Prefix Sum

# Leet Code 303

# 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.


print("Brute force:")

class NumArray:

    def __init__(self, nums: List[int]):
        # print(f"received following array: {nums}")
        self.nums = nums
        

    def sumRange(self, left: int, right: int) -> int:
        # print(f"preparing to sum from index={left} until={right}")
        sum = 0
        for i, val in enumerate(self.nums[left:right+1]):
            # print(f"i={i}, val={val}")
            sum+=val
        # print(f"sum={sum}")
        return sum
        
print("optimized with pre-sum / prefix sum")     
class NumArray:

    def __init__(self, nums: List[int]):
        self.nums = nums
        # prepare sum array
        sum = 0
        self.pre_summed = []
        for val in self.nums:
            sum+=val
            self.pre_summed.append(sum)
        print(f"pre-summed array={self.pre_summed}")
        

    def sumRange(self, left: int, right: int) -> int:
        if left==0:
            sum = self.pre_summed[right]
        else:
            sum = self.pre_summed[right] - self.pre_summed[left-1]
        return sum