{"id":4738,"date":"2019-01-30T08:41:06","date_gmt":"2019-01-30T16:41:06","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=4738"},"modified":"2019-02-06T13:48:09","modified_gmt":"2019-02-06T21:48:09","slug":"segment-tree-sp14","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/sp\/segment-tree-sp14\/","title":{"rendered":"\u82b1\u82b1\u9171 Segment Tree \u7ebf\u6bb5\u6811 SP14"},"content":{"rendered":"\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 Segment Tree \u7ebf\u6bb5\u6811 - \u5237\u9898\u627e\u5de5\u4f5c SP14\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/rYBtViWXYeI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Segment tree is a balanced binary tree with O(logn) height given n input segments.<br>Segment tree supports fast range query O(logn + k), and update O(logn).<br>Building such a tree takes O(n) time if the input is an array of numbers.<\/p>\n\n\n\n<p>Tree\u4e4b\u6240\u4ee5\u5927\u884c\u5176\u9053\u5c31\u662f\u56e0\u4e3a\u5176\u7ed3\u6784\u548c\u4eba\u7c7b\u7ec4\u7ec7\u7ed3\u6784\u975e\u5e38\u63a5\u8fd1\u3002\u5c31\u62ff\u516c\u53f8\u6765\u8bf4\u597d\u4e86\uff0cCEO\u7edf\u9886\u5168\u5c40(root)\uff0c\u4e0b\u9762CTO\uff0cCFO\u7b49\u5404\u81ea\u7ba1\u7406\u4e00\u4e2a\u90e8\u95e8\uff0c\u6bcf\u4e2a\u90e8\u95e8\u4e0b\u9762\u53c8\u6b63\u597d\u6709\u597d\u4e24\u4e2aVP\uff0c\u6bcf\u4e2aVP\u4e0b\u9762\u53c8\u6709\u4e24\u4e2adirector\uff0c\u6bcf\u4e2adirector\u4e0b\u9762\u53c8\u67092\u4e2amanager\uff0c\u6bcf\u4e2amanager\u4e0b\u9762\u53c8\u67092\u4e2a\u5e95\u5c42\u5458\u5de5(leaf)\uff0c\u4e3a\u4ec0\u4e48\u662f2\uff1f\u56e0\u4e3a\u6211\u4eec\u7528\u4e8c\u53c9\u6811\u554a~<\/p>\n\n\n\n<p>\u6545\u4e8b\u8fd8\u662f\u8981\u4eceLeetCode 307. Range Sum Query &#8211; Mutable\u8bf4\u8d77\u3002<\/p>\n\n\n\n<p>\u9898\u76ee\u5927\u610f\u662f\uff1a\u7ed9\u4f60\u4e00\u4e2a\u6570\u7ec4\uff0c\u518d\u7ed9\u4f60\u4e00\u4e2a\u8303\u56f4\uff0c\u8ba9\u4f60\u6c42\u8fd9\u4e2a\u8303\u56f4\u5185\u6240\u6709\u5143\u7d20\u7684\u548c\uff0c\u5176\u4e2d\u5143\u7d20\u7684\u503c\u662f\u53ef\u53d8\u7684\uff0c\u901a\u8fc7update(index, val)\u66f4\u65b0\u3002&nbsp;<\/p>\n\n\n\n<p>nums = [1, 3, 5]\uff0c<br>sumRange(0, 2) = 1+3+5 = 9<br>update(1, 2) =&gt; [1, 2, 5]<br>sumRange(0, 2) = 1 + 2 + 5 = 7<\/p>\n\n\n\n<p>\u66b4\u529b\u6c42\u89e3\u5c31\u662f\u626b\u63cf\u4e00\u4e0b\u8fd9\u4e2a\u8303\u56f4\u3002<\/p>\n\n\n\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aUpdate O(1), Query O(n)\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u6570\u7ec4\u5143\u7d20\u4e0d\u53d8\u7684\u8bdd\uff08303\u9898\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u6c42\u51fa\u524dn\u4e2a\u5143\u7d20\u7684\u548c\u7136\u540e\u5b58\u5728sums\u6570\u7ec4\u4e2d\u3002i\u5230j\u6240\u6709\u5143\u7d20\u7684\u548c\u7b49\u4e8e0~j\u6240\u6709\u5143\u7d20\u7684\u548c\u51cf\u53bb0~(i-1)\u6240\u6709\u5143\u7d20\u7684\u548c\uff0c\u5373\uff1a<\/p>\n\n\n\n<p>sumRange(i, j) := sums[j] &#8211; sums[i &#8211; 1] if i &gt; 0 else