java - Time and space complexity of this function to print binary tree level by level -

this algorithm printing common binary tree level level.

what time complexity , space complexity of printspecificlevel_bt() , printbt_lbl()?

i think printspecificlevel_bt's time complexity o(lg n), , space complexity o(lg n).
think printbt_lbl()'s time complexity o((lgn)^2), , space complexity o((lgn)^2).

is correct?

// print specific level of binary tree. public static void printspecificlevel_bt (node root, int level) {     if (root == null) return;     if (level == 0) system.out.print(string.format("%-6d", root.data)); // base case.     // recrusion.     printspecificlevel_bt(root.leftch, level - 1);     printspecificlevel_bt(root.rightch, level - 1); }  // height of binary tree. public static int getheight_bt (node root) {     if (root == null || (root.leftch == null && root.rightch == null)) return 0; // base case.     return 1 + math.max (getheight_bt(root.leftch), getheight_bt(root.rightch)); }  // print binary tree level level. public static void printbt_lbl (node root) {     // height of binary tree.     int height = getheight_bt(root);     (int = 0; <= height; ++) {         printspecificlevel_bt(root, i);         system.out.println();     } } 

printspecificlevel_bt o(n) since looks @ every node in tree. however, change (returning when level == 0), can make o(min(n, 2^level)).

getheight o(n) since looks @ every node in tree. printbt_lbl calls getheight once , printspecificlevel_bt height times, complexity o(n + n*height) = o(n*height).

the space complexity of each o(height) since recurses way bottom of tree. can't o(log n) since tree isn't balanced (unless is).