|
391 | 391 | "metadata": {},
|
392 | 392 | "source": [
|
393 | 393 | "## 题目\n",
|
394 |
| - "\n", |
395 | 394 | "### [kth-largest-element-in-an-array](https://leetcode-cn.com/problems/kth-largest-element-in-an-array/)\n",
|
396 |
| - "\n", |
397 |
| - "- 思路 1: sort 后取第 k 个,最简单直接,复杂度 O(N log N) 代码略\n", |
398 |
| - "\n", |
399 |
| - "- 思路 2: 使用最小堆,复杂度 O(N log k),排前k个最大的,数据流的思路,如果小于对顶直接不用加入,如果大于堆顶就将堆顶替换为该数字进行重排,最后堆顶就是我们想要的结果。\n", |
400 |
| - "\n", |
401 |
| - "- 思路 3:把整个数组建最大堆,然后按堆排序把最大的k-1个数挪后边,排序的思路\n", |
402 |
| - "\n", |
403 |
| - "- 思路 4:quick select\n" |
404 |
| - ] |
405 |
| - }, |
406 |
| - { |
407 |
| - "cell_type": "markdown", |
408 |
| - "metadata": {}, |
409 |
| - "source": [ |
410 |
| - "直接使用python原生库的思路" |
411 |
| - ] |
412 |
| - }, |
413 |
| - { |
414 |
| - "cell_type": "code", |
415 |
| - "execution_count": null, |
416 |
| - "metadata": {}, |
417 |
| - "outputs": [], |
418 |
| - "source": [ |
419 |
| - "class Solution:\n", |
420 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
421 |
| - " return heapq.nlargest(k,nums)[-1]\n", |
422 |
| - " \n", |
423 |
| - "class Solution:\n", |
424 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
425 |
| - " heap = []\n", |
426 |
| - " for num in nums:\n", |
427 |
| - " if len(heap) < k:\n", |
428 |
| - " heapq.heappush(heap,num)\n", |
429 |
| - " else:\n", |
430 |
| - " #heapreplace 删除当前堆中最小元素,然后加一个元素\n", |
431 |
| - " #heappushpop 是先推再删除最小元素,意味着有可能被删除的就是新推入的这个数本身, 应该用这种做法\n", |
432 |
| - " heapq.heappushpop(heap,num)\n", |
433 |
| - " \n", |
434 |
| - " return heap[0]" |
435 |
| - ] |
436 |
| - }, |
437 |
| - { |
438 |
| - "cell_type": "markdown", |
439 |
| - "metadata": {}, |
440 |
| - "source": [ |
441 |
| - "思路2" |
442 |
| - ] |
443 |
| - }, |
444 |
| - { |
445 |
| - "cell_type": "code", |
446 |
| - "execution_count": null, |
447 |
| - "metadata": {}, |
448 |
| - "outputs": [], |
449 |
| - "source": [ |
450 |
| - "# 单独分一个堆\n", |
451 |
| - "class Solution:\n", |
452 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
453 |
| - " def minheapify(heap,root,len_heap):\n", |
454 |
| - " p = root\n", |
455 |
| - " while p*2 + 1 < len_heap:\n", |
456 |
| - " left = p*2 + 1\n", |
457 |
| - " right = p*2 + 2\n", |
458 |
| - "\n", |
459 |
| - " min_index = left\n", |
460 |
| - " if right < len_heap and heap[right] < heap[left]:\n", |
461 |
| - " min_index = right\n", |
462 |
| - " \n", |
463 |
| - " if heap[p] > heap[min_index]:\n", |
464 |
| - " heap[p],heap[min_index] = heap[min_index],heap[p]\n", |
465 |
| - " p = min_index\n", |
466 |
| - " else:\n", |
467 |
| - " break\n", |
468 |
| - " \n", |
469 |
| - " def build_heap(heap,k):\n", |
470 |
| - " for i in range(k-1,-1,-1):\n", |
471 |
| - " minheapify(heap,i,k)\n", |
472 |
| - " \n", |
473 |
| - " min_heap = nums[:k].copy()\n", |
474 |
| - " build_heap(min_heap,k)\n", |
475 |
| - " \n", |
476 |
| - "\n", |
477 |
| - " for num in nums[k:]:\n", |
478 |
| - " if num <= min_heap[0]:\n", |
479 |
| - " continue\n", |
480 |
| - " elif num > min_heap[0]:\n", |
481 |
| - " min_heap[0] = num\n", |
482 |
| - " minheapify(min_heap,0,k)\n", |
483 |
| - "\n", |
484 |
| - " return min_heap[0]\n", |
485 |
| - " \n", |
486 |
| - "# 原地\n", |
487 |
| - "class Solution:\n", |
488 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
489 |
| - " def minheapify(root,len_heap):\n", |
490 |
| - " p = root\n", |
491 |
| - " while p*2 + 1 < len_heap:\n", |
492 |
| - " left = p*2 + 1\n", |
493 |
| - " right = p*2 + 2\n", |
494 |
| - "\n", |
495 |
| - " min_index = left\n", |
496 |
| - " if right < len_heap and nums[right] < nums[left]:\n", |
497 |
| - " min_index = right\n", |
498 |
| - " \n", |
499 |
| - " if nums[p] > nums[min_index]:\n", |
500 |
| - " nums[p],nums[min_index] = nums[min_index],nums[p]\n", |
501 |
| - " p = min_index\n", |
502 |
| - " else:\n", |
