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Question

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

Given an integer array nums, handle multiple queries of the following type:

  1. 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);
     */
    
    

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