Merge pull request DaleStudy#81 from Invidam/week03-invidam

[Vidam] Week 3 Solution | Go

Author: leokim0922

climbing-stairs/invidam.go.md

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+# Intuition
+<!-- Describe your first thoughts on how to solve this problem. -->
+This problem is a typical dynamic programming (DP) problem. (keyword: `Fibonacci`)
+
+DP has two methods: tabulation and memoization. I'll introduce both methods.
+# Approach (tabulation)
+<!-- Describe your approach to solving the problem. -->
+1. Create an array to store the results.
+2. Initiate default values for the base cases `0` and `1`.
+3. While iterating through the array, fill in the values using this formula $$f(n) = f(n-1) + f(n-2)$$
+# Complexity
+## Complexity (V1)
+- Time complexity: $$O(n)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O(n)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+# Complexity (V2)
+- Time complexity: $$O(n)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O(1)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+
+(n is value of `n`)
+# Code
+```go
+func climbStairsV1(n int) int {
+	climbData := make([]int, n+2, n+2)
+	climbData[0], climbData[1] = 1, 1
+	for s := 0; s < n; s++ {
+		climbData[s+2] = climbData[s] + climbData[s+1]
+	}
+
+	return climbData[n]
+}
+
+func climbStairsV2(n int) int {
+	prev, curr := 1, 1
+	for s := 1; s < n; s++ {
+		prev, curr = curr, prev+curr
+	}
+
+	return curr
+}
+```
+
+> As you can see in `V2`, it can be optimized. Remove the array and maintain only the `prev` and `curr` values. In Golang, `Multiple Assignment` prodives syntatic sugar.
+
+- - -
+
+# Approach (memoization)
+<!-- Describe your approach to solving the problem. -->
+1. Create an hash map (or array) to **cache** the results.
+2. Initialize default values to indicate unvisited nodes. (`-1`).
+3. Call the recursion using this formula $$f(n) = f(n-1) + f(n-2)$$.
+4. If there are cached results, return it.
+5. Pay attension to the **base case**, and always update the cache.
+
+# Complexity
+- Time complexity: $$O(n)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O(n)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+(n is value of `n`)
+# Code
+```go
+var cache map[int]int = map[int]int{}
+func climbStairs(n int) int {
+	if n == 0 || n == 1 {
+		return 1
+	} else if n < 0 {
+		return 0
+	} else if val, ok := cache[n]; ok {
+		return val
+	}
+
+	ret := climbStairs(n-1) + climbStairs(n-2)
+	cache[n] = ret
+	return ret
+}
+```

maximum-depth-of-binary-tree/invidam.go.md

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+# Intuition
+Recursuib is a natural method for iterating trees.
+
+# Approach
+<!-- Describe your approach to solving the problem. -->
+1. Child function can calculate the depth of its subtrees automatically.
+2. Parent function only select the maximum of the two depths and return +1. (i.e. `+1` means parent's depth.)
+
+# Complexity
+- Time complexity: $$O(n)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity
+    - $$O(logN)$$ (best case for balanced tree)
+    - $$O(N)$$ (worst case for  skewed tree)
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+(N: size of node.)
+# Code
+```
+func maxDepth(root *TreeNode) int {
+    if root == nil {
+        return 0
+    }
+    return max(maxDepth(root.Left), maxDepth(root.Right)) + 1
+}
+```
+- - -
+# Intuition
+Implement Queue can be troublesome, but it is effective to problem that require tracking depths or levels.
+<!-- Describe your first thoughts on how to solve this problem. -->
+
+# Approach
+<!-- Describe your approach to solving the problem. -->
+1. Maintain Element belonging to the same level in the queue.
+2. While Iterating through the queue, remove the current level and save the next level.
+- In GoLang, `range for loop` capture only first once. So We can maintain current level's easily.
+3. increase depth while iterationg through all elements until the end.
+# Complexity
+- Time complexity: $$O(n)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity
+    - $$O(logN)$$ (best case for balanced tree)
+    - $$O(N)$$ (worst case for  skewed tree)
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+(N: size of node.)
+
+# Code
+```go
+func maxDepth(root *TreeNode) int {
+	if root == nil {
+		return 0
+	}
+	depth := 0
+	currLevel := []*TreeNode{root}
+
+	for len(currLevel) != 0 {
+		depth++
+		for _, curr := range currLevel {
+			if curr.Left != nil {
+				currLevel = append(currLevel, curr.Left)
+			}
+			if curr.Right != nil {
+				currLevel = append(currLevel, curr.Right)
+			}
+			currLevel = currLevel[1:]
+		}
+	}
+
+	return depth
+}
+```
+
+# What I learned
+- [Slice](https://velog.io/@invidam/GoLang-Slice)