503 |
| - " break\n", |
504 |
| - " \n", |
505 |
| - " def build_heap(k):\n", |
506 |
| - " for i in range(k-1,-1,-1):\n", |
507 |
| - " minheapify(i,k)\n", |
508 |
| - " \n", |
509 |
| - " build_heap(k)\n", |
510 |
| - "\n", |
511 |
| - " for i in range(k,len(nums)):\n", |
512 |
| - " if nums[i] <= nums[0]:\n", |
513 |
| - " continue\n", |
514 |
| - " elif nums[i] > nums[0]:\n", |
515 |
| - " nums[0],nums[i] = nums[i],nums[0] \n", |
516 |
| - " minheapify(0,k)\n", |
517 |
| - "\n", |
518 |
| - " return nums[0]" |
519 |
| - ] |
520 |
| - }, |
521 |
| - { |
522 |
| - "cell_type": "markdown", |
523 |
| - "metadata": {}, |
524 |
| - "source": [ |
525 |
| - "思路3" |
526 |
| - ] |
527 |
| - }, |
528 |
| - { |
529 |
| - "cell_type": "code", |
530 |
| - "execution_count": null, |
531 |
| - "metadata": {}, |
532 |
| - "outputs": [], |
533 |
| - "source": [ |
534 |
| - "class Solution:\n", |
535 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
536 |
| - " \n", |
537 |
| - " def maxheapify(root,len_heap):\n", |
538 |
| - " p = root\n", |
539 |
| - " while p * 2 + 1 < len_heap:\n", |
540 |
| - " left = p*2 + 1\n", |
541 |
| - " right = p*2 + 2\n", |
542 |
| - "\n", |
543 |
| - " max_index = left \n", |
544 |
| - "\n", |
545 |
| - " if right < len_heap and nums[right] > nums[left]:\n", |
546 |
| - " max_index = right\n", |
547 |
| - " \n", |
548 |
| - " if nums[p] < nums[max_index]:\n", |
549 |
| - " nums[p],nums[max_index] = nums[max_index],nums[p]\n", |
550 |
| - " p = max_index\n", |
551 |
| - " else:\n", |
552 |
| - " break\n", |
553 |
| - "\n", |
554 |
| - " def build_heap(): \n", |
555 |
| - " for i in range(len(nums)//2 - 1, -1, -1):\n", |
556 |
| - " maxheapify(i,len(nums))\n", |
557 |
| - " \n", |
558 |
| - " build_heap()\n", |
559 |
| - " for i in range(len(nums),len(nums) - k + 1,-1):\n", |
560 |
| - " nums[0],nums[i-1] = nums[i-1],nums[0]\n", |
561 |
| - " maxheapify(0,i-1)\n", |
562 |
| - " return nums[0]" |
563 |
| - ] |
564 |
| - }, |
565 |
| - { |
566 |
| - "cell_type": "markdown", |
567 |
| - "metadata": {}, |
568 |
| - "source": [ |
569 |
| - "思路4\n", |
570 |
| - "这里就可以用迭代而非递归的方式去做,节约成本,注意用randint,同时还有pivot = random.randint(left,right)。并且我不习惯用randint,所以赋值要格外注意。除了上来nums[left],nums[pivot] = nums[pivot],nums[left] ,把quick转换成我所习惯的形式外,也要把pivot改成left。" |
571 |
| - ] |
572 |
| - }, |
573 |
| - { |
574 |
| - "cell_type": "code", |
575 |
| - "execution_count": null, |
576 |
| - "metadata": {}, |
577 |
| - "outputs": [], |
578 |
| - "source": [ |
579 |
| - "class Solution:\n", |
580 |
| - " def findKthLargest(self, nums: List[int], k: int) -> int:\n", |
581 |
| - " index = len(nums) - k \n", |
582 |
| - " left = 0\n", |
583 |
| - " right = len(nums) - 1\n", |
584 |
| - " while True:\n", |
585 |
| - " if left >= right:\n", |
586 |
| - " return nums[left]\n", |
587 |
| - " pivot = random.randint(left,right) \n", |
588 |
| - " i = left \n", |
589 |
| - " j = right\n", |
590 |
| - "\n", |
591 |
| - " nums[left],nums[pivot] = nums[pivot],nums[left]\n", |
592 |
| - "\n", |
593 |
| - " while i < j:\n", |
594 |
| - " while i < j and nums[left] <= nums[j]:\n", |
595 |
| - " j -= 1\n", |
596 |
| - " while i < j and nums[left] >= nums[i]:\n", |
597 |
| - " i += 1\n", |
598 |
| - "\n", |
599 |
| - " nums[i],nums[j] = nums[j],nums[i]\n", |
600 |
| - "\n", |
601 |
| - " nums[i],nums[left] = nums[left],nums[i]\n", |
602 |
| - "\n", |
603 |
| - " if i < index:\n", |
604 |
| - " left = i + 1\n", |
605 |
| - " elif i > index:\n", |
606 |
| - " right = i - 1\n", |
607 |
| - " elif i == index:\n", |
608 |
| - " return nums[i]" |
| 395 | + "### [链接](http://localhost:8888/notebooks/algorithm-pattern-python/data_structure/%E5%A0%86%E7%AC%94%E8%AE%B0.ipynb)\n" |
609 | 396 | ]
|
610 | 397 | }
|
611 | 398 | ],
|
|
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