From f46fa3c73929e52c6c359f128201c9289fda7265 Mon Sep 17 00:00:00 2001
From: Manohar Reddy Poreddy <manoharporeddy@outlook.com>
Date: Sat, 13 Jan 2024 21:21:00 +0530
Subject: [PATCH 1/8] Fix code, to pass test case
https://leetcode.com/problems/kth-ancestor-of-a-tree-node/
=========
Wrong Answer
Runtime: 78 ms
Case 1
Case 2
Input
["TreeAncestor","getKthAncestor"]
[[6,[-1,2,3,4,5,0]],[1,4]]
Output
[null,-1]
Expected
[null,5]
---
.../1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
index 2a8ec0566bc51..d283942ba3f23 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
@@ -218,8 +218,8 @@ class TreeAncestor {
for (let i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (let i = 0; i < n; ++i) {
- for (let j = 1; j < 18; ++j) {
+ for (let j = 1; j < 18; ++j) {
+ for (let i = 0; i < n; ++i) {
if (p[i][j - 1] === -1) {
continue;
}
From 7cecd1ece625b80e1d93d40a4ebd03d2a3152f0f Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:09:52 +0800
Subject: [PATCH 2/8] Update README_EN.md
---
.../README_EN.md | 38 +++++++++++++++----
1 file changed, 30 insertions(+), 8 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
index d283942ba3f23..288d4edd06d72 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README_EN.md
@@ -45,6 +45,28 @@ treeAncestor.getKthAncestor(6, 3); // returns -1 because there is no such ancest
## Solutions
+**Solution 1: Dynamic Programming + Binary Lifting**
+
+The problem asks us to find the $k$-th ancestor node of a node $node$. If we solve it by brute force, we need to traverse upwards from $node$ for $k$ times, which has a time complexity of $O(k)$ and will obviously exceed the time limit.
+
+We can use dynamic programming combined with the idea of binary lifting to handle this.
+
+We define $p[i][j]$ as the $2^j$-th ancestor node of node $i$, i.e., the node reached by moving $2^j$ steps upwards from node $i$. Then we can get the state transition equation:
+
+$$
+p[i][j] = p[p[i][j-1]][j-1]
+$$
+
+That is, to find the $2^j$-th ancestor node of node $i$, we can first find the $2^{j-1}$-th ancestor node of node $i$, and then find the $2^{j-1}$-th ancestor node of this node. Therefore, we need to find the ancestor node of each node at a distance of $2^j$, until we reach the maximum height of the tree.
+
+For each query later, we can decompose $k$ into its binary representation, and then according to the positions of $1$ in the binary, we accumulate the queries upwards, and finally get the $k$-th ancestor node of node $node$.
+
+In terms of time complexity, the initialization is $O(n \times \log n)$, and the query is $O(\log n)$. The space complexity is $O(n \times \log n)$, where $n$ is the number of nodes in the tree.
+
+Similar problems:
+
+- [2836. Maximize Value of Function in a Ball Passing Game](/solution/2800-2899/2836.Maximize%20Value%20of%20Function%20in%20a%20Ball%20Passing%20Game/README_EN.md)
+
<!-- tabs:start -->
### **Python3**
@@ -55,8 +77,8 @@ class TreeAncestor:
self.p = [[-1] * 18 for _ in range(n)]
for i, fa in enumerate(parent):
self.p[i][0] = fa
- for i in range(n):
- for j in range(1, 18):
+ for j in range(1, 18):
+ for i in range(n):
if self.p[i][j - 1] == -1:
continue
self.p[i][j] = self.p[self.p[i][j - 1]][j - 1]
@@ -89,8 +111,8 @@ class TreeAncestor {
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -129,8 +151,8 @@ public:
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -177,8 +199,8 @@ func Constructor(n int, parent []int) TreeAncestor {
p[i][j] = -1
}
}
- for i := range p {
- for j := 1; j < 18; j++ {
+ for j := 1; j < 18; j++ {
+ for i := range p {
if p[i][j-1] == -1 {
continue
}
From 249176d68103b2fe80a689ce223dbbef13b21d35 Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:10:31 +0800
Subject: [PATCH 3/8] Update README.md
---
.../README.md | 21 ++++++++++---------
1 file changed, 11 insertions(+), 10 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README.md b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README.md
index c96a6c5e176e1..89fe1cf6b6c5d 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README.md
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/README.md
@@ -89,8 +89,8 @@ class TreeAncestor:
self.p = [[-1] * 18 for _ in range(n)]
for i, fa in enumerate(parent):
self.p[i][0] = fa
- for i in range(n):
- for j in range(1, 18):
+ for j in range(1, 18):
+ for i in range(n):
if self.p[i][j - 1] == -1:
continue
self.p[i][j] = self.p[self.p[i][j - 1]][j - 1]
@@ -125,8 +125,8 @@ class TreeAncestor {
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -165,8 +165,8 @@ public:
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -213,8 +213,8 @@ func Constructor(n int, parent []int) TreeAncestor {
p[i][j] = -1
}
}
- for i := range p {
- for j := 1; j < 18; j++ {
+ for j := 1; j < 18; j++ {
+ for i := range p {
if p[i][j-1] == -1 {
continue
}
