LeetCode 303. Range Sum Query
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303. Range Sum Query - Immutable
一、问题描述
Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.
Note:
- You may assume that the array does not change.
- There are many calls to sumRange function.
二、输入输出
Example:
Given nums = [-2, 0, 3, -5, 2, -1]sumRange(0, 2) -> 1sumRange(2, 5) -> -1sumRange(0, 5) -> -3
三、解题思路
- 是按照DP TAG来选的题目,结果这道题我实在是看不出来DP的影子。DP是用来解决最优化问题的,这个题完全就没有最优化的影子。如果每次都从i加到j TLE错误。提示里说了会调用方法很多次。
- 全新的一个思路,只需要o(n)时间复杂度,o(n)的空间复杂度,如果不用sums数组,而是在原来的nums上修改,空间复杂度就成了o(1)
- 核心思想就是
sum(i, j) = sum(0, j) - sum(0, i-1)
就是把从0到i的和记录下来,之后让求从i到j的和,主要做一次减法就行了,只需要常数时间。
class NumArray {public: vector<int> sums; NumArray(vector<int> nums) { if (nums.empty()) return; sums.push_back(nums[0]); for (int i = 1; i < nums.size(); ++i) { int lastSum = sums[i-1]; sums.push_back(lastSum + nums[i]); } } int sumRange(int i, int j) { if(i == 0) return sums[j]; return (sums[j] - sums[i-1]); }};/** * Your NumArray object will be instantiated and called as such: * NumArray obj = new NumArray(nums); * int param_1 = obj.sumRange(i,j); */
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