Question

Formatted question description: https://leetcode.ca/all/303.html

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] <= 10⁵
0 <= left <= right < nums.length
At most 10⁴ calls will be made to sumRange.

Algorithm

Establish a cumulative sum array dp, where dp[i] represents the sum of the numbers in the interval [0, i], then [i,j] can be expressed as dp[j]-dp[i-1], pay attention here When i=0, just return dp[j] directly.

Code

public class Range_Sum_Query_Immutable {
    class NumArray {
        private int[] sum;

        public NumArray(int[] nums) {
            sum = new int[nums.length + 1];
            for (int i = 0; i < nums.length; i++) {

                // sum x meaning sumup until index x-1
                sum[i + 1] = sum[i] + nums[i];
            }
        }

        public int sumRange(int i, int j) {
            return sum[j + 1] - sum[i];
        }
    }
/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * int param_1 = obj.sumRange(i,j);
 */
}


############

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);
 */

class NumArray {
public:
    NumArray(vector<int> &nums) {
        dp.resize(nums.size() + 1, 0);
        for (int i = 1; i <= nums.size(); ++i) {
            dp[i] = dp[i - 1] + nums[i - 1];
        }
    }
    int sumRange(int i, int j) {
        return dp[j + 1] - dp[i];
    }
    
private:
    vector<int> dp;
};

'''
>>> accumulate([1,2,3])
<itertools.accumulate object at 0x108f38340>
>>> list(accumulate([1,2,3]))
[1, 3, 6]
>>> list(accumulate([1,2,3], initial=0))
[0, 1, 3, 6]
>>> list(accumulate([1,2,3], initial=10))
[10, 11, 13, 16]
'''
# note: when using python2, I always got error when importing it, via itertools.accumulate()
#       switching to python3, then all good for itertools.accumulate()
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)

############

class NumArray(object):
  def __init__(self, nums):
    """
    initialize your data structure here.
    :type nums: List[int]
    """
    self.dp = [0] * (len(nums) + 1)
    for i in range(0, len(nums)):
      self.dp[i + 1] = self.dp[i] + nums[i]

  def sumRange(self, i, j):
    """
    sum of elements nums[i..j], inclusive.
    :type i: int
    :type j: int
    :rtype: int
    """
    return self.dp[j + 1] - self.dp[i]

# Your NumArray object will be instantiated and called as such:
# numArray = NumArray(nums)
# numArray.sumRange(0, 1)
# numArray.sumRange(1, 2)

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);
 */

class NumArray {
    private s: number[];

    constructor(nums: number[]) {
        const n = nums.length;
        this.s = new 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)
 */

/**
 * @param {number[]} nums
 */
var NumArray = function (nums) {
    const n = nums.length;
    this.s = new 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)
 */

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

struct NumArray {
    sums: 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 sums = vec![0; n + 1];
        for i in 0..n {
            sums[i + 1] = sums[i] + nums[i];
        }
        Self { sums }
    }

    fn sum_range(&self, left: i32, right: i32) -> i32 {
        self.sums[(right + 1) as usize] - self.sums[left as usize]
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * let obj = NumArray::new(nums);
 * let ret_1: i32 = obj.sum_range(left, right);
 */

303 - Range Sum Query - Immutable

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