parity -- see ``_child_contrib``.

Approximations made explicit (the plan's caveats, DESIGN.md §37 point 2):

  * Every quad (leaf or internal) is approximated by a rectangle with the
    same edge-length-derived (w, h) as ``geometry.aspect`` uses --
    ``(edge0+edge2)/2`` and ``(edge1+edge3)/2`` -- exact only for a true
    rectangle/parallelogram; harbor-house-l0's plot is a near-rectangular
    trapezoid (DESIGN.md says "harbor plot is a near-rect quad"), so this is
    the intended first target, not a general solution for skew quads. This
    is deliberately NOT the quad's axis-aligned bounding box in global x/y --
    an earlier version used that and was wrong for any quad whose (locally
    orthogonal, per Urb's Straighten lineage -- see ``_dims``) walls aren't
    near-parallel to the plot's global x/y axes; edge lengths are
    rotation-invariant by construction.
  * Composition itself (which of a child's local w/h sums into its parent's
    w) is NOT approximated or measured -- an earlier version measured it
    empirically per node (comparing children's summed dims against the
    parent's) and that REGRESSED accuracy (99.0% -> 95.5% on the 200-
    topology validation, with a spurious false negative). It's an exact
    algebraic identity determined purely by ``child.rotation % 2`` -- see
    ``_child_contrib`` and the Stage 2 note above ``_dims``.
  * Leaf curves are EXACT closed forms (hyperbola/line/wedge intersection --
    no discretisation error). Internal-node composition is done on a shared
    discretised grid (log-spaced) with linear interpolation -- this is where
    approximation error enters, and is quantified in ``validate.py``.
  * ``leaf_sharing``/``co_type`` (multi-use leaves) target-adjustment is NOT
    modelled -- ``leaf_constraints`` uses each leaf's own type's base params
    only. harbor-house-l0's programme does not exercise these, so this is a
    scoping simplification, not a validated-safe omission for programmes that
    do.

Only the size/width/proportion family is modelled -- crinkliness, access,
adjacency, level/vertical connectivity are graph/topology terms, not per-leaf
shape, and are explicitly out of scope (DESIGN.md §37 point 2 caveat).
"""

from __future__ import annotations

import math
import warnings
from dataclasses import dataclass

import numpy as np

from homemaker_layout import dom as dom_mod
from homemaker_layout import geometry

# sqrt(2*ln(10)): FAIL_THRESHOLD=0.1 inversion of a unit-height Gaussian,
# gaussian(x,1,target,sigma) >= 0.1  <=>  |x-target| <= K*sigma.
_K = math.sqrt(2.0 * math.log(10.0))

Interval = tuple[float, float] | None  # None = infeasible


def _interval_add(a: Interval, b: Interval) -> Interval:
    if a is None or b is None:
        return None
    return (a[0] + b[0], a[1] + b[1])


# --------------------------------------------------------------------------- #
# Per-leaf feasible region (exact closed form; FAIL_THRESHOLD inversion of
# fitness.py's quality_size/quality_width/quality_proportion).
# --------------------------------------------------------------------------- #


@dataclass
class LeafBounds:
    amin: float
    amax: float
    wmin: float
    rmax: float  # max aspect ratio (>= 1)

    def h_range(self, w: float) -> Interval:
        if w < self.wmin - 1e-12:
            return None
        lo = self.wmin
        if self.amin > 0:
            lo = max(lo, self.amin / w)
        lo = max(lo, w / self.rmax)
        hi = w * self.rmax
        if self.amax < math.inf:
            hi = min(hi, self.amax / w)
        if lo > hi + 1e-12:
            return None
        return (lo, hi)

    def w_range(self, h: float) -> Interval:
        # symmetric in (w, h) -- same box+hyperbola+wedge shape.
        return self.h_range(h)

    def range_grid(self, grid: np.ndarray) -> list[Interval]:
        """Vectorised ``h_range``/``w_range`` (symmetric) over a whole grid."""
        lo = np.maximum(self.wmin, grid / self.rmax)
        if self.amin > 0:
            lo = np.maximum(lo, self.amin / grid)
        hi = grid * self.rmax
        if self.amax < math.inf:
            hi = np.minimum(hi, self.amax / grid)
        feasible = (grid >= self.wmin - 1e-12) & (lo <= hi + 1e-12)
        return [(float(lo[i]), float(hi[i])) if feasible[i] else None for i in range(len(grid))]


def leaf_constraints(fit, leaf: dom_mod.Node) -> LeafBounds:
    """FAIL_THRESHOLD-inverted (amin, amax, wmin, rmax) for one leaf.