@@ -246,6 +246,7 @@ func (this *TreeAncestor) GetKthAncestor(node int, k int) int {
### **TypeScript**
```ts
+class TreeAncestor {
class TreeAncestor {
private p: number[][];
@@ -254,8 +255,8 @@ class TreeAncestor {
for (let i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (let i = 0; i < n; ++i) {
- for (let j = 1; j < 18; ++j) {
+ for (let j = 1; j < 18; ++j) {
+ for (let i = 0; i < n; ++i) {
if (p[i][j - 1] === -1) {
continue;
}
From 5729a1c9cfe6c13d3d450702590fc60b7f857e58 Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:11:08 +0800
Subject: [PATCH 4/8] Update Solution.py
---
.../1400-1499/1483.Kth Ancestor of a Tree Node/Solution.py | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.py b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.py
index 708d6d0d0ca03..2f52c4dcc3b86 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.py
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.py
@@ -3,8 +3,8 @@ def __init__(self, n: int, parent: List[int]):
self.p = [[-1] * 18 for _ in range(n)]
for i, fa in enumerate(parent):
self.p[i][0] = fa
- for i in range(n):
- for j in range(1, 18):
+ for j in range(1, 18):
+ for i in range(n):
if self.p[i][j - 1] == -1:
continue
self.p[i][j] = self.p[self.p[i][j - 1]][j - 1]
From 5804e44391e82152fdaac7b8272ec45110f33375 Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:11:51 +0800
Subject: [PATCH 5/8] Update Solution.java
---
.../1483.Kth Ancestor of a Tree Node/Solution.java | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.java b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.java
index 059aa2e31e46b..fb9ccca670a93 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.java
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.java
@@ -9,8 +9,8 @@ public TreeAncestor(int n, int[] parent) {
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -36,4 +36,4 @@ public int getKthAncestor(int node, int k) {
* Your TreeAncestor object will be instantiated and called as such:
* TreeAncestor obj = new TreeAncestor(n, parent);
* int param_1 = obj.getKthAncestor(node,k);
- */
\ No newline at end of file
+ */
From 17b604149fd87697f44a3870696bf8289aa0f415 Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:12:19 +0800
Subject: [PATCH 6/8] Update Solution.cpp
---
.../1400-1499/1483.Kth Ancestor of a Tree Node/Solution.cpp | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.cpp b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.cpp
index 1e742da970f3f..1197bbe436e55 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.cpp
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.cpp
@@ -5,8 +5,8 @@ class TreeAncestor {
for (int i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (int i = 0; i < n; ++i) {
- for (int j = 1; j < 18; ++j) {
+ for (int j = 1; j < 18; ++j) {
+ for (int i = 0; i < n; ++i) {
if (p[i][j - 1] == -1) {
continue;
}
@@ -35,4 +35,4 @@ class TreeAncestor {
* Your TreeAncestor object will be instantiated and called as such:
* TreeAncestor* obj = new TreeAncestor(n, parent);
* int param_1 = obj->getKthAncestor(node,k);
- */
\ No newline at end of file
+ */
From e245fa3cc68965ed88d438a895cf7bdd5b4d2d62 Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:12:46 +0800
Subject: [PATCH 7/8] Update Solution.go
---
.../1400-1499/1483.Kth Ancestor of a Tree Node/Solution.go | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.go b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.go
index da0d002091622..04f04ede95880 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.go
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.go
@@ -10,8 +10,8 @@ func Constructor(n int, parent []int) TreeAncestor {
p[i][j] = -1
}
}
- for i := range p {
- for j := 1; j < 18; j++ {
+ for j := 1; j < 18; j++ {
+ for i := range p {
if p[i][j-1] == -1 {
continue
}
@@ -37,4 +37,4 @@ func (this *TreeAncestor) GetKthAncestor(node int, k int) int {
* Your TreeAncestor object will be instantiated and called as such:
* obj := Constructor(n, parent);
* param_1 := obj.GetKthAncestor(node,k);
- */
\ No newline at end of file
+ */
From 1e9ed3fa87f59d5ef8048e7db0c15b36796662bc Mon Sep 17 00:00:00 2001
From: Libin YANG <contact@yanglibin.info>
Date: Sun, 14 Jan 2024 09:13:11 +0800
Subject: [PATCH 8/8] Update Solution.ts
---
.../1400-1499/1483.Kth Ancestor of a Tree Node/Solution.ts | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.ts b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.ts
index 2805876c5e50f..9f704a1ddccaa 100644
--- a/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.ts
+++ b/solution/1400-1499/1483.Kth Ancestor of a Tree Node/Solution.ts
@@ -6,8 +6,8 @@ class TreeAncestor {
for (let i = 0; i < n; ++i) {
p[i][0] = parent[i];
}
- for (let i = 0; i < n; ++i) {
- for (let j = 1; j < 18; ++j) {
+ for (let j = 1; j < 18; ++j) {
+ for (let i = 0; i < n; ++i) {
if (p[i][j - 1] === -1) {
continue;
}