The ten-layer binary tree node JAVA of the 11th Blue Bridge Demo

How many nodes does a 10-layer binary tree contain at most?

Note: When a binary tree has only one node, it is a layer.

Idea: When you look at the piece, you know that it must be a moth. I drew a five-layer binary tree directly on the book. After finding the rule, I directly wrote the code. The rule is 2 to the power of 10. Answer: 1023

This solution of the first kind really looks like a han han -.- #

public class Main {
	public static void main(String[] args) {
		int n1 = 1;
		int n2 = 2;
		int n3 = n2 * 2;
		int n4 = n3 * 2;
		int n5 = n4 * 2;
		int n6 = n5 * 2;
		int n7 = n6 * 2;
		int n8 = n7 * 2;
		int n9 = n8 * 2;
		int n10 = n9 * 2;
		System.out.println(n10 + n9 + n8 + n7 + n6 + n5 + n4 + n3 + n2 + n1);
	}
}

In the second solution, the problem requires that the first layer be fixed at 1, and then enumerate 9 layers.

public class Main  {
	public static void main(String[] args) {
		int ans = 1;
		int num = 1;
		for (int i = 1; i <= 9; i++) {
			num *= 2;
			ans += num;   // 10层节点相加
		}
		System.out.println(ans);  
	}
}

The third solution, according to the law is 2 to the power of 10 -1, remember to give int type.

public class Main {
	public static void main(String[] args) {
		System.out.println((int) Math.pow(2, 10) - 1);
	}
}

Small theater: Keep your mind high. Keep your mind higt.