'''
Function generates all paths through the ball triangle
    Return: Dictionary with path name and nodes
    Input: Array of the node indices in the different layers
'''

import pandas as pd
from collections import defaultdict

def getAllPaths(indexArray = 
    [   [0], 
        [1, 2], 
        [3, 4, 5], 
        [6, 7, 8, 9], 
        [10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19, 20]] ):
   
    pathMatching = pd.DataFrame(columns=['name','path'])

    for layer, nodes in enumerate(indexArray):
        layerElements = defaultdict(list)
        for node in nodes:
            layerElements[layer] = [node]
        
            for i in range(layer-1,-1, -1):
                elems = []
                for k in layerElements[i+1]:
                    if (k - i - 2) in indexArray[i]:
                        elems.append( k - i - 2)
                    if k-i - 1 in indexArray[i]:
                        elems.append( k - i-1 ) 
                layerElements[i] = list(set(elems))

            elems = []
            for i in range(layer+1):
                if i == 0:
                    elems = [layerElements[i]]
                else:
                    tmp = []
                    for tmpPath in elems:
                        for newElem in layerElements[i]:
                            if newElem == tmpPath[i-1] + i or newElem == tmpPath[i-1] + i + 1:
                                thisPath = tmpPath.copy()
                                thisPath.append(newElem)
                                tmp.append(thisPath)
                                
                    elems = tmp.copy()
            
            for idx, indPath in enumerate(elems):
                name= "choice_" + str(node) + "_" + str(idx)
                pathMatching = pd.concat([pathMatching, pd.DataFrame.from_records([{"node" : int(node), "name":name, "path":indPath}])], ignore_index=True)
    
    pathMatching['combine'] = pathMatching[['name', 'path']].values.tolist()
    return {str(int(key)): value["combine"].tolist() for key, value in pathMatching.groupby("node")}