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| 1 | +/* |
| 2 | +333. Largest BST Subtree |
| 3 | + |
| 4 | +Given a binary tree, find the largest subtree which is a Binary Search Tree (BST), where largest means subtree with largest number of nodes in it. |
| 5 | + |
| 6 | +Note: |
| 7 | +A subtree must include all of its descendants. |
| 8 | + |
| 9 | +Example: |
| 10 | + |
| 11 | +Input: [10,5,15,1,8,null,7] |
| 12 | + |
| 13 | + 10 |
| 14 | + / \ |
| 15 | + 5 15 |
| 16 | + / \ \ |
| 17 | +1 8 7 |
| 18 | + |
| 19 | +Output: 3 |
| 20 | +Explanation: The Largest BST Subtree in this case is the highlighted one. |
| 21 | + The return value is the subtree's size, which is 3. |
| 22 | + |
| 23 | + |
| 24 | +Follow up: |
| 25 | +Can you figure out ways to solve it with O(n) time complexity? |
| 26 | +*/ |
| 27 | + |
| 28 | +/** |
| 29 | + * Definition for a binary tree node. |
| 30 | + * struct TreeNode { |
| 31 | + * int val; |
| 32 | + * struct TreeNode *left; |
| 33 | + * struct TreeNode *right; |
| 34 | + * }; |
| 35 | + */ |
| 36 | +typedef struct { |
| 37 | + int n; |
| 38 | + int min; |
| 39 | + int max; |
| 40 | + int flag; |
| 41 | +} val_t; |
| 42 | + |
| 43 | +val_t post_order(struct TreeNode *node, int *max) { |
| 44 | + val_t lval, rval, cval = { 0 }; |
| 45 | + |
| 46 | + if (!node) return cval; |
| 47 | + |
| 48 | + lval = post_order(node->left, max); |
| 49 | + rval = post_order(node->right, max); |
| 50 | + |
| 51 | + if (lval.n == -1 || rval.n == -1 || // left or right is not a BST |
| 52 | + (lval.flag && node->val <= lval.max) || // current does not qualify a BST |
| 53 | + (rval.flag && node->val >= rval.min)) { |
| 54 | + cval.n = -1; |
| 55 | + } else { |
| 56 | + cval.n = lval.n + rval.n + 1; // current qualifies a BST |
| 57 | + |
| 58 | + if (*max < cval.n) *max = cval.n; |
| 59 | + |
| 60 | + cval.min = lval.flag == 0 ? node->val : lval.min; |
| 61 | + cval.max = rval.flag == 0 ? node->val : rval.max; |
| 62 | + cval.flag = 1; |
| 63 | + } |
| 64 | + |
| 65 | + //printf("%d: %d,%d,%d\n", node->val, cval.min, cval.max, cval.n); |
| 66 | + |
| 67 | + return cval; |
| 68 | +} |
| 69 | + |
| 70 | +int largestBSTSubtree(struct TreeNode* root){ |
| 71 | + int max = 0; |
| 72 | + |
| 73 | + post_order(root, &max); |
| 74 | + |
| 75 | + return max; |
| 76 | +} |
| 77 | + |
| 78 | + |
| 79 | +/* |
| 80 | +Difficulty:Medium |
| 81 | + |
| 82 | + |
| 83 | +*/ |
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