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

Author: yanglbme

solution/0300-0399/0303.Range Sum Query - Immutable/README.md

@@ -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 -->
 
@@ -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;
 };
 
 /**
@@ -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];
  }
@@ -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];
  }
@@ -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>,
 }
 
 /**
@@ -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:
@@ -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);
 }
 
@@ -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);
+ */
 ```
 
 ### **...**

solution/0300-0399/0303.Range Sum Query - Immutable/README_EN.md

@@ -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**
@@ -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;
 };
 
 /**
@@ -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];
  }
@@ -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];
  }
@@ -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>,
 }
 
 /**
@@ -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:
@@ -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);
 }
 
@@ -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);
+ */
 ```
 
 ### **...**