Merge pull request #13 from colorbox/110

110. Balanced Binary Tree

Author: colorbox

110/step1.cpp

@@ -0,0 +1,24 @@
+// 高さ平衡の定義を勘違いしておりパスできなかったので解説を見て書く
+class Solution {
+public:
+    bool isBalanced(TreeNode* root) {
+        if (!root) {
+            return true;
+        }
+        int left_height = recursive_max_height(root->left, 0);
+        int right_height = recursive_max_height(root->right, 0);
+
+        return abs(right_height - left_height) <= 1 && isBalanced(root->left) && isBalanced(root->right);
+    }
+
+    int recursive_max_height(TreeNode* root, int current_height) {
+        if (root == nullptr) {
+            return current_height - 1;
+        }
+
+        int left_height = recursive_max_height(root->left, current_height + 1);
+        int right_height = recursive_max_height(root->right, current_height + 1);
+
+        return max(left_height, right_height);
+    }
+};

110/step2.cpp

@@ -0,0 +1,25 @@
+// 引数名を変えて　高さであることを直感的にわかるようにした
+class Solution {
+public:
+    bool isBalanced(TreeNode* root) {
+        if (!root) {
+            return true;
+        }
+
+        int left_height = height(root->left, 0);
+        int right_height = height(root->right, 0);
+
+        return abs(right_height - left_height) <=1 && isBalanced(root->left) && isBalanced(root->right);
+    }
+
+    int height(TreeNode* root, int base_height) {
+        if (!root) {
+            return base_height;
+        }
+
+        int left_height = height(root->left, base_height);
+        int right_height = height(root->right, base_height);
+
+        return max(left_height, right_height) + 1;
+    }
+};

110/step3.cpp

@@ -0,0 +1,30 @@
+// デフォルト引数を使用
+// isBalancedの再帰部分がゴチャごチャしていて読みづらさを感じたので自身のチェックと再帰を分離
+class Solution {
+public:
+    bool isBalanced(TreeNode* root) {
+        if (!root) {
+            return true;
+        }
+
+        int left_height = height(root->left);
+        int right_height = height(root->right);
+
+        if (abs(right_height - left_height) > 1) {
+            return false;
+        }
+
+        return isBalanced(root->left) && isBalanced(root->right);
+    }
+
+    int height(TreeNode* root, int base_height = 0) {
+        if (!root) {
+            return base_height;
+        }
+
+        int left_height = height(root->left);
+        int right_height = height(root->right);
+
+        return max(left_height, right_height) + 1;
+    }
+};

110/step4.cpp

@@ -0,0 +1,30 @@
+// 繰り返し呼ばれるheightについて、キャッシュで高速化を試みたがむしろ低速化した
+class Solution {
+public:
+    bool isBalanced(TreeNode* root) {
+        if (!root) {
+            return true;
+        }
+
+        int left_height = height(root->left);
+        int right_height = height(root->right);
+
+        return abs(right_height - left_height) <= 1 && isBalanced(root->left) && isBalanced(root->right);
+    }
+
+    map<TreeNode*, int> height_cache;
+    int height(TreeNode* root, int base_height = 0) {
+        if (height_cache.count(root)) {
+            return height_cache[root];
+        }
+        if (!root) {
+            return base_height;
+        }
+
+        int left_height = height(root->left);
+        int right_height = height(root->right);
+
+        height_cache[root] = max(left_height, right_height)+1;
+        return height_cache[root];
+    }
+};

110/step5.cpp

@@ -0,0 +1,30 @@
+// キャッシュを使わずにO(N)となるコード
+class Solution {
+public:
+    bool isBalanced(TreeNode* root) {
+        return GetHeight(root) != -1;
+    }
+
+    int GetHeight(TreeNode* root) {
+        if (!root) {
+            return 0;
+        }
+
+        int left_height = GetHeight(root->left);
+        if (left_height == -1) {
+            return -1;
+        }
+
+        int right_height = GetHeight(root->right);
+        if (right_height == -1) {
+            return -1;
+        }
+
+        if (abs(left_height - right_height) > 1) {
+            return -1;
+        }
+
+        return max(left_height, right_height) + 1;
+    }
+
+};