add monotonic queue algorithm

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()

data_structures/queue/monotonic_queue.py

@@ -0,0 +1,39 @@
+from __future__ import annotations
+
+from collections import deque
+
+arr = [1, 3, -1, -3, 5, 3, 6, 7]
+window_size = 3
+expect = [3, 3, 5, 5, 6, 7]
+
+
+def max_sliding_window(arr: list[float], window_size: int) -> list[float]:
+ """
+ Given an array of integers nums, there is a sliding window of size k which is moving
+ from the very left of the array to the very right.
+ Each time the sliding window of length window_size moves right by one position.
+ Return the max sliding window.
+ >>> max_sliding_window(arr, window_size) == expect
+ True
+ """
+ max_val = []
+ mono_queue: deque = deque()
+ for i in range(len(arr)):
+ # pop the element if the index is outside the window size k
+ if mono_queue and i - mono_queue[0] >= window_size:
+ mono_queue.popleft()
+ # keep the queue monotonically decreasing
+ # so that the max value is always on the top
+ while mono_queue and arr[i] >= arr[mono_queue[-1]]:
+ mono_queue.pop()
+ mono_queue.append(i)
+ # the maximum value is the first element in queue
+ if i >= window_size - 1:
+ max_val.append(arr[mono_queue[0]])
+ return max_val
+
+
+if __name__ == "__main__":
+ from doctest import testmod
+
+ testmod()