From b66312368e7e38bac0e28e4f12831d8b334d47a3 Mon Sep 17 00:00:00 2001 From: juan Date: Sun, 17 Jul 2022 11:13:12 +0800 Subject: [PATCH] vault backup: 2022-07-17 11:13:12 --- ...lating-Next-Right-Pointers-In-Each-Node.md | 152 +++++++++++++----- _files/DFS with links.png | Bin 0 -> 68127 bytes ... Leetcode Populating next right ptr-1.png} | Bin ... Leetcode Populating next right ptr-2.png} | Bin 4 files changed, 113 insertions(+), 39 deletions(-) create mode 100644 _files/DFS with links.png rename _files/{Screenshot_2022-07-16-10-09-30-062_com.microsoft.office.onenote.png => Leetcode Populating next right ptr-1.png} (100%) rename _files/{Screenshot_2022-07-16-10-07-16-238_com.microsoft.office.onenote.png => Leetcode Populating next right ptr-2.png} (100%) diff --git a/OJ notes/pages/Leetcode Populating-Next-Right-Pointers-In-Each-Node.md b/OJ notes/pages/Leetcode Populating-Next-Right-Pointers-In-Each-Node.md index 0519857..638d631 100644 --- a/OJ notes/pages/Leetcode Populating-Next-Right-Pointers-In-Each-Node.md +++ b/OJ notes/pages/Leetcode Populating-Next-Right-Pointers-In-Each-Node.md @@ -64,6 +64,13 @@ Initially, all next pointers are set to `NULL`. > [!summary] > This is a #BFS problem, and cam be optimized +> It relies on the fact that it is perfect binary tree. +> The core part for optimization is utilizing ptr->next + +Using ptr->next in DFS and iteration enable us to traverse +between branches like in BFS + +![[DFS with links.png]] ##### BFS way of doing this, O(n)time, O(n + 1)space @@ -71,19 +78,33 @@ simple BFS, for each level, connect the node to the next. Remember to get the for loop right. -##### BFS-like iteration, two pointers +##### BFS-like iteration, two pointers, O(n)time, O(n + 1)space -We utilize the ->next property to link ptr->left->right->next to ptr->right->left +We utilize the ->next property to link +ptr->left->right->next to ptr->right->left +![[Leetcode Populating next right ptr-2.png]] -##### Also can be done with DFS +We can't use ptr->left->right->next = ptr->right->left, +since this is only one level, and doesn't work on two levels: +![[Leetcode Populating next right ptr-1.png]] +##### Also can be done with DFS O(n), O(n) + +We recursively fill next pointers the level below current. + +Base case: +- Root->left is empty, which means this is the leaf level, quit. + +Pseudo-code: +1. Check for base case +1. link root->left and root->right +1. link root->right and root->next->left (if root->next is valid.) ### Solution - -BFS unoptimized: +DFS: ```cpp /* // Definition for a Node. @@ -104,40 +125,93 @@ public: */ class Solution { -public: - Node* connect(Node* root) { - // BFS. - // Can we do it with DFS? - queue todo; - - if (root && root->left && root->right) { - todo.push(root->left); - todo.push(root->right); - } - - Node *ptr, *nextPtr; - - while (!todo.empty()) { - nextPtr = todo.front(); - todo.pop(); - for (size_t i = 0, size = todo.size(); i < size; i++) { - ptr = nextPtr; - nextPtr = todo.front(); - todo.pop(); - - ptr->next = nextPtr; - if (ptr->left) { - todo.push(ptr->left); - todo.push(ptr->right); - } - } - if (nextPtr->left) { - todo.push(nextPtr->left); - todo.push(nextPtr->right); - } - } - - return root; + void conn(Node *root) { + // preorder DFS, here we go! + // It assumes at least one level, which doesn't include [] + if (root->left) { + root->left->next = root->right; + if (root->next) { + root->right->next = root->next->left; + } + conn(root->left); + conn(root->right); } + } + +public: + Node *connect(Node *root) { + if (root) { + conn(root); + } + return root; + } +}; +``` + +Iterative, O(n)time O(1)space +```cpp +class Solution { +public: + Node *connect(Node *root) { + // iteration + Node *ptr = root; + Node *nextPtr = nullptr; + while (ptr && ptr->left) { + ptr->left->next = ptr->right; + if (!nextPtr) { + nextPtr = ptr->left; + } + if (!ptr->next) { + ptr = nextPtr; + nextPtr = nullptr; + } else { + ptr->right->next = ptr->next->left; + ptr = ptr->next; + } + } + return root; + } +}; + +``` + +BFS unoptimized: +```cpp +class Solution { +public: + Node *connect(Node *root) { + // BFS. + // Can we do it with DFS? + queue todo; + + if (root && root->left && root->right) { + todo.push(root->left); + todo.push(root->right); + } + + Node *ptr, *nextPtr; + + while (!todo.empty()) { + nextPtr = todo.front(); + todo.pop(); + for (size_t i = 0, size = todo.size(); i < size; i++) { + ptr = nextPtr; + nextPtr = todo.front(); + todo.pop(); + + ptr->next = nextPtr; + if (ptr->left) { + todo.push(ptr->left); + todo.push(ptr->right); + } + } + if (nextPtr->left) { + todo.push(nextPtr->left); + todo.push(nextPtr->right); + } + } + + return root; + } }; ``` \ No newline at end of file diff --git a/_files/DFS with links.png b/_files/DFS with links.png new file mode 100644 index 0000000000000000000000000000000000000000..24ac470ce4acd1f379da19ce0ec6d3dfa3e8f508 GIT binary patch literal 68127 zcmeFZ^;cD0)HZww>27K14ke|#yIV?7O6hI{=}rleknV1jPU%LvLAv2v=YGcX{qX(? z?|9D`4u*2}+I!D6=Umsk<~9AQsw{(!LW}}|K+xr6CDkDiI9Tu}8VLdXOU-CL3HSly zq%I>4DIX=>1Al>c5|`6N0v~TAi!ca;5+Wxlrs@9eaM?>&%W^^FU&Sk=Lv)64e?(Q7 z)occ&VBqRs z0WN(K9SpAAymfB>N)FN8Jsj`x$a$&HN=DoDoo~5Kxk6Uml|H8IM)U0X()IF?`_m>Z z7B=|A6&p@Z;!;vUKPTptqLSc~CyoXm2K{J;1wj7$5(+2Qe_v65g#Zivh9uK(QGe(+ 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