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#https://docs.python.org/2/tutorial/datastructures.html
from collections import deque

def bfs(g, root_node):
    """ Implementation of a breadth first search (BFS)
    BFS is useful e.g. when we need to find a route between 
    It is NOT recursive
    
    Algo:
    1. Enqueue root node;

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def dfs(g, curr_node, visited=None):
    """
    
    Parameters
    ----------
    graph: dictionary
        dictionary of nodes and its neighbors
    node: list
    
    Returns

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class GraphNode:
    
    def __init__(self, value, neighbors):
        """Initialize graph node
        
        Parameters
        ----------
        
        name: str
            node identifier

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import numpy as np

def linear_regression(x, y, lr=1.0e-4, n_steps=10000, lr_decay=0.5):
    """Solves 1 dimensional regression problem: provides w=(w_1, ..., w_n) such that:
    
    w* = min_{w} sum_{i=1}{m}[(<w, x_i> - y_i)**2]  (mean squared error)
    
    L(w) = sum_{i=1}{m}[(<w, x_i> - y_i)**2]
    
    <w, x_i> = w_1*x_{i1} + w_2*x_{i2} + ... w_n*x_{in}

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import numpy as np

def linear_regression_1d(x, y):
    """Solves 1 dimensional regression problem: provides w=(w_1, ..., w_n) such that:
    
    w* = min_{w} sum_{i=1}{m}[(<w, x_i> - y_i)**2]
    
    L(w) = sum_{i=1}{m}[(<w, x_i> - y_i)**2]
    
    <w, x_i> = w_1*x_{i1} + w_2*x_{i2} + ... w_n*x_{in}

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class BinaryTreeNode:
    
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

    def insert(self, value):
        "insert elements in the way to maintain binary search tree structure"
        if self.value >= value:

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def set_bit(x, i):
    bi = 0b1 << i
    return x | bi

def xor_bit(x, i):
    bi = 0b1 << i
    return x ^ bi

def clear_bit(x, i):
    bi = ~(0b1 << i)

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def is_permuted_palindrome(s):
    """Checks if the string is a permuted version of a palindrome
    
    Upper case do not matter, spaces can be ignored.
    
    Example:
    
    "cat cat" -> Yes (palindrome: "cat tac")
    "cat do"  -> No
    

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#!/usr/bin/env python
# coding: utf-8

# In[32]:


import numpy as np

def hist_pdf(x, data, n_bins=10, minv=None, maxv=None):
    """Histogram density estimator

sergeyprokudin

import numpy as np

def hist_pdf(x, data, n_bins=10, minv=None, maxv=None):
    """Histogram density estimator
    
    [minv, minv+delta, , minv+delta*2, ..., 1]
    
    for any x in B_l=[minv+delta*j, minv+delta*(j+1)] density is estimated in the following way
    
    p(x) = p(x | x \in B_l) * p(x \in B_l) = (1/delta) * (\sum_{x_j}{I(x_j \in B_l)} / N)