Leetcode 303. Range Sum Query - Immutable

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本文介绍如何使用动态编程算法实现一个名为NumArray的类，用于计算给定整数数组nums中指定区间内元素的和。初始化时，通过计算列表和来存储每个位置的累计和，sumRange方法利用这些和快速计算区间和。

Problem

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]).

Algorithm

Dynamic Programming (DP). Use a list sums to save the sum from 0 to i, and sumRange(left, right) = sums[right] - sums[left-1]

Code

class NumArray:

    def __init__(self, nums: List[int]):
        nlen = len(nums)
        self.sums = [nums[0]] * nlen
        for i in range(1, nlen):
            self.sums[i] = self.sums[i-1] + nums[i]

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