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Jul 31, 2025
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feat: add solutions to lc problem: No.0118 #4608

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61 changes: 38 additions & 23 deletions solution/0100-0199/0118.Pascal's Triangle/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -57,7 +57,7 @@ tags:

我们先创建一个答案数组 $f$，然后将 $f$ 的第一行元素设为 $[1]$。接下来，我们从第二行开始，每一行的开头和结尾元素都是 $1$，其它 $f[i][j] = f[i - 1][j - 1] + f[i - 1][j]$。

时间复杂度 $O(n^2)$，空间复杂度 $O(n^2)$。其中 $n$ 是行数。
时间复杂度 $O(n^2)$，其中 $n$ 为给定的行数。忽略答案的空间消耗，空间复杂度 $O(1)$。

<!-- tabs:start -->

Expand All @@ -83,8 +83,8 @@ class Solution {
for (int i = 0; i < numRows - 1; ++i) {
List<Integer> g = new ArrayList<>();
g.add(1);
for (int j = 0; j < f.get(i).size() - 1; ++j) {
g.add(f.get(i).get(j) + f.get(i).get(j + 1));
for (int j = 1; j < f.get(i).size(); ++j) {
g.add(f.get(i).get(j - 1) + f.get(i).get(j));
}
g.add(1);
f.add(g);
Expand All @@ -105,8 +105,8 @@ public:
for (int i = 0; i < numRows - 1; ++i) {
vector<int> g;
g.push_back(1);
for (int j = 0; j < f[i].size() - 1; ++j) {
g.push_back(f[i][j] + f[i][j + 1]);
for (int j = 1; j < f[i].size(); ++j) {
g.push_back(f[i][j - 1] + f[i][j]);
}
g.push_back(1);
f.push_back(g);
Expand All @@ -123,8 +123,8 @@ func generate(numRows int) [][]int {
f := [][]int{[]int{1}}
for i := 0; i < numRows-1; i++ {
g := []int{1}
for j := 0; j < len(f[i])-1; j++ {
g = append(g, f[i][j]+f[i][j+1])
for j := 1; j < len(f[i]); j++ {
g = append(g, f[i][j-1]+f[i][j])
}
g = append(g, 1)
f = append(f, g)
Expand All @@ -140,8 +140,8 @@ function generate(numRows: number): number[][] {
const f: number[][] = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g: number[] = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand All @@ -154,21 +154,17 @@ function generate(numRows: number): number[][] {

```rust
impl Solution {
#[allow(dead_code)]
pub fn generate(num_rows: i32) -> Vec<Vec<i32>> {
let mut ret_vec: Vec<Vec<i32>> = Vec::new();
let mut cur_vec: Vec<i32> = Vec::new();

for i in 0..num_rows as usize {
let mut new_vec: Vec<i32> = vec![1; i + 1];
for j in 1..i {
new_vec[j] = cur_vec[j - 1] + cur_vec[j];
let mut f = vec![vec![1]];
for i in 1..num_rows {
let mut g = vec![1];
for j in 1..f[i as usize - 1].len() {
g.push(f[i as usize - 1][j - 1] + f[i as usize - 1][j]);
}
cur_vec = new_vec.clone();
ret_vec.push(new_vec);
g.push(1);
f.push(g);
}

ret_vec
f
}
}
```
Expand All @@ -184,8 +180,8 @@ var generate = function (numRows) {
const f = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand All @@ -194,6 +190,25 @@ var generate = function (numRows) {
};
```

#### C#

```cs
public class Solution {
public IList<IList<int>> Generate(int numRows) {
var f = new List<IList<int>> { new List<int> { 1 } };
for (int i = 1; i < numRows; ++i) {
var g = new List<int> { 1 };
for (int j = 1; j < f[i - 1].Count; ++j) {
g.Add(f[i - 1][j - 1] + f[i - 1][j]);
}
g.Add(1);
f.Add(g);
}
return f;
}
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down
63 changes: 39 additions & 24 deletions solution/0100-0199/0118.Pascal's Triangle/README_EN.md
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Expand Up @@ -44,9 +44,9 @@ tags:

### Solution 1: Simulation

First, we create an answer array $f$, and then set the first row of $f$ to $[1]$. Next, starting from the second row, the first and last elements of each row are $1$, and the other elements are calculated by $f[i][j] = f[i - 1][j - 1] + f[i - 1][j]$.
We first create an answer array $f$, then set the first row of $f$ to $[1]$. Next, starting from the second row, the first and last elements of each row are $1$, and for other elements $f[i][j] = f[i - 1][j - 1] + f[i - 1][j]$.

