From db3b8fffd7cd0dce41962c3a2d55e313c13d3a85 Mon Sep 17 00:00:00 2001 From: liu <3330176274@qq.com> Date: Sun, 16 Feb 2025 22:40:18 +0800 Subject: [PATCH 1/3] =?UTF-8?q?0654=E6=9C=80=E5=A4=A7=E4=BA=8C=E5=8F=89?= =?UTF-8?q?=E6=A0=91.md=E5=A2=9E=E5=8A=A0=E6=96=B0=E9=9D=9E=E9=80=92?= =?UTF-8?q?=E5=BD=92=E7=AE=97=E6=B3=95=EF=BC=8C=E4=B8=80=E5=BC=A0=E5=9B=BE?= =?UTF-8?q?=E7=89=87=E6=94=BE=E5=9C=A8=E4=BA=86pics=E6=96=87=E4=BB=B6?= =?UTF-8?q?=E5=A4=B9=E4=B8=AD?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...7\344\272\214\345\217\211\346\240\221.png" | Bin 0 -> 6409 bytes ...47\344\272\214\345\217\211\346\240\221.md" | 90 ++++++++++++++++++ 2 files changed, 90 insertions(+) create mode 100644 "pics/654\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.png" diff --git "a/pics/654\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.png" "b/pics/654\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.png" new file mode 100644 index 0000000000000000000000000000000000000000..91f985bf5557d55d342ffade70133b9665c09294 GIT binary patch literal 6409 zcmcgxX;@QPw!MHYmY{-I5CK6=30NW+2?S-bG$dLI$RH>LLIss5V*nWg0WBl}0%a+p zfPh3nWfV|A22n{OG6rRyiD3#PGK4Y1yVzg9@9Wn;`u*tY{5+&Re6m zZB^Y00Km30r;&C5AWa1TDaw}3;0XWA4-5c+w4Xu#;t-lKJBY<&CaNY!on%#h`WOQ% zKO!yr;tv^(yYKIx-n(-uR{QJzoq7(rv7cs6LZ6m+Rg^$qwKq_obn#*wuRngJ*iD! zaCs};udYVsdtAA4uXS{6s+kz@LA?w1`p-AiMXRjg6<-$)>c7jOOr7BioNVg1=G?>FkF=K|ztx!qsBICPPop1Ap6H1^+kC|bGWS&9db{&+IN-w(8WAnJzY zvd1ZcFeTtiYFVZN-Z4ip`@k2EQF_eeG%w+0RttLd*4k~X7jm|bm_f|dUotn|71(W{ zwiA!r@Jn=CzQ)2ZkMh_F@jK4bX4hM{#7tRVOF>J5?Hkt0q^OUW7|CfQPp3czQ(MYU z1P0_PW;b3Sxeh2KR_Tbx2P!z*EnJvg9+n14iLGqlUOsW5={I{zc$Om`7trM zV1(0pWdmVLnAN2m1C;nY_0X_BazcB1lNn)uQC%23Am6Vh?5K5ZS)hk>iw#^F{_@kq zySC1*>S+m|hd&Okj%X(_DNHAo&dSiLa8jI%b3A?%-kD>(T;2JNOHqk3-cw2Q zor9x_%?_mB{SUz5jkBLmuX9sVB4 zvfze>DS|DB=~)w^1K|1&JMWs+RpEk?rsxmNq%yxp39LB8%$HED9PyI3x;b3&X*d#j zOlvKfUTE*RFex7fqh zkI<4YxdC3zQob(e_+~`^GlC?vSybuiQ{_L7>3Oc$^D}Ep`@J``YEO3fktFp#q8Fb` z9vZ##u~={DApQMY-Us}Nv*1&=fw5b2e0UAOAwHt#!N;Oxxu zBMgS9vH=wIHff>}xaE_r>j+bsag^cfppKH)<)f9>5qQ8w3%u(E5-dL70x{0+FmYLF zrUqbKT^21zo0dI}WdBG(MPE(Pj33=dj0cg=?+H&&2{CX-73{FWBj5+{8rL`;i?ScQ z@)=Fcv9DK?x6}liGThv(7#Q_P-=EBDY0!F4CD7P{1s4O@!sPUeolLnM^d8N8uBVb; 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第二版相应的终止条件，是遇到空节点，也就是数组区间为0，就终止了。 +### 非递归方法 + +将原数组转化为二叉树时，使数字飘起来，可以想象：越大的数字飘得越高（越接近根节点）。 + +如原题 【3,2,1,6,0,5】： + +image-20250216223034714 + +以 **从左到右遍历数组** 的方式构造最大二叉树，避免了递归方法带来的额外栈空间消耗，时间效能上也优一些。 + +1. 首先创建一个存放各个节点的地址的vector， 可以先把各个节点创建出来，也可以在遍历的过程中创建。 + +2. 遍历 `nums` 逐步构造树 + +```cpp +for (int i = 1; i < nums.size(); i++) { + TreeNode* t = new TreeNode(nums[i]); + arr.push_back(t); +``` + +- 依次读取 `nums[i]` 并新建 `TreeNode`，同时存入 `arr` 数组。 + +3. **找到 `nums[i]` 前面第一个比它大的数`nump[j]`，则 i 对应的节点应该是 j 节点的右子树，并把 j 原来的右子树(在数组的位置是 i 左边)放在 i 的左子树上。** + +```cpp +int j = i - 1; +for (; j >= 0; j--) { + if (nums[j] > nums[i]) { + TreeNode* l = arr[j]->right; + arr[j]->right = t; + t->left = l; + break; + } +} +``` + +- 从 `nums[i]` **向左遍历**，找到 **第一个比 `nums[i]` 大的数 `nums[j]`**。 +- 构造父子关系： + - `nums[i]` 作为 `nums[j]` 的**右子节点**。 + - 若 `nums[j]` 原本已有右子树 `l`，则 `l` 作为 `nums[i]` 的**左子节点**。 + +4. .处理 `nums[i]` 是当前最大值的情况 + +``` +cpp复制编辑if (j == -1) { + t->left = root; + root = t; +} +``` + +- 如果 `nums[i]` 比前面所有数都大，则为新的根节点： + - 设 `t->left = root`，即将 `root` 作为 `t` 的左子树。 + - 更新 `root = t`，因为 `nums[i]` 是当前最大值，必须作为新的根节点。 + +代码如下: + +```cpp +class Solution { + public: + TreeNode* constructMaximumBinaryTree(vector& nums) { + // new一个根节点 + TreeNode* root = new TreeNode(nums[0]); + // 创建一个存放各个node地址的数组，方便修改，与nums顺序一致 + vector arr; + // 先把第一个节点设为根节点，放入数组 + arr.push_back(root); + for(int i = 1; i < nums.size(); i++) { + TreeNode* t = new TreeNode(nums[i]); + arr.push_back(t); + int j = i-1; + for(; j >= 0; j--) { + /* 找到前面第一个大于该数的已有节点 */ + if(nums[j] > nums[i]){ + TreeNode* l = arr[j]->right; + arr[j]->right = t; + t->left = l; + break; + } + } + if(j == -1){ + /* 若没有更大的，说明这个数是目前最大的，设为根节点 */ + t->left = root; + root = t; + } + } + return root; + } + }; +``` + ## 总结 From c531422db92a0d09d8b9ca6f626b172c7aba740e Mon Sep 17 00:00:00 2001 From: liu <3330176274@qq.com> Date: Sun, 16 Feb 2025 22:46:02 +0800 Subject: [PATCH 2/3] =?UTF-8?q?0654=E6=9C=80=E5=A4=A7=E4=BA=8C=E5=8F=89?= =?UTF-8?q?=E6=A0=91.md=E5=A2=9E=E5=8A=A0=E6=96=B0=E9=9D=9E=E9=80=92?= =?UTF-8?q?=E5=BD=92=E7=AE=97=E6=B3=95=EF=BC=8C=E4=B8=80=E5=BC=A0=E5=9B=BE?= =?UTF-8?q?=E7=89=87=E6=94=BE=E5=9C=A8=E4=BA=86pics=E6=96=87=E4=BB=B6?= =?UTF-8?q?=E5=A4=B9=E4=B8=AD?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...34\200\345\244\247\344\272\214\345\217\211\346\240\221.md" | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git "a/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" "b/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" index 7dd3f6f669..18f9162ed9 100644 --- "a/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" +++ "b/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" @@ -255,8 +255,8 @@ for (; j >= 0; j--) { 4. .处理 `nums[i]` 是当前最大值的情况 -``` -cpp复制编辑if (j == -1) { +```cpp +if (j == -1) { t->left = root; root = t; } From d89a14b6435029cf09bce96dcd376755003313f7 Mon Sep 17 00:00:00 2001 From: liu <3330176274@qq.com> Date: Sun, 16 Feb 2025 22:47:39 +0800 Subject: [PATCH 3/3] =?UTF-8?q?0654=E6=9C=80=E5=A4=A7=E4=BA=8C=E5=8F=89?= =?UTF-8?q?=E6=A0=91.md=E5=A2=9E=E5=8A=A0=E6=96=B0=E9=9D=9E=E9=80=92?= =?UTF-8?q?=E5=BD=92=E7=AE=97=E6=B3=95=EF=BC=8C=E4=B8=80=E5=BC=A0=E5=9B=BE?= =?UTF-8?q?=E7=89=87=E6=94=BE=E5=9C=A8=E4=BA=86pics=E6=96=87=E4=BB=B6?= =?UTF-8?q?=E5=A4=B9=E4=B8=AD?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git "a/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" "b/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" index 18f9162ed9..f45adb0a4d 100644 --- "a/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" +++ "b/problems/0654.\346\234\200\345\244\247\344\272\214\345\217\211\346\240\221.md" @@ -218,7 +218,7 @@ root->right = traversal(nums, maxValueIndex + 1, right); 如原题 【3,2,1,6,0,5】： -image-20250216223034714 +image-20250216223034714 以 **从左到右遍历数组** 的方式构造最大二叉树，避免了递归方法带来的额外栈空间消耗，时间效能上也优一些。