sums[j]<\/p>\n\n\n\n<p>\u8fd9\u6837\u5c31\u53ef\u4ee5\u628aquery\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u5230O(1)\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\u8fd9\u9053\u9898\u5143\u7d20\u7684\u503c\u53ef\u53d8\uff0c\u90a3\u4e48\u5c31\u9700\u8981\u7ef4\u62a4sums\uff0c\u867d\u7136\u53ef\u4ee5\u628aquery\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u964d\u4f4e\u5230\u4e86O(1)\uff0c\u4f46update\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n)\uff0c\u5e76\u6ca1\u6709\u6bd4\u66b4\u529b\u6c42\u89e3\u5feb\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u65f6\u5019\u5c31\u8981\u8bf7\u51fa\u6211\u4eec\u4eca\u5929\u7684\u4e3b\u4eba\u516cSegment Tree\u4e86\uff0c\u53ef\u4ee5\u505a\u5230<\/p>\n\n\n\n<p>Update: O(logn)\uff0cQuery: O(logn+k)<\/p>\n\n\n\n<p>\u5176\u5b9eSegment Tree\u7684\u601d\u60f3\u8fd8\u662f\u5f88\u597d\u7406\u89e3\u7684\uff0c\u6bd4\u6211\u4eec\u4e4b\u524d\u8bb2\u8fc7\u7684Binary Indexed Tree\u8981\u5bb9\u6613\u7406\u89e3\u7684\u591a\uff08\u56de\u590d&nbsp;<strong>SP3<\/strong>&nbsp;\u83b7\u53d6\u89c6\u9891\uff09\uff0c\u4f46\u662f\u4ee3\u7801\u91cf\u53c8\u662f\u53e6\u5916\u4e00\u56de\u4e8b\u60c5\u4e86&#8230;<\/p>\n\n\n\n<p>\u56de\u5230\u4e00\u5f00\u59cb\u8bb2\u7684\u516c\u53f8\u7ec4\u7ec7\u7ed3\u6784\u4e0a\u9762\uff0c\u5047\u8bbe\u4e00\u4e2a\u516c\u53f8\u6709200\u4e2a\u5e95\u5c42\u5458\u5de5\uff0c<\/p>\n\n\n\n<p>\u6700\u539f\u59cb\u7684\u4fe1\u606f\uff08\u5143\u7d20\u7684\u503c\uff09\u53ea\u638c\u63e1\u5728\u4ed6\u4eec\u5de5\u624b\u91cc\uff0c\u5c42\u5c42\u4e0a\u62a5\u3002\u6bcf\u4e2amanager\u628a\u4ed6\u6240\u7ba1\u7406\u7684\u4eba\u7684\u5143\u7d20\u503c\u6c42\u548c\u4e4b\u540e\u7ee7\u7eed\u4e0a\u62a5\uff0c\u76f4\u5230CEO\u3002CEO\u77e5\u9053\u4f46\u4ec5\u77e5\u90530-199\u7684\u548c\u3002<\/p>\n\n\n\n<p>\u5f53\u4f60\u95eeCEO\uff0c5\u5230199\u7684\u548c\u662f\u591a\u5c11\uff1f\u4ed6\u624b\u4e0a\u53ea\u67090-199\u7684\u548c\uff0c\u4e00\u4e0b\u5b50\u614c\u4e86\uff0c\u8d76\u7d27\u627e\u6765CTO\uff0cCFO\u8bf4\u4f60\u4eec\u628a5\u5230199\u7684\u548c\u7ed9\u62a5\u4e0a\u6765\uff0cCFO\u4e00\u770b\u62a5\u8868\uff0c\u5fc3\u4e2d\u6697\u559c\uff1a\u8fd8\u597d\u6211\u8d1f\u8d23\u7684\u8fd9\u4e2a\u533a\u95f4(100~199)\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u4e86\uff0c\u5c31\u76f4\u63a5\u628a\u4e4b\u524d\u7684\u603b\u548c\u4e0a\u62a5\u4e86\u3002CTO\u4e00\u770b\u62a5\u8868\uff0c\u81ea\u5df1\u8d1f\u8d230-99\u8fd9\u4e2a\u533a\u95f4\uff0c\u53ea\u77e5\u90530-99\u7684\u548c\uff0c\u4f465-99\u7684\u548c\uff0c\u8fd8\u662f\u95ee\u4e0b\u9762\u7684\u4eba\u5427&#8230; \u6700\u540e\u7ed3\u679c\u518d\u4e00\u5c42\u5c42\u8fd4\u56de\u7ed9CEO\u3002<\/p>\n\n\n\n<p>\u8bf4\u5230\u8fd9\u91cc\u5927\u5bb6\u5e94\u8be5\u5df2\u7ecf\u80fd\u60f3\u8c61Segment