LeetCode //C - 987. Vertical Order Traversal of a Binary Tree

987. Vertical Order Traversal of a Binary Tree

Given the root of a binary tree, calculate the vertical order traversal of the binary tree.

For each node at position (row, col), its left and right children will be at positions (row + 1, col - 1) and (row + 1, col + 1) respectively. The root of the tree is at (0, 0).

The vertical order traversal of a binary tree is a list of top-to-bottom orderings for each column index starting from the leftmost column and ending on the rightmost column. There may be multiple nodes in the same row and same column. In such a case, sort these nodes by their values.

Return the vertical order traversal of the binary tree.
 

Example 1:

Input: root = [3,9,20,null,null,15,7]
Output: [[9],[3,15],[20],[7]]
Explanation:
Column -1: Only node 9 is in this column.
Column 0: Nodes 3 and 15 are in this column in that order from top to bottom.
Column 1: Only node 20 is in this column.
Column 2: Only node 7 is in this column.

Example 2:

Input: root = [1,2,3,4,5,6,7]
Output: [[4],[2],[1,5,6],[3],[7]]
Explanation:
Column -2: Only node 4 is in this column.
Column -1: Only node 2 is in this column.
Column 0: Nodes 1, 5, and 6 are in this column.
1 is at the top, so it comes first.
5 and 6 are at the same position (2, 0), so we order them by their value, 5 before 6.
Column 1: Only node 3 is in this column.
Column 2: Only node 7 is in this column.

Example 3:

Input: root = [1,2,3,4,6,5,7]
Output: [[4],[2],[1,5,6],[3],[7]]
Explanation:
This case is the exact same as example 2, but with nodes 5 and 6 swapped.
Note that the solution remains the same since 5 and 6 are in the same location and should be ordered by their values.

Constraints:

• The number of nodes in the tree is in the range [1, 1000].
• 0 <= Node.val <= 1000

From: LeetCode
Link: 987. Vertical Order Traversal of a Binary Tree

Solution:

Ideas:

• DFS the tree and record each node as (col, row, value) where left = col-1, right = col+1.
• Sort all records by col, then row, then value (this handles the “same row+col sort by value” rule).
• Scan the sorted list, group by col, and output each group as one vertical column.

Code:

/** * Definition for a binary tree node. * struct TreeNode { * int val; * struct TreeNode *left; * struct TreeNode *right; * }; */typedefstruct{int col;int row;int val;} Trip;typedefstruct{ Trip *a;int sz;int cap;} Vec;staticvoidvec_push(Vec *v,int col,int row,int val){if(v->sz == v->cap){ v->cap =(v->cap ==0)?64: v->cap *2; v->a =(Trip *)realloc(v->a,(size_t)v->cap *sizeof(Trip));} v->a[v->sz++]=(Trip){col, row, val};}staticvoiddfs(structTreeNode*node,int row,int col, Vec *v){if(!node)return;vec_push(v, col, row, node->val);dfs(node->left, row +1, col -1, v);dfs(node->right, row +1, col +1, v);}staticintcmp_trip(constvoid*p1,constvoid*p2){const Trip *a =(const Trip *)p1;const Trip *b =(const Trip *)p2;if(a->col != b->col)return(a->col < b->col)?-1:1;if(a->row != b->row)return(a->row < b->row)?-1:1;if(a->val != b->val)return(a->val < b->val)?-1:1;return0;}/** * Return an array of arrays of size *returnSize. * The sizes of the arrays are returned as *returnColumnSizes array. * Note: Both returned array and *columnSizes array must be malloced, assume caller calls free(). */int**verticalTraversal(structTreeNode* root,int* returnSize,int** returnColumnSizes){*returnSize =0;*returnColumnSizes =NULL;if(!root)returnNULL; Vec v ={0};dfs(root,0,0,&v);qsort(v.a,(size_t)v.sz,sizeof(Trip), cmp_trip);// Count distinct columnsint cols =0;for(int i =0; i < v.sz;){ cols++;int c = v.a[i].col;while(i < v.sz && v.a[i].col == c) i++;}int**res =(int**)malloc((size_t)cols *sizeof(int*));int*colSizes =(int*)malloc((size_t)cols *sizeof(int));// Build result by grouping same columnint idx =0;for(int i =0; i < v.sz;){int c = v.a[i].col;int start = i;while(i < v.sz && v.a[i].col == c) i++;int len = i - start; colSizes[idx]= len; res[idx]=(int*)malloc((size_t)len *sizeof(int));for(int k =0; k < len; k++){ res[idx][k]= v.a[start + k].val;} idx++;}free(v.a);*returnSize = cols;*returnColumnSizes = colSizes;return res;}