meeting-rooms/invidam.go.md

@@ -0,0 +1,34 @@
+# Intuition
+It is a simple `greedy` problem.
+간단한 그리디 분류의 문제다. 
+# Approach 
+1. To find earliest interval, sort intervals by start time in ascending order.
+2. After sorting, while iterating through the array, check for conflict: the current interval's start time shoud be smaller than the next interval's end time.
+# Complexity
+- Time complexity: $$O(nlog(n))$$
+- Space complexity: $$O(n)$$
+
+(n is length of `intervals`)
+# Code
+```go
+func CanAttendMeetings(intervals []*Interval) bool {
+	sort.Slice(intervals, func(i, j int) bool {
+		return intervals[i].Start < intervals[j].Start
+	})
+
+	curr := &Interval{-1, -1}
+	for _, next := range intervals {
+		if curr.End > next.Start {
+			return false
+		}
+		curr = next
+	}
+
+	return true
+}
+```
+
+# What I learned
+GoLang Sort
+- mechanism: [Pattern-defeating Quicksort](https://www.youtube.com/watch?v=jz-PBiWwNjc)
+- usage: https://hackthedeveloper.com/how-to-sort-in-go/ 

same-tree/invidam.go.md

@@ -0,0 +1,82 @@
+# Intuition (DFS, Recursion)
+<!-- Describe your first thoughts on how to solve this problem. -->
+Recursion is natural method to iterate trees. (Particularly, multiple trees!)
+# Approach
+<!-- Describe your approach to solving the problem. -->
+1. Child nodes(i.e. Left and Right) are compared eqaulity with their subtrees.
+2. Parent nodes check their own values (`Val`) and their children's comparisions.
+
+(Tip: Comparing the values of nodes before recursion is more efficient. due to **short circuit**, which stops further evaluation(`isSameTree(p.Left, q.Left) && isSameTree(p.Right, q.Right)`) when the outcome is already determined by comparing `p.Val == q.Val`)
+# Complexity
+- Time complexity: $$O(n+m)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O(h_n + h_m)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+
+(n and m are number of nodes in trees p and q. $$h_n$$ and $$h_m$$ are their heights.)
+# Code
+```go
+func isSameTree(p *TreeNode, q *TreeNode) bool {
+	if p == nil || q == nil {
+		return p == nil && q == nil
+	}
+
+	return p.Val == q.Val && isSameTree(p.Left, q.Left) && isSameTree(p.Right, q.Right)
+}
+```
+- - -
+# BFS
+# Approach
+<!-- Describe your approach to solving the problem. -->
+1. Like a typical BFS solution, Create Queue and iterate through the tree. However, in this case, mulitple queues are required.
+2. While Iterating, Check equality two nodes in p and q.
+# Complexity
+- Time complexity: $$O(n+m)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O(n + m)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+
+(n and m are number of nodes in trees p and q.)
+# Code
+```go
+func updateQueue(node *TreeNode, queue []*TreeNode) []*TreeNode {
+	queue = append(queue, node.Left)
+	queue = append(queue, node.Right)
+
+	return queue
+}
+
+func isSameTree(p *TreeNode, q *TreeNode) bool {
+	if p == nil || q == nil {
+		return p == nil && q == nil
+	}
+	pQueue := []*TreeNode{p}
+	qQueue := []*TreeNode{q}
+
+	for len(pQueue) != 0 {
+        pCurr := pQueue[0]
+        qCurr := qQueue[0]
+
+        pQueue = pQueue[1:]
+        qQueue = qQueue[1:]
+
+        if pCurr == nil && qCurr == nil {
+            continue
+        }
+
+        if (pCurr == nil || qCurr == nil) || (pCurr.Val != qCurr.Val) {
+            return false
+        }
+        pQueue = updateQueue(pCurr, pQueue)
+        qQueue = updateQueue(qCurr, qQueue)
+	}
+
+	return true
+}
+```
+
+# What I learned
+- Short circuit In Go.
+- Function couldn't update original value (like `updateQueue()'s queue`)

