原文:
给定一个整数 n ，任务是找到从nt4 节点到以下形式的二叉树根的路径:
- binary tree is a up to [t2】 n t7 node level.
- the node numbers are 1 to n , and 1 from the root.
- the structure of the tree is as follows:
1 / \ 2 3 / \ / \ 4 5 6 7 ................ / \ ............ n - 1 n ............
示例:
输入: n = 7 输出: 7 3 1 解释:从节点 7 到根的路径是 7 - > 3 - > 1。
输入: n = 11 输出: 11 5 2 1 说明:从节点 11 到根的路径是 11 - > 5 - > 2 - > 1。
天真方法:解决问题最简单的方法是从给定节点执行 直到遇到根节点并打印路径。
时间复杂度: o(n) 辅助空间: o(1)
高效方法:上述方法可以基于给定二叉树的结构进行优化。可以观察到，每个 n 的父节点都是 n / 2 。因此，重复打印 n 的当前值，并将 n 更新为 n / 2 ，直到 n 等于 1 ，即到达根节点。
下面是上述方法的实现:
c
// c program for the above approach
#include
using namespace std;
// function to print the path
// from node to root
void path_to_root(int node)
{
// iterate until root is reached
while (node >= 1) {
// print the value of
// the current node
cout << node << ' ';
// move to parent of
// the current node
node /= 2;
}
}
// driver code
int main()
{
int n = 7;
path_to_root(n);
return 0;
}
java 语言(一种计算机语言，尤用于创建网站)
// java program for the above approach
import java.util.*;
class gfg{
// function to print the path
// from node to root
static void path_to_root(int node)
{
// iterate until root is reached
while (node >= 1)
{
// print the value of
// the current node
system.out.print(node " ");
// move to parent of
// the current node
node /= 2;
}
}
// driver code
public static void main(string[] args)
{
int n = 7;
path_to_root(n);
}
}
// this code is contributed by shivanisinghss2110
python 3
# python3 program for the above approach
# function to print the path
# from node to root
def path_to_root(node):
# iterate until root is reached
while (node >= 1):
# print the value of
# the current node
print(node, end = " ")
# move to parent of
# the current node
node //= 2
# driver code
if __name__ == '__main__':
n = 7
path_to_root(n)
# this code is contributed by mohit kumar 29
c
// c# program for the above approach
using system;
class gfg
{
// function to print the path
// from node to root
static void path_to_root(int node)
{
// iterate until root is reached
while (node >= 1)
{
// print the value of
// the current node
console.write(node " ");
// move to parent of
// the current node
node /= 2;
}
}
// driver code
public static void main(string[] args)
{
int n = 7;
path_to_root(n);
}
}
// this code is contributed by shivanisinghss2110
java 描述语言
output:
7 3 1
时间复杂度:o(log2(n)) 辅助空间: o(1)
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