From 1f3eaed0757d1d19311f350d0b1da4a194913598 Mon Sep 17 00:00:00 2001 From: Alonza0314 Date: Wed, 16 Apr 2025 13:21:22 +0800 Subject: [PATCH 1/4] feat: basic setup --- Hard/124 Binary Tree Maximum Path Sum.md | 18 ++++++++++++++++++ Hard/834 Sum of Distances in Tree.md | 18 ++++++++++++++++++ ... Lowest Common Ancestor of a Binary Tree.md | 18 ++++++++++++++++++ README.md | 3 +++ 4 files changed, 57 insertions(+) create mode 100644 Hard/124 Binary Tree Maximum Path Sum.md create mode 100644 Hard/834 Sum of Distances in Tree.md create mode 100644 Medium/236 Lowest Common Ancestor of a Binary Tree.md diff --git a/Hard/124 Binary Tree Maximum Path Sum.md b/Hard/124 Binary Tree Maximum Path Sum.md new file mode 100644 index 0000000..49e538b --- /dev/null +++ b/Hard/124 Binary Tree Maximum Path Sum.md @@ -0,0 +1,18 @@ +# 124. Binary Tree Maximum Path Sum + +## Intuition + +## Approach + +## Complexity + +- Time complexity: +- Space complexity: + +## Keywords + +## Code + +```go + +``` diff --git a/Hard/834 Sum of Distances in Tree.md b/Hard/834 Sum of Distances in Tree.md new file mode 100644 index 0000000..3fbb419 --- /dev/null +++ b/Hard/834 Sum of Distances in Tree.md @@ -0,0 +1,18 @@ +# 834. Sum of Distances in Tree + +## Intuition + +## Approach + +## Complexity + +- Time complexity: +- Space complexity: + +## Keywords + +## Code + +```go + +``` diff --git a/Medium/236 Lowest Common Ancestor of a Binary Tree.md b/Medium/236 Lowest Common Ancestor of a Binary Tree.md new file mode 100644 index 0000000..19d4149 --- /dev/null +++ b/Medium/236 Lowest Common Ancestor of a Binary Tree.md @@ -0,0 +1,18 @@ +# 236. Lowest Common Ancestor of a Binary Tree + +## Intuition + +## Approach + +## Complexity + +- Time complexity: +- Space complexity: + +## Keywords + +## Code + +```go + +``` diff --git a/README.md b/README.md index 23c8040..fa192e2 100644 --- a/README.md +++ b/README.md @@ -18,9 +18,11 @@ | 50 | Pow(x, n) | [go](/Medium/50%20Pow(x,%20n).md) | M | | 51 | N-Queens | [go](/Hard/51%20N-Queens.md) | H | | 105 | Construct Binary Tree from Preorder and Inorder Tranversal | [go](/Medium/105%20Construct%20Binary%20Tree%20from%20Preorder%20and%20Inorder%20Tranversal.md) | M | +| 124 | Binary Tree Maximum Path Sum | [go](Hard/124%20Binary%20Tree%20Maximum%20Path%20Sum.md) | H | | 135 | Candy | [go](/Hard/135%20Candy.md) | H | | 140 | Word Break II | [go](/Hard/140%20Word%20Break%20II.md) | H | | 146 | LRU Cache | [go](/Medium/146%20LRU%20Cache.md) | M | +| 236 | Lowest Common Ancestor of a Binary Tree | [go](/Medium/236%20Lowest%20Common%20Ancestor%20of%20a%20Binary%20Tree.md) | M | | 239 | Sliding Window Maximum | [go](/Hard/239%20Sliding%20Window%20Maximum.md) | H | | 322 | Coin Change | [go](/Medium/322%20Coin%20Change.md) | M | | 460 | LFU Cache | [go](/Hard/460%20LFU%20Cache.md) | H | @@ -29,6 +31,7 @@ | 757 | Set Intersection Size At Least Two | [go](/Hard/757%20Set%20Intersection%20Size%20At%20Least%20Two.md) | H | | 815 | Bus Routes | [go](/Hard/815%20Bus%20Routes.md) | H | | 765 | Couples Holding Hands | [go](/Hard/765%20Couples%20Holding%20Hands.md) | H | +| 834 | Sum of Distances in Tree | [go](/Hard/834%20Sum%20of%20Distances%20in%20Tree.md) | H | | 840 | Magic Squares In Grid | [go](/Medium/840%20Magic%20Squares%20In%20Grid.md) | M | | 881 | Boats to Save People | [go](/Medium/881%20Boats%20to%20Save%20People.md) | M | | 912 | Sort an Array | [go](/Medium/912%20Sort%20an%20Array.md) | M | From cb06c173c28d41b0c97abcb11e773a584dd9ccd1 Mon Sep 17 00:00:00 2001 From: Alonza0314 Date: Wed, 16 Apr 2025 13:25:24 +0800 Subject: [PATCH 2/4] feat: add 236 --- ...Lowest Common Ancestor of a Binary Tree.md | 54 +++++++++++++- Week8/236 AC.png | Bin 0 -> 121007 bytes ...Lowest Common Ancestor of a Binary Tree.md | 66 ++++++++++++++++++ 3 files changed, 117 insertions(+), 3 deletions(-) create mode 100644 Week8/236 AC.png create mode 100644 Week8/236 Lowest Common Ancestor of a Binary Tree.md diff --git a/Medium/236 Lowest Common Ancestor of a Binary Tree.md b/Medium/236 Lowest Common Ancestor of a Binary Tree.md index 19d4149..057b591 100644 --- a/Medium/236 Lowest Common Ancestor of a Binary Tree.md +++ b/Medium/236 Lowest Common Ancestor of a Binary Tree.md @@ -2,17 +2,65 @@ ## Intuition + We can use a post-order traversal approach where we first check the left and right subtrees, then process the current node. + ## Approach +1. We use a recursive helper function `find` that takes the current node and the two target nodes p and q. +2. The base cases are: + - If the current node is nil, return nil + - If the current node is either p or q, return the current node +3. We recursively search in both left and right subtrees +4. The logic for determining the LCA is: + - If both left and right subtrees return nil, return nil (neither p nor q found) + - If only one subtree returns a non-nil value, return that value (one of p or q found) + - If both subtrees return non-nil values, the current node is the LCA + ## Complexity -- Time complexity: -- Space complexity: +- Time complexity: O(n) +- Space complexity: O(h) ## Keywords +- Binary Tree +- Recursion +- DFS +- Post-order Traversal +- Lowest Common Ancestor + ## Code ```go - +/** + * Definition for a binary tree node. + * type TreeNode struct { + * Val int + * Left *TreeNode + * Right *TreeNode + * } + */ +func find(node, p, q *TreeNode) *TreeNode { + if node == nil { + return nil + } + if node == p || node == q { + return node + } + left := find(node.Left, p, q) + right := find(node.Right, p, q) + if left == nil && right == nil { + return nil + } + if left != nil && right == nil { + return left + } + if left == nil && right != nil { + return right + } + return node +} +func lowestCommonAncestor(root, p, q *TreeNode) *TreeNode { + return find(root, p, q) +} ``` diff --git a/Week8/236 AC.png b/Week8/236 AC.png new file mode 100644 index 0000000000000000000000000000000000000000..439cbe16ee0eb0a321cf0e55ab2d46df2636f6fb GIT binary patch literal 121007 zcmdqIWmp}}vNnvnEP}fvKyY{W5G)Dq?(Xic2@u>#fZ*;d+}+&??(XnS&aU9BfU@t&AZcK7=Qz!mB9`;ACpXeG@jzkwF9_QgHZv2Wdd;OH^RQ zLF5GCA<()QeeS4@gtgi$3NwK3j(LxR(-Yz?A|auUi|n#3hqTvJ?se+5w*0u}JNmRc z+~_z2k?j)k_RV(o0mN@4*$R4$yU(?8-zQ1lGqLv)8Chp=!8^LBK+bORNL zT0wh@gJiDp&4u=ip5)l9)#AGb@Om#A`(P`jug3gRyKtI0AN}B~NlXCptsn#3uL+h63m)GO&4gtX< zJ5s#G^3rG`OGahUBHv>df#f4G5D3G)xD4FH5=`rHuZ&PL^KMG+Q99e@F;LesFM*Fc zg2@+sb*9QH9q&_$WZjA<%NMr#{Qg5!kQ%l@-_ucpUGP|PuB^)MZ(r5k(2cA?ZK}00 zzY{L|ik%-BXo&q{+;}f`*~4jyG#`uPl}*MbsH8($5UjlLV8y@8y9D8~ErWRD@{ zxN#00_}j5B^E?