    Mirrors the branching of ``Fitness.quality_size``/``quality_width``/
    ``quality_proportion`` (fitness.py) but returns the (target, sigma)-derived
    hard bounds instead of evaluating a Gaussian against actual geometry.
    Ignores leaf-sharing/co_type target adjustment (see module docstring).
    """
    t0 = leaf.type[0].lower() if leaf.type else ""

    # --- size -> (amin, amax) ---
    if t0 in ("o", "s"):
        amin, amax = 0.0, math.inf
    else:
        params = fit.conf("size_circulation") if t0 == "c" else fit.get_space_params(leaf.type, "size")
        target, sigma = params[0], params[1]
        # NB: quality_size's ``target > 0`` gate governs only the leaf-sharing/
        # co_type k-scaling of (target, sigma) (not modelled here, see module
        # docstring) -- the underlying gaussian(area, target, sigma) test
        # always applies, including target==0 (e.g. size_circulation's [0.0,
        # 14.0] default: a real one-sided "as small as possible" constraint,
        # not "unconstrained").
        amin, amax = max(0.0, target - _K * sigma), target + _K * sigma

    # --- width -> wmin ---
    if (
        t0 in ("o", "s")
        and not dom_mod.is_covered(leaf)
        and not dom_mod.is_supported(leaf)
        and dom_mod.level_of(leaf)
    ):
        wmin = 0.0
    else:
        if t0 in ("o", "s"):
            params = fit.conf("width_outside")
        elif t0 == "c":
            params = fit.conf("width_circulation")
        else:
            params = fit.get_space_params(leaf.type, "width")
        target, sigma = params[0], params[1]
        wmin = max(0.0, target - _K * sigma)

    # --- proportion -> rmax ---
    if t0 in ("o", "s"):
        params = fit.conf("proportion_outside")
    elif t0 == "c":
        params = fit.conf("proportion_circulation")
    else:
        params = fit.get_space_params(leaf.type, "proportion")
    target, sigma = params[0], params[1]
    rmax = max(1.0 + 1e-9, target + _K * sigma)

    return LeafBounds(amin=amin, amax=amax, wmin=wmin, rmax=rmax)


# --------------------------------------------------------------------------- #
# Local-edge-length dimensions + EXACT rotation-parity composition.
#
# NB (fixed after initial review, in two stages):
#
# Stage 1: the first version measured (w, h) from each quad's axis-aligned
# bounding box in GLOBAL x/y -- correct only when the plot/walls happen to be
# near-parallel to the global axes (true for harbor-house-l0's near-
# rectangular trapezoid, ~7.5% bbox-area error there, but WRONG in general: a
# perfectly rectangular room whose walls run at 45 deg to the survey/CRS axes
# gets a bbox up to 2x its true area -- confirmed by rotating harbor-house-l0's
# plot 45 deg: bbox area error jumped from 7.5% to 102%). Urb's Perl ancestor
# (Urb::Quad::Straighten/Straighten_Root) keeps internal walls mutually
# orthogonal but NEVER assumes them axis-aligned; this port's equal-offset
# division convention gives that same local straightness for free, so each
# node's own 4 corners already form a near-rectangle in ITS OWN frame
# regardless of the plot's global orientation -- (edge0+edge2)/2 and
# (edge1+edge3)/2 (the pairing geometry.aspect() uses) measure that local
# rectangle's two dimensions with no global-axis dependency (``_dims``).
#
# Stage 2: switching to local edge lengths alone was NOT sufficient and
# initially REGRESSED accuracy (99.0% -> 95.5% on the harbor-house-l0 200-
# topology validation, with a false negative appearing for the first time).
# Root cause: geometry.coordinate() applies a node's OWN ``rotation`` field
# even when reading ITS OWN corners as inherited from its parent -- a node
# with odd rotation has its local edge0/edge2 pair correspond to its PARENT's
# edge1/edge3 pair instead of edge0/edge2 (rotation parity selects between a
# quad's two possible opposite-edge pairings). A prior version tried to
# detect this empirically (comparing children's summed dims against the
# parent's, picking whichever of two hypotheses fit better) -- but the
# relationship is not a matter of degree to be measured, it's an EXACT
# algebraic identity determined purely by ``child.rotation % 2``: verified
# numerically (float-exact) that ``left.w + right.h == parent.w`` whenever
# left.rotation is even and right.rotation is odd (and the symmetric case
# generally), for ANY topology, independent of skew or global orientation.
# ``_child_contrib`` below applies this directly -- no geometry measurement,
# no baseline-ratio pass, no heuristic threshold.
# --------------------------------------------------------------------------- #


