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.csdn.net/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