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feat: add solutions to lc problems: No.303~305 #2142

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feat: add solutions to lc problems: No.303~305
yanglbme Dec 22, 2023
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Update README.md
yanglbme Dec 22, 2023
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90 changes: 37 additions & 53 deletions solution/0300-0399/0303.Range Sum Query - Immutable/README.md
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -54,9 +54,9 @@ numArray.sumRange(0, 5); // return -3 ((-2) + 0 + 3 + (-5) + 2 + (-1))

**方法一：前缀和**

前缀和计算公式：`s[i + 1] = s[i] + nums[i]`。
我们创建一个长度为 $n + 1$ 的前缀和数组 $s$，其中 $s[i]$ 表示前 $i$ 个元素的前缀和，即 $s[i] = \sum_{j=0}^{i-1} nums[j]$，那么索引 $[left, right]$ 之间的元素的和就可以表示为 $s[right + 1] - s[left]$。

初始化的时间复杂度是 $O(n)$，每次查询的时间复杂度是 $O(1)$。其中 $n$ 是数组的长度。
初始化前缀和数组 $s$ 的时间复杂度为 $O(n)$，查询的时间复杂度为 $O(1)$。空间复杂度 $O(n)$。

<!-- tabs:start -->

Expand Down Expand Up @@ -111,17 +111,20 @@ class NumArray {
```cpp
class NumArray {
public:
vector<int> s;

NumArray(vector<int>& nums) {
int n = nums.size();
s.resize(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
}

int sumRange(int left, int right) {
return s[right + 1] - s[left];
}

private:
vector<int> s;
};

/**
Expand Down Expand Up @@ -166,7 +169,7 @@ func (this *NumArray) SumRange(left int, right int) int {
*/
var NumArray = function (nums) {
const n = nums.length;
this.s = new Array(n + 1).fill(0);
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
Expand Down Expand Up @@ -196,7 +199,7 @@ class NumArray {

constructor(nums: number[]) {
const n = nums.length;
this.s = new Array(n + 1).fill(0);
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
Expand All @@ -218,34 +221,7 @@ class NumArray {

```rust
struct NumArray {
nums: Vec<i32>,
}

/**
* `&self` means the method takes an immutable reference.
* If you need a mutable reference, change it to `&mut self` instead.
*/
impl NumArray {
fn new(nums: Vec<i32>) -> Self {
Self {
nums,
}
}

fn sum_range(&self, left: i32, right: i32) -> i32 {
let (left, right) = (left as usize, right as usize);
self.nums[left..=right].iter().sum::<i32>()
}
}/**
* Your NumArray object will be instantiated and called as such:
* let obj = NumArray::new(nums);
* let ret_1: i32 = obj.sum_range(left, right);
*/
```

```rust
struct NumArray {
sums: Vec<i32>,
s: Vec<i32>,
}

/**
Expand All @@ -255,15 +231,15 @@ struct NumArray {
impl NumArray {
fn new(mut nums: Vec<i32>) -> Self {
let n = nums.len();
let mut sums = vec![0; n + 1];
let mut s = vec![0; n + 1];
for i in 0..n {
sums[i + 1] = sums[i] + nums[i];
s[i + 1] = s[i] + nums[i];
}
Self { sums }
Self { s }
}

fn sum_range(&self, left: i32, right: i32) -> i32 {
self.sums[(right + 1) as usize] - self.sums[left as usize]
self.s[(right + 1) as usize] - self.s[left as usize]
}
}/**
* Your NumArray object will be instantiated and called as such:
Expand All @@ -276,25 +252,26 @@ impl NumArray {

```c
typedef struct {
int* sums;
int* s;
} NumArray;

NumArray* numArrayCreate(int* nums, int numsSize) {
int* sums = malloc(sizeof(int) * (numsSize + 1));
memset(sums, 0, numsSize + 1);
for (int i = 0; i < numsSize; i++) {
sums[i + 1] = sums[i] + nums[i];
NumArray* numArrayCreate(int* nums, int n) {
int* s = malloc(sizeof(int) * (n + 1));
s[0] = 0;
for (int i = 0; i < n; i++) {
s[i + 1] = s[i] + nums[i];
}
NumArray* res = malloc(sizeof(NumArray));
res->sums = sums;
return res;
NumArray* obj = malloc(sizeof(NumArray));
obj->s = s;
return obj;
}

int numArraySumRange(NumArray* obj, int left, int right) {
return obj->sums[right + 1] - obj->sums[left];
return obj->s[right + 1] - obj->s[left];
}

void numArrayFree(NumArray* obj) {
free(obj->s);
free(obj);
}

Expand All @@ -315,20 +292,27 @@ class NumArray {
* @param Integer[] $nums
*/
function __construct($nums) {
$this->sum = [0];
for ($i = 0; $i < count($nums); $i++) {
array_push($this->sum, $this->sum[$i] + $nums[$i]);
$this->s = [0];
foreach ($nums as $x) {
$this->s[] = $this->s[count($this->s) - 1] + $x;
}
}

/**
* @param Integer $left
* @param Integer $right
* @return Integer
*/
function sumRange($left, $right) {
return $this->sum[$right + 1] - $this->sum[$left];
return $this->s[$right + 1] - $this->s[$left];
}
}

/**
* Your NumArray object will be instantiated and called as such:
* $obj = NumArray($nums);
* $ret_1 = $obj->sumRange($left, $right);
*/
```

