Question

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

303	Range Sum Query - Immutable

 Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

 Example:
 Given nums = [-2, 0, 3, -5, 2, -1]

 sumRange(0, 2) -> 1
 sumRange(2, 5) -> -1
 sumRange(0, 5) -> -3

 Note:
 You may assume that the array does not change.
 There are many calls to sumRange function.

 @tag-array

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

Java

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 {
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;
};

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)

303 - Range Sum Query - Immutable

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