subtree-of-another-tree/invidam.go.md

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+# Intuition (DFS & BFS)
+<!-- Describe your first thoughts on how to solve this problem. -->
+We need two main function: one to check the equality of nodes and the subtrees, and another to iterate through the main tree.
+
+We will use both DFS and BFS methods to solve this problem.
+
+Reference. [Same Tree](ttps://leetcode.com/problems/same-tree/solutions/5159658/go-simple-solution)
+
+# Approach
+<!-- Describe your approach to solving the problem. -->
+1. Create a function that, while iterating using DFS(Recursion) or BFS(Queue),checks if the two trees are equal.
+2. First, check if the two trees are equal. If not, iterate through the children of main tree. (`root.Left`, `root.Right`)
+# Complexity (DFS)
+- Time complexity: $$O(n * m)$$
+  (This complexity is $$O(n * m)$$. because the `isSubtree()` iterates throuth all modes while **simultaneously** calling the `isEqualtree()` for each node.
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O({h_n} + {h_m})$$
+  (This complexity is determined. because the maximun depth of the call stack, which doesn't exceed the sum of heights of both trees.)
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+
+# Code
+```
+func isEqualTree(root *TreeNode, subRoot *TreeNode) bool {
+    if (root == nil) || (subRoot == nil) {
+        return root == subRoot
+    }
+
+    return (root.Val == subRoot.Val) && isEqualTree(root.Left, subRoot.Left) && isEqualTree(root.Right, subRoot.Right)
+}
+
+func isSubtree(root *TreeNode, subRoot *TreeNode) bool {
+    if root == nil {
+        //assert subRoot != nil
+        return false
+    }
+    
+    return isEqualTree(root, subRoot) || isSubtree(root.Left, subRoot) || isSubtree(root.Right, subRoot)
+}
+```
+- - -
+# Complexity (BFS)
+- Time complexity: $$O(n * m)$$
+  (This complexity is $$O(n * m)$$. because the `isSubtree()` iterates throuth all modes while **simultaneously** calling the `isEqualtree()` for each node.
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity: $$O({h_n} + {h_m})$$
+  (This complexity is determined. because the maximun sizes of the queues (`q`, `q1`, `q2`), which doesn't exceed the sum of sizes of both trees.)
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+# Code
+```go
+func isEqualTree(root *TreeNode, subRoot *TreeNode) bool {
+	q1 := []*TreeNode{root}
+	q2 := []*TreeNode{subRoot}
+
+	for len(q1) != 0 {
+		f1 := q1[0]
+		f2 := q2[0]
+
+		q1 = q1[1:]
+		q2 = q2[1:]
+
+		if (f1 == nil) && (f2 == nil) {
+			continue
+		}
+		if (f1 == nil) || (f2 == nil) || (f1.Val != f2.Val) {
+			return false
+		}
+
+		q1 = append(q1, f1.Left)
+		q1 = append(q1, f1.Right)
+
+		q2 = append(q2, f2.Left)
+		q2 = append(q2, f2.Right)
+	}
+
+	return true
+}
+
+func isSubtree(root *TreeNode, subRoot *TreeNode) bool {
+	if root == nil {
+		//assert subRoot != nil
+		return false
+	}
+
+	q := []*TreeNode{root}
+
+	for len(q) != 0 {
+		node := q[0]
+		q = q[1:]
+
+		if node == nil {
+			continue
+		}
+		if isEqualTree(node, subRoot) {
+			return true
+		}
+
+		q = append(q, node.Left)
+		q = append(q, node.Right)
+	}
+
+	return false
+}
+```