303. Range Sum Query - Immutable dynamic programming

原创于 2017-06-19 15:14:18 发布 · 215 阅读

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本文介绍了一种使用前缀和数组优化区间和查询的方法。通过预处理数组中的前缀和，可以快速计算出任意两个索引之间的元素总和，适用于数组不变而查询频繁的场景。

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.

用一个数组存储前 i 个元素的和，并在求i-j范围内元素和的时候直接res[i]-res[j]；

class NumArray {
private:
    vector<int> res;
public:
    NumArray(vector<int> nums) {
        res = nums;
        for (int i = 1; i < nums.size(); i++){
            res[i] = res[i - 1] + nums[i];
        }
    }

    int sumRange(int i, int j) {
        if (i < 0 || j < 0 || i > j)return 0;
        if (i == 0)return res[j];
        return res[j] - res[i - 1];
    }
};