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110 lines
2.6 KiB
Markdown
Executable File
110 lines
2.6 KiB
Markdown
Executable File
# [303. Range Sum Query - Immutable](https://leetcode.com/problems/range-sum-query-immutable/)
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## 题目
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Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.
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**Example**:
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Given nums = [-2, 0, 3, -5, 2, -1]
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sumRange(0, 2) -> 1
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sumRange(2, 5) -> -1
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sumRange(0, 5) -> -3
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**Note**:
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1. You may assume that the array does not change.
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2. There are many calls to sumRange function.
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## 题目大意
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给定一个整数数组 nums，求出数组从索引 i 到 j (i ≤ j) 范围内元素的总和，包含 i, j 两点。
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示例：
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```
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给定 nums = [-2, 0, 3, -5, 2, -1]，求和函数为 sumRange()
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sumRange(0, 2) -> 1
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sumRange(2, 5) -> -1
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sumRange(0, 5) -> -3
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```
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说明:
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- 你可以假设数组不可变。
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- 会多次调用 sumRange 方法。
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## 解题思路
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- 给出一个数组，数组里面的数都是`**不可变**`的，设计一个数据结构能够满足查询数组任意区间内元素的和。
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- 这一题由于数组里面的元素都是`**不可变**`的，所以可以用 2 种方式来解答，第一种解法是用 prefixSum，通过累计和相减的办法来计算区间内的元素和，初始化的时间复杂度是 O(n)，但是查询区间元素和的时间复杂度是 O(1)。第二种解法是利用线段树，构建一颗线段树，父结点内存的是两个子结点的和，初始化建树的时间复杂度是 O(log n)，查询区间元素和的时间复杂度是 O(log n)。
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## 代码
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```go
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package leetcode
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import (
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"github.com/halfrost/LeetCode-Go/template"
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)
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//解法一 线段树，sumRange 时间复杂度 O(1)
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// NumArray define
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type NumArray struct {
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st *template.SegmentTree
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}
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// Constructor303 define
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func Constructor303(nums []int) NumArray {
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st := template.SegmentTree{}
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st.Init(nums, func(i, j int) int {
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return i + j
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})
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return NumArray{st: &st}
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}
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// SumRange define
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func (ma *NumArray) SumRange(i int, j int) int {
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return ma.st.Query(i, j)
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}
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//解法二 prefixSum，sumRange 时间复杂度 O(1)
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// // NumArray define
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// type NumArray struct {
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// prefixSum []int
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// }
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// // Constructor303 define
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// func Constructor303(nums []int) NumArray {
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// for i := 1; i < len(nums); i++ {
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// nums[i] += nums[i-1]
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// }
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// return NumArray{prefixSum: nums}
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// }
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// // SumRange define
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// func (this *NumArray) SumRange(i int, j int) int {
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// if i > 0 {
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// return this.prefixSum[j] - this.prefixSum[i-1]
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// }
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// return this.prefixSum[j]
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// }
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/**
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* Your NumArray object will be instantiated and called as such:
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* obj := Constructor(nums);
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* param_1 := obj.SumRange(i,j);
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*/
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``` |