The time complexity is $O(n^2)$, and the space complexity is $O(n^2)$. Here, $n$ is the number of rows.
The time complexity is $O(n^2)$, where $n$ is the given number of rows. Ignoring the space consumption of the answer, the space complexity is $O(1)$.

<!-- tabs:start -->

Expand All @@ -72,8 +72,8 @@ class Solution {
for (int i = 0; i < numRows - 1; ++i) {
List<Integer> g = new ArrayList<>();
g.add(1);
for (int j = 0; j < f.get(i).size() - 1; ++j) {
g.add(f.get(i).get(j) + f.get(i).get(j + 1));
for (int j = 1; j < f.get(i).size(); ++j) {
g.add(f.get(i).get(j - 1) + f.get(i).get(j));
}
g.add(1);
f.add(g);
Expand All @@ -94,8 +94,8 @@ public:
for (int i = 0; i < numRows - 1; ++i) {
vector<int> g;
g.push_back(1);
for (int j = 0; j < f[i].size() - 1; ++j) {
g.push_back(f[i][j] + f[i][j + 1]);
for (int j = 1; j < f[i].size(); ++j) {
g.push_back(f[i][j - 1] + f[i][j]);
}
g.push_back(1);
f.push_back(g);
Expand All @@ -112,8 +112,8 @@ func generate(numRows int) [][]int {
f := [][]int{[]int{1}}
for i := 0; i < numRows-1; i++ {
g := []int{1}
for j := 0; j < len(f[i])-1; j++ {
g = append(g, f[i][j]+f[i][j+1])
for j := 1; j < len(f[i]); j++ {
g = append(g, f[i][j-1]+f[i][j])
}
g = append(g, 1)
f = append(f, g)
Expand All @@ -129,8 +129,8 @@ function generate(numRows: number): number[][] {
const f: number[][] = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g: number[] = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand All @@ -143,21 +143,17 @@ function generate(numRows: number): number[][] {

```rust
impl Solution {
#[allow(dead_code)]
pub fn generate(num_rows: i32) -> Vec<Vec<i32>> {
let mut ret_vec: Vec<Vec<i32>> = Vec::new();
let mut cur_vec: Vec<i32> = Vec::new();

for i in 0..num_rows as usize {
let mut new_vec: Vec<i32> = vec![1; i + 1];
for j in 1..i {
new_vec[j] = cur_vec[j - 1] + cur_vec[j];
let mut f = vec![vec![1]];
for i in 1..num_rows {
let mut g = vec![1];
for j in 1..f[i as usize - 1].len() {
g.push(f[i as usize - 1][j - 1] + f[i as usize - 1][j]);
}
cur_vec = new_vec.clone();
ret_vec.push(new_vec);
g.push(1);
f.push(g);
}

ret_vec
f
}
}
```
Expand All @@ -173,8 +169,8 @@ var generate = function (numRows) {
const f = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand All @@ -183,6 +179,25 @@ var generate = function (numRows) {
};
```

#### C#