### **...**
Expand Down
92 changes: 41 additions & 51 deletions solution/0300-0399/0303.Range Sum Query - Immutable/README_EN.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -46,6 +46,12 @@ numArray.sumRange(0, 5); // return (-2) + 0 + 3 + (-5) + 2 + (-1) = -3

## Solutions

**Solution 1: Prefix Sum**

We create a prefix sum array $s$ of length $n + 1$, where $s[i]$ represents the prefix sum of the first $i$ elements, that is, $s[i] = \sum_{j=0}^{i-1} nums[j]$. Therefore, the sum of the elements between the indices $[left, right]$ can be expressed as $s[right + 1] - s[left]$.

The time complexity for initializing the prefix sum array $s$ is $O(n)$, and the time complexity for querying is $O(1)$. The space complexity is $O(n)$.

<!-- tabs:start -->

### **Python3**
Expand Down Expand Up @@ -95,17 +101,20 @@ class NumArray {
```cpp
class NumArray {
public:
vector<int> s;

NumArray(vector<int>& nums) {
int n = nums.size();
s.resize(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
}

int sumRange(int left, int right) {
return s[right + 1] - s[left];
}

private:
vector<int> s;
};

/**
Expand Down Expand Up @@ -150,7 +159,7 @@ func (this *NumArray) SumRange(left int, right int) int {
*/
var NumArray = function (nums) {
const n = nums.length;
this.s = new Array(n + 1).fill(0);
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
Expand Down Expand Up @@ -180,7 +189,7 @@ class NumArray {

constructor(nums: number[]) {
const n = nums.length;
this.s = new Array(n + 1).fill(0);
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
Expand All @@ -202,34 +211,7 @@ class NumArray {

```rust
struct NumArray {
nums: Vec<i32>,
}

/**
* `&self` means the method takes an immutable reference.
* If you need a mutable reference, change it to `&mut self` instead.
*/
impl NumArray {
fn new(nums: Vec<i32>) -> Self {
Self {
nums,
}
}

fn sum_range(&self, left: i32, right: i32) -> i32 {
let (left, right) = (left as usize, right as usize);
self.nums[left..=right].iter().sum::<i32>()
}
}/**
* Your NumArray object will be instantiated and called as such:
* let obj = NumArray::new(nums);
* let ret_1: i32 = obj.sum_range(left, right);
*/
```

```rust
struct NumArray {
sums: Vec<i32>,
s: Vec<i32>,
}

/**
Expand All @@ -239,15 +221,15 @@ struct NumArray {
impl NumArray {
fn new(mut nums: Vec<i32>) -> Self {
let n = nums.len();
let mut sums = vec![0; n + 1];
let mut s = vec![0; n + 1];
for i in 0..n {
sums[i + 1] = sums[i] + nums[i];
s[i + 1] = s[i] + nums[i];
}
Self { sums }
Self { s }
}

fn sum_range(&self, left: i32, right: i32) -> i32 {
self.sums[(right + 1) as usize] - self.sums[left as usize]
self.s[(right + 1) as usize] - self.s[left as usize]
}
}/**
* Your NumArray object will be instantiated and called as such:
Expand All @@ -260,25 +242,26 @@ impl NumArray {

```c
typedef struct {
int* sums;
int* s;
} NumArray;

NumArray* numArrayCreate(int* nums, int numsSize) {
int* sums = malloc(sizeof(int) * (numsSize + 1));
memset(sums, 0, numsSize + 1);
for (int i = 0; i < numsSize; i++) {
sums[i + 1] = sums[i] + nums[i];
NumArray* numArrayCreate(int* nums, int n) {
int* s = malloc(sizeof(int) * (n + 1));
s[0] = 0;
for (int i = 0; i < n; i++) {
s[i + 1] = s[i] + nums[i];
}
NumArray* res = malloc(sizeof(NumArray));
res->sums = sums;
return res;
NumArray* obj = malloc(sizeof(NumArray));
obj->s = s;
return obj;
}

int numArraySumRange(NumArray* obj, int left, int right) {
return obj->sums[right + 1] - obj->sums[left];
return obj->s[right + 1] - obj->s[left];
}

void numArrayFree(NumArray* obj) {
free(obj->s);
free(obj);
}

Expand All @@ -299,20 +282,27 @@ class NumArray {
* @param Integer[] $nums
*/
function __construct($nums) {
$this->sum = [0];
for ($i = 0; $i < count($nums); $i++) {
array_push($this->sum, $this->sum[$i] + $nums[$i]);
$this->s = [0];
foreach ($nums as $x) {
$this->s[] = $this->s[count($this->s) - 1] + $x;
}
}

/**
* @param Integer $left
* @param Integer $right
* @return Integer
*/
function sumRange($left, $right) {
return $this->sum[$right + 1] - $this->sum[$left];
return $this->s[$right + 1] - $this->s[$left];
}
}

/**
* Your NumArray object will be instantiated and called as such:
* $obj = NumArray($nums);
* $ret_1 = $obj->sumRange($left, $right);
*/
```

### **...**
Expand Down
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