leetcode 303. Range Sum Query - Immutable

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:

1. You may assume that the array does not change.
2. There are many calls to sumRange function.

题目大意：给定一个数组，返回小标[i, j]的元素之和。

用途：在窗口一定大小时，做滑动平均。可用于图像中的均值滤波

思路一：每次给定[i, j]，直接计算。

class NumArray {
private:
    vector<int> sum;
public:
    NumArray(vector<int>& nums) {
        sum = nums;
    }
    
    int sumRange(int i, int j) {
        int ans = 0;
        for (int k = i; k <= j; ++k) {
            ans += sum[k];
        }
        return ans;
    }
};

思路二：

sum[k] 记录 [0,k]的累加和，计算下标[i, j]的元素和为sum[j] - sum[i - 1], k = 0时，sum[0] = nums[0];

class NumArray {
private:
    vector<int> sum;
public:
    NumArray(vector<int>& nums) {
        sum.assign(nums.begin(), nums.end());
        for (int i = 1; i < nums.size(); ++i) {
            sum[i] = sum[i - 1] + nums[i];
        }
    }
    
    int sumRange(int i, int j) {
        if (i == 0) return sum[j];
        return sum[j] - sum[i - 1];
    }
};

 python3：

class NumArray:
    def __init__(self, nums: List[int]):
        self.lists = [] #定义实例变量
        for i, v in enumerate(nums):
            if i == 0:
                self.lists.append(v)
            else:
                self.lists.append(self.lists[-1] + v)

    def sumRange(self, i: int, j: int) -> int:
        if i == 0:
            return self.lists[j]
        return self.lists[j] - self.lists[i - 1]

 

class NumArray:    def __init__(self, nums: List[int]):        self.lists = []        for i, v in enumerate(nums):            if i == 0:                self.lists.append(v)            else:                self.lists.append(self.lists[i-1] + v)
    def sumRange(self, i: int, j: int) -> int:        if i == 0:            return self.lists[j]        return self.lists[j] - self.lists[i - 1]