def _dims(n: dom_mod.Node) -> tuple[float, float]:
    """Rotation-invariant (w, h) of a quad from its own edge lengths (mirrors
    the (edge0+edge2) vs (edge1+edge3) pairing ``geometry.aspect`` uses)."""
    w = (geometry.edge_length(n, 0) + geometry.edge_length(n, 2)) / 2
    h = (geometry.edge_length(n, 1) + geometry.edge_length(n, 3)) / 2
    return (w, h)


# --------------------------------------------------------------------------- #
# The DP itself
# --------------------------------------------------------------------------- #


@dataclass
class Curve:
    """A node's feasible region, both ways: w_of_h[i] is the feasible w-range
    at h=grid[i]; h_of_w[j] is the feasible h-range at w=grid[j]. Same shared
    grid at every node, so composition needs no cross-node interpolation."""

    w_of_h: list[Interval]
    h_of_w: list[Interval]


def _interp_range(grid: np.ndarray, arr: list[Interval], x: float) -> Interval:
    if x <= grid[0]:
        return arr[0]
    if x >= grid[-1]:
        return arr[-1]
    j = int(np.searchsorted(grid, x)) - 1
    j = max(0, min(j, len(grid) - 2))
    a, b = arr[j], arr[j + 1]
    if a is None or b is None:
        return a if x - grid[j] < grid[j + 1] - x else b
    t = (x - grid[j]) / (grid[j + 1] - grid[j])
    return (a[0] * (1 - t) + b[0] * t, a[1] * (1 - t) + b[1] * t)


def _invert(grid: np.ndarray, arr: list[Interval]) -> list[Interval]:
    """Given arr[i] = feasible cross-range at grid[i], return the inverse:
    inv[j] = {y : arr's cross-range at y contains grid[j]}, assumed contiguous
    in y (true for the monotonic hyperbola/line/wedge-composed regions this
    DP produces). O(N^2) but numpy-vectorised (the naive Python double loop
    was ~70% of total DP wall-clock, profiled on harbor-house-l0)."""
    lo_arr = np.array([r[0] if r is not None else np.nan for r in arr])
    hi_arr = np.array([r[1] if r is not None else np.nan for r in arr])
    # mask[i, j]: does grid[i]'s range contain grid[j]?
    mask = (lo_arr[:, None] - 1e-9 <= grid[None, :]) & (hi_arr[:, None] + 1e-9 >= grid[None, :])
    grid_masked = np.where(mask, grid[:, None], np.nan)
    any_feasible = mask.any(axis=0)
    with np.errstate(invalid="ignore"), warnings.catch_warnings():
        warnings.simplefilter("ignore", category=RuntimeWarning)
        inv_lo = np.where(any_feasible, np.nanmin(grid_masked, axis=0), np.nan)
        inv_hi = np.where(any_feasible, np.nanmax(grid_masked, axis=0), np.nan)
    return [None if np.isnan(lo) else (float(lo), float(hi)) for lo, hi in zip(inv_lo, inv_hi)]


def make_grid(wmax: float, n: int = 400, wmin: float = 0.1) -> np.ndarray:
    return np.geomspace(wmin, wmax, n)


def _child_contrib(curve: "Curve", rotation: int) -> list[Interval]:
    """The child's curve, reinterpreted in the PARENT's frame: parent.w is
    ALWAYS the sum of its two children's ``_child_contrib`` (see module
    docstring) -- even rotation contributes the child's own w_of_h directly;
    odd rotation swaps w<->h (child.h sums; child.w is the one that
    approximates the parent's shared/cross dimension)."""
    return curve.w_of_h if rotation % 2 == 0 else curve.h_of_w


@dataclass
class Feasibility:
    feasible: bool
    h_range_at_w: Interval
    w_range_at_h: Interval


def check_feasible(root_curve: Curve, grid: np.ndarray, w_plot: float, h_plot: float) -> Feasibility:
    hr = _interp_range(grid, root_curve.h_of_w, w_plot)
    wr = _interp_range(grid, root_curve.w_of_h, h_plot)
    ok_h = hr is not None and hr[0] - 1e-6 <= h_plot <= hr[1] + 1e-6
    ok_w = wr is not None and wr[0] - 1e-6 <= w_plot <= wr[1] + 1e-6
    return Feasibility(feasible=bool(ok_h or ok_w), h_range_at_w=hr, w_range_at_h=wr)


