Description
Given an integer array nums, handle multiple queries of the following type:
- Calculate the sum of the elements of
nums between indices left and right inclusive where left <= right.
Implement the NumArray class:
NumArray(int[] nums) Initializes the object with the integer array nums.int sumRange(int left, int right) Returns the sum of the elements of nums between indices left and right inclusive (i.e. nums[left] + nums[left + 1] + ... + nums[right]).
Example 1:
Input
["NumArray", "sumRange", "sumRange", "sumRange"]
[[[-2, 0, 3, -5, 2, -1]], [0, 2], [2, 5], [0, 5]]
Output
[null, 1, -1, -3]
Explanation
NumArray numArray = new NumArray([-2, 0, 3, -5, 2, -1]);
numArray.sumRange(0, 2); // return (-2) + 0 + 3 = 1
numArray.sumRange(2, 5); // return 3 + (-5) + 2 + (-1) = -1
numArray.sumRange(0, 5); // return (-2) + 0 + 3 + (-5) + 2 + (-1) = -3
Constraints:
1 <= nums.length <= 104-105 <= nums[i] <= 1050 <= left <= right < nums.length- At most
104 calls will be made to sumRange.
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] = ∑_{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).
PythonJavaC++GoTypeScriptRustJavaScriptPHPCKotlin
class NumArray:
def __init__(self, nums: List[int]):
self.s = list(accumulate(nums, initial=0))
def sumRange(self, left: int, right: int) -> int:
return self.s[right + 1] - self.s[left]
# Your NumArray object will be instantiated and called as such:
# obj = NumArray(nums)
# param_1 = obj.sumRange(left,right)(code-box)
class NumArray {
private int[] s;
public NumArray(int[] nums) {
int n = nums.length;
s = new int[n + 1];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
}
public int sumRange(int left, int right) {
return s[right + 1] - s[left];
}
}
/**
* Your NumArray object will be instantiated and called as such:
* NumArray obj = new NumArray(nums);
* int param_1 = obj.sumRange(left,right);
*/(code-box)
class NumArray {
public:
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];
}
}
int sumRange(int left, int right) {
return s[right + 1] - s[left];
}
private:
vector<int> s;
};
/**
* Your NumArray object will be instantiated and called as such:
* NumArray* obj = new NumArray(nums);
* int param_1 = obj->sumRange(left,right);
*/(code-box)
type NumArray struct {
s []int
}
func Constructor(nums []int) NumArray {
n := len(nums)
s := make([]int, n+1)
for i, v := range nums {
s[i+1] = s[i] + v
}
return NumArray{s}
}
func (this *NumArray) SumRange(left int, right int) int {
return this.s[right+1] - this.s[left]
}
/**
* Your NumArray object will be instantiated and called as such:
* obj := Constructor(nums);
* param_1 := obj.SumRange(left,right);
*/(code-box)
class NumArray {
private s: number[];
constructor(nums: number[]) {
const n = nums.length;
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
}
sumRange(left: number, right: number): number {
return this.s[right + 1] - this.s[left];
}
}
/**
* Your NumArray object will be instantiated and called as such:
* var obj = new NumArray(nums)
* var param_1 = obj.sumRange(left,right)
*/(code-box)
struct NumArray {
s: 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(mut nums: Vec<i32>) -> Self {
let n = nums.len();
let mut s = vec![0; n + 1];
for i in 0..n {
s[i + 1] = s[i] + nums[i];
}
Self { s }
}
fn sum_range(&self, left: i32, right: i32) -> i32 {
self.s[(right + 1) as usize] - self.s[left as usize]
}
}(code-box)
/**
* @param {number[]} nums
*/
var NumArray = function (nums) {
const n = nums.length;
this.s = Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
this.s[i + 1] = this.s[i] + nums[i];
}
};
/**
* @param {number} left
* @param {number} right
* @return {number}
*/
NumArray.prototype.sumRange = function (left, right) {
return this.s[right + 1] - this.s[left];
};
/**
* Your NumArray object will be instantiated and called as such:
* var obj = new NumArray(nums)
* var param_1 = obj.sumRange(left,right)
*/(code-box)
class NumArray {
/**
* @param Integer[] $nums
*/
function __construct($nums) {
$this->s = [0];
foreach ($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 $this->s[$right + 1] - $this->s[$left];
}
}
/**
* Your NumArray object will be instantiated and called as such:
* $obj = NumArray($nums);
* $ret_1 = $obj->sumRange($left, $right);
*/(code-box)
typedef struct {
int* s;
} NumArray;
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* obj = malloc(sizeof(NumArray));
obj->s = s;
return obj;
}
int numArraySumRange(NumArray* obj, int left, int right) {
return obj->s[right + 1] - obj->s[left];
}
void numArrayFree(NumArray* obj) {
free(obj->s);
free(obj);
}
/**
* Your NumArray struct will be instantiated and called as such:
* NumArray* obj = numArrayCreate(nums, numsSize);
* int param_1 = numArraySumRange(obj, left, right);
* numArrayFree(obj);
*/(code-box)
class NumArray(nums: IntArray) {
private val prefix_sums: IntArray
init {
val nums_size = nums.size
this.prefix_sums = IntArray(nums_size + 1)
for (i in 0..<nums_size) {
this.prefix_sums[i + 1] = this.prefix_sums[i] + nums[i]
}
}
fun sumRange(left: Int, right: Int): Int = this.prefix_sums[right + 1] - this.prefix_sums[left]
}
/**
* Your NumArray object will be instantiated and called as such: var obj = NumArray(nums) var
* param_1 = obj.sumRange(left,right)
*/(code-box)
