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CheezItMan
reviewed
May 1, 2021
lib/heapsort.js
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| // Time Complexity: O(n log n). The while loops both run for | ||
| // every element in list, so on their own have O(n). Within them | ||
| // they call either heap.add or heap.remove, which has O(log n) | ||
| // time complexity. | ||
| // Space Complexity: O(1). The function does make a new data structure -- | ||
| // a heap -- but it only adds to the heap one element for every element it | ||
| // pops off of the list, so the list is taking less space as the heap takes | ||
| // more. Then, the process is reversed with the heap taking less space | ||
| // so the list can be rebuilt and take more space. Increasing the size of | ||
| // the list is not going to change the additional amount of space the function uses. | ||
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| function heapsort(list) { |
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👍 But the space complexity of your solution is O(n) because you're building a heap here.
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| // Time Complexity: O(log n). Pushing the new value to array is O(1), | ||
| // then it calls heapUp which is O(log n). | ||
| // Space Complexity: O(log n). The space for actually adding is O(1), | ||
| // but it calls heapUp which is O(log n). | ||
| add(key, value = key) { |
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| // Time Complexity: O(log n). The swap and pop are both O(1), | ||
| // then it calls heapDown which is O(log n). | ||
| // Space Complexity: O(log n). The space for removing is O(1), | ||
| // but it calls heapDown which is O(log n). | ||
| remove() { |
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| // Time complexity: O(1), just checks array length. | ||
| // Space complexity: O(1), doesn't need any additional data structures. | ||
| isEmpty() { |
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| // Time complexity: O(log n). The calculation, swap, and comparison | ||
| // are all constant, but the function will need to be called as | ||
| // many times as there are levels in the heap, which scales | ||
| // logarithmically with the heap's size. | ||
| // Space complexity: O(log n). Since it is a recursive function | ||
| // it will have at worst as many function calls on the stack | ||
| // as times it will be called, which is controlled by number of levels | ||
| // in the heap and scales logarithmically with size. | ||
| heapUp(index) { |
| if (this.store[parentIndex].key < this.store[index].key) return; | ||
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| this.swap(index, parentIndex); | ||
| this.heapUp(parentIndex); | ||
| } | ||
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| // This helper method takes an index and | ||
| // moves it up the heap if it's smaller | ||
| // than it's parent node. | ||
| heapDown(index) { |
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Heaps Practice
Congratulations! You're submitting your assignment!
Comprehension Questions
heap_up&heap_downmethods useful? Why?