# --------------------------------------------------------------------------- #
# Top-down back-substitution: realise one feasible point as division ratios.
# --------------------------------------------------------------------------- #


def realise(
    node: dom_mod.Node,
    curves: dict[int, tuple[Curve, Curve]],
    grid: np.ndarray,
    w: float,
    h: float,
) -> None:
    """Write ``division`` on every free branch under ``node`` so its subtree
    realises the (w, h) target, given each descendant's precomputed curves.
    ``curves[id(n)] = (left_curve, right_curve)`` for internal nodes.

    ``node.w`` (the summed dimension) is ALWAYS ``w`` -- the parent-child cut
    convention is fixed (see module docstring), not orientation-dependent.
    Only each CHILD's rotation parity determines which of ITS OWN (w, h) the
    allocated share becomes: even rotation -> child's own w; odd rotation ->
    child's own h (the two are swapped for that recursive call).
    """
    if not node.divided:
        return
    cl, cr = curves[id(node)]
    contrib_l = _child_contrib(cl, node.left.rotation)
    contrib_r = _child_contrib(cr, node.right.rotation)
    rl = _interp_range(grid, contrib_l, h)
    rr = _interp_range(grid, contrib_r, h)
    lo = max(rl[0], w - rr[1])
    hi = min(rl[1], w - rr[0])
    wl = min(max((lo + hi) / 2.0, rl[0]), rl[1])
    wl = min(max(wl, w - rr[1]), w - rr[0])
    wr = w - wl
    t = wl / w if w > 0 else 0.5
    node.division = [t, t]
    if node.left.rotation % 2 == 0:
        realise(node.left, curves, grid, wl, h)
    else:
        realise(node.left, curves, grid, h, wl)
    if node.right.rotation % 2 == 0:
        realise(node.right, curves, grid, wr, h)
    else:
        realise(node.right, curves, grid, h, wr)


def build_curves_with_children(
    node: dom_mod.Node, fit, grid: np.ndarray,
    out: dict[int, tuple[Curve, Curve]],
) -> Curve:
    """Bottom-up: leaf curves are exact closed forms; internal nodes compose
    on ``grid`` via the EXACT rotation-parity rule (``_child_contrib``), also
    recording each internal node's (left, right) curves in ``out`` for
    ``realise`` to consume."""
    if not node.divided:
        b = leaf_constraints(fit, node)
        w_of_h = h_of_w = b.range_grid(grid)
        return Curve(w_of_h=w_of_h, h_of_w=h_of_w)

    cl = build_curves_with_children(node.left, fit, grid, out)
    cr = build_curves_with_children(node.right, fit, grid, out)
    out[id(node)] = (cl, cr)
    contrib_l = _child_contrib(cl, node.left.rotation)
    contrib_r = _child_contrib(cr, node.right.rotation)
    w_of_h = [_interval_add(contrib_l[i], contrib_r[i]) for i in range(len(grid))]
    h_of_w = _invert(grid, w_of_h)
    return Curve(w_of_h=w_of_h, h_of_w=h_of_w)


def solve(level_root: dom_mod.Node, fit, grid_n: int = 150) -> tuple[bool, dict]:
    """End-to-end: compute plot dims, build curves, check root feasibility,
    and (if feasible) write realising ratios in place. Returns (feasible,
    info) where info carries timing-relevant intermediates for the caller."""
    w_plot, h_plot = _dims(level_root)
    grid = make_grid(max(w_plot, h_plot) * 1.2, n=grid_n)

    curves_by_node: dict[int, tuple[Curve, Curve]] = {}
    root_curve = build_curves_with_children(level_root, fit, grid, curves_by_node)

    feas = check_feasible(root_curve, grid, w_plot, h_plot)
    if feas.feasible:
        realise(level_root, curves_by_node, grid, w_plot, h_plot)
        geometry.clear_cache()
    return feas.feasible, {
        "w_plot": w_plot, "h_plot": h_plot,
        "grid": grid, "h_range_at_w": feas.h_range_at_w, "w_range_at_h": feas.w_range_at_h,
    }