Tree\u662f\u600e\u4e48\u5de5\u4f5c\u4e86\u5427\uff1a<\/p>\n\n\n\n<p>\u6bcf\u4e2aleaf\u8d1f\u8d23\u4e00\u4e2a\u5143\u7d20\u7684\u503c<\/p>\n\n\n\n<p>\u6bcf\u4e2aparent\u8d1f\u8d23\u7684\u8303\u56f4\u662f\u4ed6\u7684children\u6240\u8d1f\u8d23\u7684\u8303\u56f4\u7684union\uff0c\u5e76\u628a\u6240\u6709\u8303\u56f4\u5185\u7684\u5143\u7d20\u503c\u76f8\u52a0\u3002<\/p>\n\n\n\n<p>\u540c\u4e00\u5c42\u7684\u8282\u70b9\u6ca1\u6709overlap\u3002<\/p>\n\n\n\n<p>root\u5b58\u50a8\u7684\u662f\u6240\u6709\u5143\u7d20\u7684\u548c\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u4e00\u4e2aSegmentTreeNode\u9700\u8981\u8bb0\u5f55\u4ee5\u4e0b\u4fe1\u606f<\/p>\n\n\n\n<p>start #\u8d77\u59cb\u8303\u56f4<br>end #\u7ec8\u6b62\u8303\u56f4<br>mid #\u62c6\u5206\u70b9\uff0c\u901a\u5e38\u662f (start + end) \/\/ 2<br>val #\u6240\u6709\u5b50\u5143\u7d20\u7684\u548c<br>left #\u5de6\u5b50\u6811<br>right #\u53f3\u5b50\u6811<\/p>\n\n\n\n<p>Update: \u7531\u4e8e\u6bcf\u6b21\u53ea\u66f4\u65b0\u4e00\u4e2a\u5143\u7d20\u7684\u503c\uff0c\u6240\u4ee5CEO\u77e5\u9053\u8fd9\u4e2a\u5458\u5de5\u662f\u54ea\u4e2a\u4eba\u7ba1\u7684\uff0c\u6d3e\u53d1\u4e0b\u53bb\u5c31\u884c\u4e86\uff0c\u7136\u540e\u628a\u65b0\u7684\u7ed3\u679c\u518d\u8fd4\u56de\u56de\u6765\u3002<\/p>\n\n\n\n<pre lang=\"python\">\ndef update(root, index, val):\n  # \u5230\u5e95\u5c42\u5458\u5de5\u4e86\uff0c\u76f4\u63a5\u66f4\u65b0\n  if root.start == index and root.end == index:\n    root.val = val\n    return\n  # \u6839\u636e\u62c6\u5206\u70b9\uff0c\u66f4\u65b0\u5de6\u5b50\u6811\u6216\u53f3\u5b50\u6811\n  if val <= root.mid:\n    update(root.left, index, val)\n  else:\n    update(root.right, index, val)\n  # \u91cd\u65b0\u8ba1\u7b97\u548c\n  root.val = root.left?.val + root.right?.val\n<\/pre>\n\n\n\n<p>T(n) = T(n\/2) + 1 =&gt; O(logn)<\/p>\n\n\n\n<p>Query: query\u7684range\u53ef\u4ee5\u662f\u4efb\u610f\u7684\uff0c\u5c31\u6709\u4ee5\u4e0b\u4e09\u79cd\u60c5\u51b5\uff1a<\/p>\n\n\n\n<p>case 1: \u8fd9\u4e2arange\u6b63\u597d\u548c\u6211\u8d1f\u8d23\u7684range\u5b8c\u5168\u76f8\u540c\u3002\u6bd4\u5982sumQuery(CTO, 0, 99)\uff0c\u8fd9\u4e2a\u65f6\u5019CTO\u76f4\u63a5\u8fd4\u56de\u5df2\u7ecf\u6c42\u89e3\u8fc7\u7684\u6240\u6709\u4e0b\u5c5e\u7684\u548c\u5373\u53ef\u3002<\/p>\n\n\n\n<p>case 2: \u8fd9\u4e2arange\u53ea\u7531\u6211\u5176\u4e2d\u4e00\u4e2a\u4e0b\u5c5e\u8d1f\u8d23\u3002\u6bd4\u5982sumQuery(CEO, 0, 10)\uff0cCEO\u77e5\u90530~10\u5168\u90e8\u7531CFO\u8d1f\u8d23\uff0c\u90a3\u4e48\u4ed6\u5c31\u76f4\u63a5\u8fd4\u56desumQuery(CTO, 0, 10)\u3002<\/p>\n\n\n\n<p>case 3: \u8fd9\u4e2arange\u8986\u76d6\u4e86\u6211\u7684\u4e24\u4e2a\u4e0b\u5c5e\uff0c\u90a3\u4e48\u6211\u5c31\u9700\u8981\u8c03\u75282\u6b21\u3002\u6bd4\u5982sumQuery(CEO, 80, 120)\uff0cCEO\u77e5\u90530~99\u7531CTO\u7ba1\uff0c100~199\u7531CFO\u7ba1\uff0c\u6240\u4ee5\u4ed6\u53ea\u9700\u8981\u8fd4\u56de\uff1a<\/p>\n\n\n\n<p>sumQuery(CTO, 80, 99) + sumQuery(CFO, 100, 120)<br><\/p>\n\n\n\n<p>\u7531\u6b64\u53ef\u89c1sumQuery\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u4e0d\u786e\u5b9a\u7684\uff0c\u8fd0\u6c14\u597d\u65f6O(1)\uff0c\u8fd0\u6c14\u4e0d\u597d\u65f6\u662fO(logn+k)\uff0ck\u662f\u9700\u8981\u8bbf\u95ee\u7684\u8282\u70b9\u7684\u6570\u91cf\u3002 <\/p>\n\n\n\n<p>\u6211\u505a\u4e86\u4e00\u4e2a\u5b9e\u9a8c\uff0c\u7ed9\u5b9aN\uff0c\u5c1d\u8bd5\u6240\u6709\u7684(i,j)\u7ec4\u5408\uff0c\u770bsumQuery\u7684\u6700\u574f\u60c5\u51b5\u548c\u5e73\u5747\u60c5\u51b5\uff0c\u7ed3\u679c\u5982\u4e0b\u56fe\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"371\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/02\/query_nodes.png\" alt=\"\" class=\"wp-image-4795\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/02\/query_nodes.png 600w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/02\/query_nodes-300x186.png 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p>Query\u9700\u8981\u8bbf\u95ee\u5230\u7684\u8282\u70b9\u6570\u91cf\u7684worst\u548caverage case\u3002Worst case \u5927\u7ea6\u8bbf\u95ee 4*logn - 3 \u4e2a\u8282\u70b9\uff0c\u8fd9\u4e2a\u6570\u5b57\u8fdc\u8fdc\u5c0f\u4e8en\u3002\u548cn\u6210\u5bf9\u6570\u5173\u7cfb\u3002<br><\/p>\n\n\n\n<p>\u867d\u7136\u4e0d\u50cfBinary Indexed Tree query\u662f\u4e25\u683c\u7684O(logn)\uff0c\u4f46Segment tree query\u7684worst case\u589e\u957f\u7684\u975e\u5e38\u6162\uff0c\u53ef\u4ee5\u8bf4\u662f\u5bf9\u6570\u7ea7\u522b\u7684\u3002\u5f53N\u662f2^20\u7684\u65f6\u5019\uff0cworst case\u4e5f\u201c\u53ea\u9700\u8981\u201d\u8bbf\u95ee77\u4e2a\u8282\u70b9\u3002<\/p>\n\n\n\n<p>\u6700\u540e\u6211\u4eec\u518d\u6765\u8bb2\u4e00\u4e0b\u8fd9\u68f5\u6811\u662f\u600e\u4e48\u521b\u5efa\u7684\uff0c\u5176\u5b9e\u65b9\u6cd5\u6709\u5f88\u591a\u79cd\uff0c\u4e00\u5206\u4e3a\u4e8c\u662f\u6bd4\u8f83\u5e38\u89c4\u7684\u4e00\u79cd\u505a\u6cd5\u3002<\/p>\n\n\n\n<p>CEO\u7ba1200\u4eba\uff0c\u90a3\u4e48\u5c31\u627e2\u4e2a\u4eba(CTO\uff0cCFO\u5404\u7ba1100\u4eba\u3002CTO\u7ba1100\u4eba\uff0c\u518d\u627e2\u4e2aVP\u5404\u7ba150\u4eba\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230manager\u7ba12\u4e2a\u4eba\uff0c2\u4e2a\u4eba\u90fd\u662f\u5e95\u5c42\u5458\u5de5(leaf)\uff0c\u6ca1\u6709\u4eba\u7ba1\uff08\u53cc\u5173\uff09\u3002<\/p>\n\n\n\n<pre lang=\"python\">def buildTree(start, end):\n  # \u8d85\u8fc7\u8303\u56f4\u8fd4\u56de\u7a7a\u8282\u70b9\n  if start &gt; end: return None\n  boss.start = start\n  boss.end = end\n  # \u5982\u679c\u662f\u53f6\u5b50\u8282\u70b9\uff0c\u8bb0\u5f55\u5143\u7d20\u7684\u503c\n  if start == end: boss.val = nums[start]\n  boss.mid = (start + end) \/\/ 2\n  # \u9012\u5f52\u6784\u5efa\u5b50\u6811\n  boss.left = buildTree(start, mid)\n  boss.right = buildTree(mid + 1, end)\n  # \u6c42\u548c\n  boss.val += boss.left?.val + boss.right?.val\n  return boss\n<\/pre>\n\n\n\n<p>CEO = buildTree(0, 199)<\/p>\n\n\n\n<p>CEO.left # CTO \u8d1f\u8d230~99<br>CEO.right # CFO&nbsp;\u8d1f\u8d23100~199<\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-1.png\" alt=\"\" class=\"wp-image-4739\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-1.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-1-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-1-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-2.png\" alt=\"\" class=\"wp-image-4740\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-2.