```cs
public class Solution {
public IList<IList<int>> Generate(int numRows) {
var f = new List<IList<int>> { new List<int> { 1 } };
for (int i = 1; i < numRows; ++i) {
var g = new List<int> { 1 };
for (int j = 1; j < f[i - 1].Count; ++j) {
g.Add(f[i - 1][j - 1] + f[i - 1][j]);
}
g.Add(1);
f.Add(g);
}
return f;
}
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down
4 changes: 2 additions & 2 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,8 @@ class Solution {
for (int i = 0; i < numRows - 1; ++i) {
vector<int> g;
g.push_back(1);
for (int j = 0; j < f[i].size() - 1; ++j) {
g.push_back(f[i][j] + f[i][j + 1]);
for (int j = 1; j < f[i].size(); ++j) {
g.push_back(f[i][j - 1] + f[i][j]);
}
g.push_back(1);
f.push_back(g);
Expand Down
14 changes: 14 additions & 0 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.cs
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Original file line number Diff line number Diff line change
@@ -0,0 +1,14 @@
public class Solution {
public IList<IList<int>> Generate(int numRows) {
var f = new List<IList<int>> { new List<int> { 1 } };
for (int i = 1; i < numRows; ++i) {
var g = new List<int> { 1 };
for (int j = 1; j < f[i - 1].Count; ++j) {
g.Add(f[i - 1][j - 1] + f[i - 1][j]);
}
g.Add(1);
f.Add(g);
}
return f;
}
}
4 changes: 2 additions & 2 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.go
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Original file line number Diff line number Diff line change
Expand Up @@ -2,8 +2,8 @@ func generate(numRows int) [][]int {
f := [][]int{[]int{1}}
for i := 0; i < numRows-1; i++ {
g := []int{1}
for j := 0; j < len(f[i])-1; j++ {
g = append(g, f[i][j]+f[i][j+1])
for j := 1; j < len(f[i]); j++ {
g = append(g, f[i][j-1]+f[i][j])
}
g = append(g, 1)
f = append(f, g)
Expand Down
4 changes: 2 additions & 2 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.java
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Original file line number Diff line number Diff line change
Expand Up @@ -5,8 +5,8 @@ public List<List<Integer>> generate(int numRows) {
for (int i = 0; i < numRows - 1; ++i) {
List<Integer> g = new ArrayList<>();
g.add(1);
for (int j = 0; j < f.get(i).size() - 1; ++j) {
g.add(f.get(i).get(j) + f.get(i).get(j + 1));
for (int j = 1; j < f.get(i).size(); ++j) {
g.add(f.get(i).get(j - 1) + f.get(i).get(j));
}
g.add(1);
f.add(g);
Expand Down
4 changes: 2 additions & 2 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.js
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Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,8 @@ var generate = function (numRows) {
const f = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand Down
20 changes: 8 additions & 12 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.rs
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Original file line number Diff line number Diff line change
@@ -1,18 +1,14 @@
impl Solution {
#[allow(dead_code)]
pub fn generate(num_rows: i32) -> Vec<Vec<i32>> {
let mut ret_vec: Vec<Vec<i32>> = Vec::new();
let mut cur_vec: Vec<i32> = Vec::new();

for i in 0..num_rows as usize {
let mut new_vec: Vec<i32> = vec![1; i + 1];
for j in 1..i {
new_vec[j] = cur_vec[j - 1] + cur_vec[j];
let mut f = vec![vec![1]];
for i in 1..num_rows {
let mut g = vec![1];
for j in 1..f[i as usize - 1].len() {
g.push(f[i as usize - 1][j - 1] + f[i as usize - 1][j]);
}
cur_vec = new_vec.clone();
ret_vec.push(new_vec);
g.push(1);
f.push(g);
}

ret_vec
f
}
}
4 changes: 2 additions & 2 deletions solution/0100-0199/0118.Pascal's Triangle/Solution.ts
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Original file line number Diff line number Diff line change
Expand Up @@ -2,8 +2,8 @@ function generate(numRows: number): number[][] {
const f: number[][] = [[1]];
for (let i = 0; i < numRows - 1; ++i) {
const g: number[] = [1];
for (let j = 0; j < f[i].length - 1; ++j) {
g.push(f[i][j] + f[i][j + 1]);
for (let j = 1; j < f[i].length; ++j) {
g.push(f[i][j - 1] + f[i][j]);
}
g.push(1);
f.push(g);
Expand Down