def subset_sum_k(k: int, input: list, output: list, index: int) -> None:
# Base Case 1
if k == 0:
print_array_inline(output) # Directly printing it Notice
return
# Base Case 2
if index >= len(input): # Don't proceed further
return
curr_element = input[index]
if curr_element <= k: # Have both options, Include it & Excluding it
# Excluding it
output_when_excluding = list.copy(output)
subset_sum_k(k, input, output_when_excluding,
index + 1) # input, output changed, not k
# Including It
output_when_including = list.copy(output)
output_when_including.append(curr_element) # output, input & k changed
subset_sum_k(k - curr_element, input, output_when_including, index + 1)
else: # Excluding it if > k
output_when_excluding = list.copy(output)
subset_sum_k(k, input, output_when_excluding,
index + 1) # input, output changed, not k
pass
def vertical_order(root):
x_table: Dict[int, list] = dict() # map of number, list
finding_x_for_each_node__level_order(root, x_table)
# for x in sorted(x_table.keys()): <<<<<<<<<<<<< Removing sorting Notice
# print_array_inline(x_table[x])
min_hd, max_hd = float("inf"), float("-inf")
for key in x_table.keys():
min_hd = min(min_hd, key)
max_hd = max(max_hd, key)
for i in range(min_hd, max_hd + 1): # so that we include max_hd as well
print_array_inline(x_table[i])
def sort_nearly_sorted_array(arr, k) -> None:
sorted_arr = [
] # we are not doing it Inplace, but can be done with a little more effor
heap = [] # Empty Min-Heap
heapify(heap)
for element in arr:
heappush(heap, element)
if len(heap) > k:
curr = heappop(heap) # this is the first element of the
sorted_arr.append(curr)
# empty the heap
while len(heap) != 0:
curr = heappop(heap) # this is the first element of the
sorted_arr.append(curr)
print_array_inline(sorted_arr)
def vertical_order(root):
x_table: Dict[int, list] = dict() # map of number, list
finding_x_for_each_node__pre_order(root, x_table)
for x in sorted(x_table.keys()):
print_array_inline(x_table[x])
def frequency_sort(nums):
freq = get_frequencies_in_integer_array(nums)
# Instead of writing a comparison function, we will gonna use Heap, and heapify on the basis of freq
# create an empty heap, (which underline is a list)
heap = [
] # We want to use it as a MaxHeap, so need to negate the value of freq, so that freq comes on top
for number, frequency in freq.items():
heappush(
heap, (-frequency, number)
) # we put frequency first, as we are heapify-ing on the basis of freq
# print(heap)
freq_sorted_array = []
while len(heap) != 0:
frequency, number = heappop(heap)
frequency *= -1 # Making Freq +ve Again
for i in range(frequency):
freq_sorted_array.append(number)
return freq_sorted_array
if __name__ == "__main__":
array = input_array()
f_sorted_array = frequency_sort(array)
print_array_inline(f_sorted_array)
"""
2 5 2 8 5 6 8 8
"""
# Not Inplace
def prefix_sum(array) -> list:
arr = [num for num in array] # making a copy of actual_array # Notice : only change
for i in range(1, len(array)): # From 1 to n-1
arr[i] = arr[i] + arr[i - 1]
return arr
# Via Itertools
def prefix_sum_via_itertools(array):
rolling_sum = itertools.accumulate(array, operator.add)
print(type(rolling_sum))
return list(rolling_sum)
if __name__ == "__main__":
given_array = input_array()
print_array_inline(prefix_sum(given_array))
print_array_inline(prefix_sum_via_itertools(given_array))
"""
Input : 6 3 -2 4 -1 0 -5
Result: 6 9 7 11 10 10 5
Input : 2 1 -2 4 8
Result: 2 3 1 5 13
"""
else:
C.append(B[b])
b += 1
# if B is exhausted then put all the elements of A
while a < len(A):
C.append(A[a])
a += 1
# if A is exhausted then put all the elements of B
while b < len(B):
C.append(B[b])
b += 1
return C
if __name__ == "__main__":
arrA = input_array()
arrB = input_array()
arr = merge_2_sorted_arrays(arrA, arrB)
print_array_inline(arr)
"""
arrA = 1 3 5 7 9
arrB = 0 2 4 6 8
arrA = 1 1 5 5 10
arrB = -1 0 0 1 1 8
"""
# Sort B, by putting B[0] at its correct position in B, to maintain the sorted order of B.
# Note: B[1 ... n-1] is already sorted
for i in range(1, m):
if B[i - 1] > B[i]:
B[i - 1], B[i] = B[i], B[i - 1] # swap
# sort the array B, as it might be distorted :
# Using Insertion sort (as it will take O(n) only) --> as the array is partially sorted only
# Note : You can't just call insertion_sort algorithm, because that will assume all the elements un-sorted
# and will apply sorting on all of them, which will result in O(n^2) time,
# Instead ::: we should just sort this element only by putting it onto the correct location --> O(n) time
if __name__ == "__main__":
arrA = input_array()
arrB = input_array()
merge_2_sorted_arrays_without_space(arrA, arrB)
print_array_inline(arrA)
print_array_inline(arrB)
"""
arrA = 1 3 5 7 9
arrB = 0 2 4 6 8
arrA = 1 1 5 5 10
arrB = -1 0 0 1 1 8
X = 1 4 7 8 10
Y = 2 3 9
"""
# Induction
if nums[n - 1] == key: # last element is similar to key
all_indices.append(n - 1)
def find_index_of_all_occurrence__backward(nums, key) -> List[int]:
all_indices = []
find_all_occurrence__backward(nums, key, len(nums), all_indices)
return all_indices
if __name__ == "__main__":
setrecursionlimit(11000)
n = int(input())
arr = list(int(i) for i in input().strip().split(' '))
x = int(input())
print_array_inline(find_index_of_all_occurrence__forward(arr, x))
print_array_inline(find_index_of_all_occurrence__backward(arr, x))
'''
4
9 8 10 8
8
5
9 8 10 8 8
8
'''
def vertical_order(root):
x_y_table: Dict[int, list] = dict() # map of number, list
pre_order__to__fill_x_y_for_each_node(root, x_y_table)
for x in sorted(x_y_table.keys()):
print_array_inline(x_y_table[x])
