# This file contains routines from Lisbon Machine Learning summer school.
# The code is freely distributed under a MIT license. https://github.com/LxMLS/lxmls-toolkit/

import numpy as np
import sys
from collections import defaultdict, namedtuple
from operator import itemgetter


def parse_proj(scores, gold=None):
    '''
    Parse using Eisner's algorithm.
    '''
    nr, nc = np.shape(scores)
    if nr != nc:
        raise ValueError("scores must be a squared matrix with nw+1 rows")

    N = nr - 1 # Number of words (excluding root).

    # Initialize CKY table.
    complete = np.zeros([N+1, N+1, 2]) # s, t, direction (right=1). 
    incomplete = np.zeros([N+1, N+1, 2]) # s, t, direction (right=1). 
    complete_backtrack = -np.ones([N+1, N+1, 2], dtype=int) # s, t, direction (right=1). 
    incomplete_backtrack = -np.ones([N+1, N+1, 2], dtype=int) # s, t, direction (right=1).

    incomplete[0, :, 0] -= np.inf

    # Loop from smaller items to larger items.
    for k in xrange(1,N+1):
        for s in xrange(N-k+1):
            t = s+k
            
            # First, create incomplete items.
            # left tree
            incomplete_vals0 = complete[s, s:t, 1] + complete[(s+1):(t+1), t, 0] + scores[t, s] + (0.0 if gold is not None and gold[s]==t else 1.0)
            incomplete[s, t, 0] = np.max(incomplete_vals0)
            incomplete_backtrack[s, t, 0] = s + np.argmax(incomplete_vals0)
            # right tree
            incomplete_vals1 = complete[s, s:t, 1] + complete[(s+1):(t+1), t, 0] + scores[s, t] + (0.0 if gold is not None and gold[t]==s else 1.0)
            incomplete[s, t, 1] = np.max(incomplete_vals1)
            incomplete_backtrack[s, t, 1] = s + np.argmax(incomplete_vals1)

            # Second, create complete items.
            # left tree
            complete_vals0 = complete[s, s:t, 0] + incomplete[s:t, t, 0]
            complete[s, t, 0] = np.max(complete_vals0)
            complete_backtrack[s, t, 0] = s + np.argmax(complete_vals0)
            # right tree
            complete_vals1 = incomplete[s, (s+1):(t+1), 1] + complete[(s+1):(t+1), t, 1]
            complete[s, t, 1] = np.max(complete_vals1)
            complete_backtrack[s, t, 1] = s + 1 + np.argmax(complete_vals1)
        
    value = complete[0][N][1]
    heads = [-1 for _ in range(N+1)] #-np.ones(N+1, dtype=int)
    backtrack_eisner(incomplete_backtrack, complete_backtrack, 0, N, 1, 1, heads)

    value_proj = 0.0
    for m in xrange(1,N+1):
        h = heads[m]
        value_proj += scores[h,m]

    return heads


def backtrack_eisner(incomplete_backtrack, complete_backtrack, s, t, direction, complete, heads):
    '''
    Backtracking step in Eisner's algorithm.
    - incomplete_backtrack is a (NW+1)-by-(NW+1) numpy array indexed by a start position,
    an end position, and a direction flag (0 means left, 1 means right). This array contains
    the arg-maxes of each step in the Eisner algorithm when building *incomplete* spans.
    - complete_backtrack is a (NW+1)-by-(NW+1) numpy array indexed by a start position,
    an end position, and a direction flag (0 means left, 1 means right). This array contains
    the arg-maxes of each step in the Eisner algorithm when building *complete* spans.
    - s is the current start of the span
    - t is the current end of the span
    - direction is 0 (left attachment) or 1 (right attachment)
    - complete is 1 if the current span is complete, and 0 otherwise
    - heads is a (NW+1)-sized numpy array of integers which is a placeholder for storing the 
    head of each word.
    '''
    if s == t:
        return
    if complete:
        r = complete_backtrack[s][t][direction]
        if direction == 0:
            backtrack_eisner(incomplete_backtrack, complete_backtrack, s, r, 0, 1, heads)
            backtrack_eisner(incomplete_backtrack, complete_backtrack, r, t, 0, 0, heads)
            return
        else:
            backtrack_eisner(incomplete_backtrack, complete_backtrack, s, r, 1, 0, heads)
            backtrack_eisner(incomplete_backtrack, complete_backtrack, r, t, 1, 1, heads)
            return
    else:
        r = incomplete_backtrack[s][t][direction]
        if direction == 0:
            heads[s] = t
            backtrack_eisner(incomplete_backtrack, complete_backtrack, s, r, 1, 1, heads)
            backtrack_eisner(incomplete_backtrack, complete_backtrack, r+1, t, 0, 1, heads)
            return
        else:
            heads[t] = s
            backtrack_eisner(incomplete_backtrack, complete_backtrack, s, r, 1, 1, heads)
            backtrack_eisner(incomplete_backtrack, complete_backtrack, r+1, t, 0, 1, heads)
            return

