Question 30

You are given a binary tree in which each node contains an integer value.Find the number of paths that sum to a given value.The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).
The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.

root = [10,5,-3,3,2,None,11,3,-2,None,1], sum = 8

      10
     /  \
    5   -3
   / \    \
  3   2   11
 / \   \
3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11

def spilt_array(input_matrix, sum_first_element, array, a):

    if sum_first_element == len(input_matrix):

        array.append(input_matrix)

        return

    left=input_matrix[:sum_first_element]

    right=input_matrix[:sum_first_element]

    a=1

    ele_left=a

    ele_right=a

    for i in input_matrix[sum_first_element:]:

        if i==None:

            i=0

        if ele_left==0 and ele_right==0:

            a*=2

            ele_left=a

            ele_right=a

        if ele_left==0 and ele_right>0:

            right.append(i)

            ele_right-=1

        if ele_left>0:

            left.append(i)

            ele_left-=1

    spilt_array(left, sum_first_element+1, array, a)

    spilt_array(right, sum_first_element+1, array, a)

    return array



def sum_tree(input_matrix,sum_val):

    array=[]

    a=1

    sum_first_element = 1

    result = []

    all_paths = spilt_array(input_matrix, sum_first_element, array, a)

    for i in all_paths:

        if sum(i[1:-1]) == sum_val:

            if i[1:-1] not in result:

                result.append(i[1:-1])

        if sum(i[:-1]) == sum_val:

            if i[:-1] not in result:

                result.append(i[:-1])

        if sum(i[1:]) == sum_val:

            if i[1:] not in result:

                result.append(i[1:])

    return len(result)



if __name__ == "__main__":

    input_matrix = [10,5,-3,3,2,None,11,3,-2,None,1]

    sum_val = 8

    print(sum_tree(input_matrix,sum_val))