From 82c8d39e5595547115f6a8d8b5d6d751d83395f3 Mon Sep 17 00:00:00 2001
From: fengzw <zhiwei.feng1995@gmail.com>
Date: Sat, 8 May 2021 19:52:24 +0800
Subject: [PATCH] add: original solution for
 Challenge3_Count_of_Structurally_Unique_Binary_Search_Trees

---
 .../solution.go                               | 81 ++++++++++++-------
 1 file changed, 54 insertions(+), 27 deletions(-)

diff --git a/Pattern10 - Subsets/Challenge3-Count_of_Structurally_Unique_Binary_Search_Trees/solution.go b/Pattern10 - Subsets/Challenge3-Count_of_Structurally_Unique_Binary_Search_Trees/solution.go
index b3104da..2a0c206 100644
--- a/Pattern10 - Subsets/Challenge3-Count_of_Structurally_Unique_Binary_Search_Trees/solution.go	
+++ b/Pattern10 - Subsets/Challenge3-Count_of_Structurally_Unique_Binary_Search_Trees/solution.go	
@@ -4,38 +4,65 @@ package Challenge3_Count_of_Structurally_Unique_Binary_Search_Trees
 已经在challenge2中实现
 ref: https://leetcode-cn.com/problems/unique-binary-search-trees/
 */
+
 func numTrees(n int) int {
-	var bfs func(int, int) int
-	var m = make(map[Range]int)
-	bfs = func(start, end int) int {
-		var res = 0
-		if start == end {
-			return 1
-		}
-		if v, ok := m[Range{start, end}]; ok {
+	var m = make(map[int]int)
+
+	var countTrees func(int) int
+	countTrees = func(n int) int {
+		if v,ok:=m[n];ok{
 			return v
 		}
-		for i := start; i <= end; i++ {
-			if i == start {
-				res += bfs(i+1, end)
-				continue
-			}
-			if i == end {
-				res += bfs(start, i-1)
-				continue
-			}
-			left := bfs(start, i-1)
-			right := bfs(i+1, end)
-			res += left * right
+		if n<=1 {
+			return 1
+		}
+
+		count := 0
+		for i:=1;i<=n;i++{
+			leftTrees := countTrees(i-1)
+			rightTrees := countTrees(n-i)
+			count += leftTrees*rightTrees
 		}
-		m[Range{start, end}] = res
-		return res
+		
+		m[n]=count
+		return count
 	}
 
-	return bfs(1, n)
+	return countTrees(n)
 }
 
-type Range struct {
-	start int
-	end   int
-}
+// func numTreesBackup(n int) int {
+// 	var bfs func(int, int) int
+// 	var m = make(map[Range]int)
+// 	bfs = func(start, end int) int {
+// 		var res = 0
+// 		if start == end {
+// 			return 1
+// 		}
+// 		if v, ok := m[Range{start, end}]; ok {
+// 			return v
+// 		}
+// 		for i := start; i <= end; i++ {
+// 			if i == start {
+// 				res += bfs(i+1, end)
+// 				continue
+// 			}
+// 			if i == end {
+// 				res += bfs(start, i-1)
+// 				continue
+// 			}
+// 			left := bfs(start, i-1)
+// 			right := bfs(i+1, end)
+// 			res += left * right
+// 		}
+// 		m[Range{start, end}] = res
+// 		return res
+// 	}
+
+// 	return bfs(1, n)
+// }
+
+// type Range struct {
+// 	start int
+// 	end   int
+// }