>Q9w`GoH^5KrUM-zsFkIzs%j78?L}LqAY3ZY%Za|-@27&uii&Oy@ zTfA@RvOBVhTYuuh>&%!8szR778yeBdoDAIvQp8hNjI<^076uv(6o}FekA`GoCLUKJ 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For any given node, the maximum path sum could be: + +1. The node's value itself +2. The node's value plus the maximum path from its left subtree +3. The node's value plus the maximum path from its right subtree +4. The node's value plus both left and right maximum paths + ## Approach +We use a post-order traversal approach to solve this problem: + +1. For each node, we recursively calculate the maximum path sum from its left and right subtrees +2. We update the global maximum by considering all possible combinations: + - The current node's value alone + - Current node + left path + - Current node + right path + - Current node + left path + right path +3. We return the maximum path sum that can be extended from the current node to its parent (which can only include at most one of its children) + ## Complexity -- Time complexity: -- Space complexity: +- Time complexity: O(n) +- Space complexity: O(h) ## Keywords +- Binary Tree +- Post-order Traversal +- Recursion + ## Code ```go - +/** + * Definition for a binary tree node. + * type TreeNode struct { + * Val int + * Left *TreeNode + * Right *TreeNode + * } + */ +func maxPathSum(root *TreeNode) int { + ret := math.MinInt + var postOrder func(node *TreeNode) int + postOrder = func(node *TreeNode) int { + if node == nil { + return 0 + } + left, right := postOrder(node.Left), postOrder(node.Right) + ret = max(ret, left + right + node.Val, left + node.Val, right + node.Val, node.Val) + return max(left + node.Val, right + node.Val, node.Val) + } + ret = max(ret, postOrder(root)) + return ret +} ``` diff --git a/Week8/124 AC.png b/Week8/124 AC.png new file mode 100644 index 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[PATCH 4/4] feat: add 834 --- Hard/834 Sum of Distances in Tree.md | 58 ++++++++++++++++++++- Week8/834 AC.png | Bin 0 -> 41063 bytes Week8/834 Sum of Distances in Tree.md | 72 ++++++++++++++++++++++++++ 3 files changed, 128 insertions(+), 2 deletions(-) create mode 100644 Week8/834 AC.png create mode 100644 Week8/834 Sum of Distances in Tree.md diff --git a/Hard/834 Sum of Distances in Tree.md b/Hard/834 Sum of Distances in Tree.md index 3fbb419..c4cef75 100644 --- a/Hard/834 Sum of Distances in Tree.md +++ b/Hard/834 Sum of Distances in Tree.md @@ -2,17 +2,71 @@ ## Intuition +A key observation is that we can leverage the tree structure and parent-child relationships to compute these sums efficiently. Instead of calculating distances from scratch for each node, we can use the results from a parent node to derive the results for its children. + ## Approach +The solution uses a two-pass DFS approach: + +1. First DFS (dfs1): + - Calculates the number of child nodes for each node + - Computes the initial sum of distances for the root node (0) + - This pass builds the foundation for the second pass +2. Second DFS (dfs2): + - Uses the results from the first pass to compute distances for all other nodes + - For each child node, the sum of distances can be derived from its parent's sum using the formula: + `ret[child] = ret[parent] + (n - 2 * childNodes[child])` + - This formula works because moving from parent to child: + - Increases distance by 1 for all nodes not in the child's subtree + - Decreases distance by 1 for all nodes in the child's subtree + ## Complexity -- Time complexity: -- Space complexity: +- Time complexity: O(n) +- Space complexity: O(n) ## Keywords +- DFS +- Distance Calculation + ## Code ```go +func sumOfDistancesInTree(n int, edges [][]int) []int { + ret, childNodes, tree := make([]int, n), make([]int, n), make([][]int, n) + for _, edge := range edges { + a, b := edge[0], edge[1] + tree[a], tree[b] = append(tree[a], b), append(tree[b], a) + } + + var dfs1 func(cur, prev int) + dfs1 = func(cur, prev int) { + childNodes[cur] = 1 + for _, neighbor := range tree[cur] { + if neighbor == prev { + continue + } + dfs1(neighbor, cur) + childNodes[cur] += childNodes[neighbor] + ret[cur] += ret[neighbor] + childNodes[neighbor] + } + } + + var dfs2 func(cur, prev int) + dfs2 = func(cur, prev int) { + for _, neighbor := range tree[cur] { + if neighbor == prev { + continue + } + ret[neighbor] = ret[cur] + (n- 2 * childNodes[neighbor]) + dfs2(neighbor, cur) + } + } + + dfs1(0, -1) + dfs2(0, -1) + return ret +} ``` diff --git a/Week8/834 AC.png b/Week8/834 AC.png new file mode 100644 index 0000000000000000000000000000000000000000..afc402110d512d016eb127f8f1ec4ea7afd187d2 GIT binary patch literal 41063 zcmeFZRa70@7A=YfhlM1#yIXK~cXx-N3wH_b5}e=(1b2eFdxE=Lf=hzSEw-Jr&uj1h ze%!RSS`}4OYWf&`^qxp%MJW_SJVXcx2oxD;lnH1cmr(+q_H(>i_gWB3LawlClX$F#GpJm*K!vck>TYw-4Y4t-UrWguXNlz@^{V-_Yhcw zO6Gf8cLz%?M4o|Yq`&g;p{ZQF7*cfe-uTX66|ae@{dSP|>d&G7@Uw1^oE1MUWzzL0 zI6%*J_k!v3orpCH6TdJ%wc@dt{<)x2XI^0h8kQc4phlMcnMAu4Z4yZbC2CDj2Dv{O 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Sum of Distances in Tree + +## Intuition + +A key observation is that we can leverage the tree structure and parent-child relationships to compute these sums efficiently. Instead of calculating distances from scratch for each node, we can use the results from a parent node to derive the results for its children. + +## Approach + +The solution uses a two-pass DFS approach: + +1. First DFS (dfs1): + - Calculates the number of child nodes for each node + - Computes the initial sum of distances for the root node (0) + - This pass builds the foundation for the second pass +2. Second DFS (dfs2): + - Uses the results from the first pass to compute distances for all other nodes + - For each child node, the sum of distances can be derived from its parent's sum using the formula: + `ret[child] = ret[parent] + (n - 2 * childNodes[child])` + - This formula works because moving from parent to child: + - Increases distance by 1 for all nodes not in the child's subtree + - Decreases distance by 1 for all nodes in the child's subtree + +## Complexity + +- Time complexity: O(n) +- Space complexity: O(n) + +## Keywords + +- DFS +- Distance Calculation + +## Code + +```go +func sumOfDistancesInTree(n int, edges [][]int) []int { + ret, childNodes, tree := make([]int, n), make([]int, n), make([][]int, n) + for _, edge := range edges { + a, b := edge[0], edge[1] + tree[a], tree[b] = append(tree[a], b), append(tree[b], a) + } + + var dfs1 func(cur, prev int) + dfs1 = func(cur, prev int) { + childNodes[cur] = 1 + for _, neighbor := range tree[cur] { + if neighbor == prev { + continue + } + dfs1(neighbor, cur) + childNodes[cur] += childNodes[neighbor] + ret[cur] += ret[neighbor] + childNodes[neighbor] + } + } + + var dfs2 func(cur, prev int) + dfs2 = func(cur, prev int) { + for _, neighbor := range tree[cur] { + if neighbor == prev { + continue + } + ret[neighbor] = ret[cur] + (n- 2 * childNodes[neighbor]) + dfs2(neighbor, cur) + } + } + + dfs1(0, -1) + dfs2(0, -1) + + return ret +} +```