LeetCode 303. Range Sum Query - Immutable

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本文介绍了一种利用动态规划解决数组中指定区间元素之和的问题。通过预处理数组，实现快速查询任意区间的元素总和。适用于数组不变但频繁进行区间求和操作的场景。

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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.

Since the elements are not immutable, we can just use simple DP to solve it.

class NumArray {
private:
    vector<int> dp;
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];
    }
};