|
| 1 | +from heapq import * |
| 2 | + |
| 3 | +def median_sliding_window(nums, k): |
| 4 | + |
| 5 | + # To store medians |
| 6 | + medians = [] |
| 7 | + |
| 8 | + # To track values to be removed from heaps |
| 9 | + outgoing_nums = {} |
| 10 | + |
| 11 | + # Max heap for small values and min heap for large values |
| 12 | + max_heap = [] |
| 13 | + min_heap = [] |
| 14 | + |
| 15 | + # Initialize max heap by multiplying each element by -1 |
| 16 | + for i in range(k): |
| 17 | + heappush(max_heap, -1 * nums[i]) |
| 18 | + |
| 19 | + # Tranfer top half of numbers from max to min heap (and update sign) |
| 20 | + for i in range(k // 2): |
| 21 | + element = heappop(max_heap) |
| 22 | + heappush(min_heap, -1 * element) |
| 23 | + |
| 24 | + # Variable to keep heaps balanced |
| 25 | + balance = 0 |
| 26 | + |
| 27 | + i = k |
| 28 | + |
| 29 | + while True: |
| 30 | + |
| 31 | + # Check if the window size is odd |
| 32 | + if (k & 1) == 1: |
| 33 | + medians.append(float(max_heap[0] * -1)) |
| 34 | + else: |
| 35 | + medians.append((float(max_heap[0] * -1) + float(min_heap[0])) * 0.5) |
| 36 | + |
| 37 | + # Break the loop if all elements have been processed |
| 38 | + if i >= len(nums): |
| 39 | + break |
| 40 | + |
| 41 | + # Set outgoing number |
| 42 | + out_num = nums[i - k] |
| 43 | + |
| 44 | + # Set incoming number |
| 45 | + in_num = nums[i] |
| 46 | + i += 1 |
| 47 | + |
| 48 | + # If outgoing number is from max heap |
| 49 | + if out_num <= (max_heap[0] * -1): |
| 50 | + balance -= 1 |
| 51 | + else: |
| 52 | + balance += 1 |
| 53 | + |
| 54 | + # Add/update the outgoing number in the hash map |
| 55 | + if out_num in outgoing_nums: |
| 56 | + outgoing_nums[out_num] = outgoing_nums[out_num] + 1 |
| 57 | + else: |
| 58 | + outgoing_nums[out_num] = 1 |
| 59 | + |
| 60 | + # Check if the incoming number is less than the top of max heap |
| 61 | + if max_heap and in_num <= (max_heap[0] * -1): |
| 62 | + balance += 1 |
| 63 | + heappush(max_heap, in_num * -1) |
| 64 | + # Otherwise, add to the min heap |
| 65 | + else: |
| 66 | + balance -= 1 |
| 67 | + heappush(min_heap, in_num) |
| 68 | + |
| 69 | + # Rebalance the heaps |
| 70 | + if balance < 0: |
| 71 | + heappush(max_heap, (-1 * min_heap[0])) |
| 72 | + heappop(min_heap) |
| 73 | + elif balance > 0: |
| 74 | + heappush(min_heap, (-1 * max_heap[0])) |
| 75 | + heappop(max_heap) |
| 76 | + |
| 77 | + # Reset balance to zero |
| 78 | + balance = 0 |
| 79 | + |
| 80 | + # Remove invalid numbers in hash map from top of max heap |
| 81 | + while(max_heap[0] * -1) in outgoing_nums and (outgoing_nums[max_heap[0] * -1] > 0): |
| 82 | + outgoing_nums[max_heap[0] * -1] = outgoing_nums[max_heap[0] * -1] - 1 |
| 83 | + heappop(max_heap) |
| 84 | + |
| 85 | + # Remove invalid number in hash map from top of min heap |
| 86 | + while min_heap and min_heap[0] in outgoing_nums and (outgoing_nums[min_heap[0]] > 0): |
| 87 | + outgoing_nums[min_heap[0]] = outgoing_nums[min_heap[0]] - 1 |
| 88 | + heappop(min_heap) |
| 89 | + |
| 90 | + return medians |
| 91 | + |
| 92 | + |
| 93 | + |
| 94 | +# Time Complexity = O(nlogn) |
| 95 | +# Space Complexity = O(n) |
| 96 | + |
| 97 | + |
| 98 | + |
| 99 | +############################################################### |
| 100 | + |
| 101 | + |
| 102 | + |
| 103 | +def main(): |
| 104 | + input = ( |
| 105 | + ([3, 1, 2, -1, 0, 5, 8],4), |
| 106 | + ([1, 2], 1), |
| 107 | + ([4, 7, 2, 21], 2), |
| 108 | + ([22, 23, 24, 56, 76, 43, 121, 1, 2, 0, 0, 2, 3, 5], 5), |
| 109 | + ([1, 1, 1, 1, 1], 2)) |
| 110 | + x = 1 |
| 111 | + for i in input: |
| 112 | + print(x, ".\tInput array: ", i[0], ", k = ", i[1], sep = "") |
| 113 | + print("\tMedians: ", median_sliding_window(i[0], i[1]), sep = "") |
| 114 | + print(100*"-", "\n", sep = "") |
| 115 | + x += 1 |
| 116 | + |
| 117 | + |
| 118 | +if __name__ == "__main__": |
| 119 | + main() |
| 120 | + |
| 121 | + |
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