LintCode 903 · Range Addition (差分数组经典题)-优快云博客

文章讨论了解决数组更新操作的问题，介绍使用差分数组的方法，以及前缀和数组、线段树和树状数组在处理区间增减数操作中的区别和适用场景。

LintCode 903 · Range Addition
Algorithms
Medium
Description
Description
Assume you have an array of length n initialized with all 0’s and are given k update operations.

Each operation is represented as a triplet: [startIndex, endIndex, inc] which increments each element of subarray A[startIndex … endIndex] (startIndex and endIndex inclusive) with inc.

Return the modified array after all k operations were executed.
Example
Given:
length = 5,
updates =
[
[1, 3, 2],
[2, 4, 3],
[0, 2, -2]
]
return [-2, 0, 3, 5, 3]

Explanation:
Initial state:
[ 0, 0, 0, 0, 0 ]
After applying operation [1, 3, 2]:
[ 0, 2, 2, 2, 0 ]
After applying operation [2, 4, 3]:
[ 0, 2, 5, 5, 3 ]
After applying operation [0, 2, -2]:
[-2, 0, 3, 5, 3 ]

解法1：差分数组

class Solution {
public:
    /**
     * @param length: the length of the array
     * @param updates: update operations
     * @return: the modified array after all k operations were executed
     */
    vector<int> getModifiedArray(int length, vector<vector<int>> &updates) {
        int n = updates.size();
        if (n == 0) return {};
        vector<int> diffs(length, 0);
        vector<int> res(length, 0);
        for (int i = 0; i < n; i++) {
            diffs[updates[i][0]] += updates[i][2];
            if (updates[i][1] + 1 < length) {  //注意这个细节！
                diffs[updates[i][1] + 1] -= updates[i][2];
            }
        }
        res[0] = diffs[0];
        for (int i = 1; i < length; i++) {
            res[i] = res[i - 1] + diffs[i];
        }
        return res;
    }
};

注意：什么时候用前缀和数组？什么时候用差分数组？什么时候又用线段树和树状数组?
根据链接：https://blog.youkuaiyun.com/weixin_55516868/article/details/128717574
前缀和数组、差分数组、线段树、树状数组均用于处理区间问题，但有不同应用场景
前缀和数组：用于处理连续多次取区间和操作的情况，取区间和期间不能对原数组进行区间增减数操作
差分数组：用于处理多次区间增减数操作，最后读取一次区间和（即修改期间读取不频繁）操作的情况
线段树：用于处理多次区间增减数操作，期间多次读取区间和（即修改期间读取频繁）操作的情况
树状数组：用于处理多次区间增减数操作，期间多次读取区间和（即修改期间读取频繁）操作的情况，同线段树的情况、但树状数组更加简单且不支持区间更新，线段树支持区间更新但编码复杂

解法2：线段树应该也可以做

解法3：树状数组应该也可以做