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-2-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-2-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-3.png\" alt=\"\" class=\"wp-image-4741\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-3.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-3-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-3-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-4.png\" alt=\"\" class=\"wp-image-4742\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-4.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-4-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/01\/sp14-4-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>Query: # of nodes visited: Average and worst are both ~O(logn)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Applications<\/h2>\n\n\n\n<p><a href=\"https:\/\/zxi.mytechroad.com\/blog\/data-structure\/307-range-sum-query-mutable\/\">LeetCode&nbsp;307&nbsp;Range&nbsp;Sum&nbsp;Query&nbsp;-&nbsp;Mutable<\/a><\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"c++\">\n\/\/ Author: Huahua, running time: 24 ms\nclass SegmentTreeNode {\npublic:\n  SegmentTreeNode(int start, int end, int sum,\n                  SegmentTreeNode* left = nullptr,\n                  SegmentTreeNode* right = nullptr): \n    start(start),\n    end(end),\n    sum(sum),\n    left(left),\n    right(right){}      \n  SegmentTreeNode(const SegmentTreeNode&) = delete;\n  SegmentTreeNode& operator=(const SegmentTreeNode&) = delete;\n  ~SegmentTreeNode() {\n    delete left;\n    delete right;\n    left = right = nullptr;\n  }\n  \n  int start;\n  int end;\n  int sum;\n  SegmentTreeNode* left;\n  SegmentTreeNode* right;\n};\n\nclass NumArray {\npublic:\n  NumArray(vector<int> nums) {\n    nums_.swap(nums);\n    if (!nums_.empty())\n      root_.reset(buildTree(0, nums_.size() - 1));\n  }\n\n  void update(int i, int val) {\n    updateTree(root_.get(), i, val);\n  }\n\n  int sumRange(int i, int j) {\n    return sumRange(root_.get(), i, j);\n  }\nprivate:\n  vector<int> nums_;\n  std::unique_ptr<SegmentTreeNode> root_;\n  \n  SegmentTreeNode* buildTree(int start, int end) {  \n    if (start == end) {      \n      return new SegmentTreeNode(start, end, nums_[start]);\n    }\n    int mid = start + (end - start) \/ 2;\n    auto left = buildTree(start, mid);\n    auto right = buildTree(mid + 1, end);\n    auto node = new SegmentTreeNode(start, end, left->sum + right->sum, left, right);    \n    return node;\n  }\n  \n  void updateTree(SegmentTreeNode* root, int i, int val) {\n    if (root->start == i && root->end == i) {\n      root->sum = val;\n      return;\n    }\n    int mid = root->start + (root->end - root->start) \/ 2;\n    if (i <= mid) {\n      updateTree(root->left, i, val);\n    } else {      \n      updateTree(root->right, i, val);\n    }\n    root->sum = root->left->sum + root->right->sum;\n  }\n  \n  int sumRange(SegmentTreeNode* root, int i, int j) {    \n    if (i == root->start && j == root->end) {\n      return root->sum;\n    }\n    int mid = root->start + (root->end - root->start) \/ 2;\n    if (j <= mid) {\n      return sumRange(root->left, i, j);\n    } else if (i > mid) {\n      return sumRange(root->right, i, j);\n    } else {\n      return sumRange(root->left, i, mid) + sumRange(root->right, mid + 1, j);\n    }\n  }\n};\n<\/pre>\n\n<\/div><h2 class=\"tabtitle\">Python3<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"python\">\n# Author: Huahua, running time: 176 ms\nclass SegmentTreeNode:\n  def __init__(self, start, end, val, left=None, right=None):\n    self.start = start\n    self.end = end\n    self.mid = start + (end - start) \/\/ 2\n    self.val = val\n    self.left = left\n    self.right = right\n\nclass NumArray:\n  def __init__(self, nums):\n    self.nums = nums\n    if self.nums:\n      self.root = self._buildTree(0, len(nums) - 1)\n\n  def update(self, i, val):      \n    self._updateTree(self.root, i, val)\n\n  def sumRange(self, i, j):\n    return self._sumRange(self.root, i, j)\n    \n  \n  def _buildTree(self, start, end):\n    if start == end: return SegmentTreeNode(start, end, self.nums[start])\n    mid = start + (end - start) \/\/ 2\n    left = self._buildTree(start, mid)\n    right = self._buildTree(mid + 1, end)\n    return SegmentTreeNode(start, end, left.val + right.val, left, right)\n  \n  def _updateTree(self, root, i, val):\n    if root.start == i and root.end == i:\n      root.val = val\n      return    \n    if i <= root.mid:\n      self._updateTree(root.left, i, val)\n    else:\n      self._updateTree(root.right, i, val)\n    root.val = root.left.val + root.right.val\n  \n  def _sumRange(self, root, i, j):\n    if root.start == i and root.end == j:\n      return root.val\n    if j <= root.mid:\n      return self._sumRange(root.left, i, j)\n    elif i > root.mid:\n      return self._sumRange(root.right, i, j)\n    else:\n      return self._sumRange(root.left, i, root.mid) + self._sumRange(root.right, root.mid + 1, j)\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Segment tree is a balanced binary tree with O(logn) height given n input segments.Segment tree supports fast range query O(logn + k), and update O(logn).Building&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[170],"tags":[459,201,458,28],"class_list":["post-4738","post","type-post","status-publish","format-standard","hentry","category-sp","tag-ologn","tag-range-sum","tag-segment-tree","tag-tree","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=4738"}],"version-history":[{"count":11,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4738\/revisions"}],"predecessor-version":[{"id":4804,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4738\/revisions\/4804"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=4738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=4738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=4738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}