目录
一、题目
1、题目描述
给你一棵树，树上有
n个节点，按从0到n-1编号。树以父节点数组的形式给出，其中parent[i]是节点i的父节点。树的根节点是编号为0的节点。树节点的第
k个祖先节点是从该节点到根节点路径上的第k个节点。实现
TreeAncestor类：
TreeAncestor（int n， int[] parent）对树和父数组中的节点数初始化对象。getKthAncestor``(int node, int k)返回节点node的第k个祖先节点。如果不存在这样的祖先节点，返回-1。
2、接口描述
python3
python
class TreeAncestor:
def __init__(self, n: int, parent: List[int]):
def getKthAncestor(self, node: int, k: int) -> int:
# Your TreeAncestor object will be instantiated and called as such:
# obj = TreeAncestor(n, parent)
# param_1 = obj.getKthAncestor(node,k)cpp
cpp
class TreeAncestor {
TreeAncestor(int n, List<int> parent) {
}
int getKthAncestor(int node, int k) {
}
}
/**
* Your TreeAncestor object will be instantiated and called as such:
* TreeAncestor obj = TreeAncestor(n, parent);
* int param1 = obj.getKthAncestor(node,k);
*/3、原题链接
二、解题报告
1、思路分析
关于ST表求LCA见：LCA算法-倍增算法-CSDN博客
比ST表求LCA板子题还要简单的题
我们预处理出f[u][i]，代表u向上跳2^i层的祖先
然后对于查询向上第k个祖先我们只需要将k二进制拆分往上跳即可
2、复杂度
时间复杂度： 预处理O(nlogn) 查询:O(k)空间复杂度：O(nlogn)
3、代码详解
python3
python
class TreeAncestor:
def __init__(self, n: int, parent: List[int]):
H = n.bit_length()
fa = [[0] * H] + [[p + 1] + [0] * (H - 1) for p in parent]
for i in range(1, H):
for j in range(1, n + 1):
fa[j][i] = fa[fa[j][i - 1]][i - 1]
self.fa = fa
def getKthAncestor(self, x: int, k: int) -> int:
x += 1
fa = self.fa
for i in range(k.bit_length()):
if k >> i & 1:
x = fa[x][i]
return x - 1
# Your TreeAncestor object will be instantiated and called as such:
# obj = TreeAncestor(n, parent)
# param_1 = obj.getKthAncestor(node,k)cpp
cpp
const int N = 5e4 + 10, H = 16;
int fa[N][H];
class TreeAncestor {
public:
TreeAncestor(int n, vector<int>& parent) {
for(int i = 1; i < n; i++)
fa[i + 1][0] = parent[i] + 1;
for(int i = 1, ed = 32 - __builtin_clz(n); i < ed; i++)
for(int j = 1; j <= n; j++)
fa[j][i] = fa[fa[j][i - 1]][i - 1];
}
int getKthAncestor(int x, int k) {
++x;
for(int i = 32 - __builtin_clz(k); i >= 0; i--)
if(k >> i & 1)
x = fa[x][i];
return x - 1;
}
};
/**
* Your TreeAncestor object will be instantiated and called as such:
* TreeAncestor* obj = new TreeAncestor(n, parent);
* int param_1 = obj->getKthAncestor(node,k);
*/