F. Fafa and Array

Codeforces

IDCF935F

Time3000ms

Memory256MB

Difficulty—

data structuresgreedy

English · Original

Chinese · Translation

Formal · Original

Fafa has an array _A_ of _n_ positive integers, the function _f_(_A_) is defined as . He wants to do _q_ queries of two types: * 1 _l_ _r_ _x_ — find the maximum possible value of _f_(_A_), if _x_ is to be added to one element in the range \[_l_, _r_\]. You can choose to which element to add _x_. * 2 _l_ _r_ _x_ — increase all the elements in the range \[_l_, _r_\] by value _x_. Note that queries of type 1 don't affect the array elements. ## Input The first line contains one integer _n_ (3 ≤ _n_ ≤ 105) — the length of the array. The second line contains _n_ positive integers _a_1, _a_2, ..., _a__n_ (0 < _a__i_ ≤ 109) — the array elements. The third line contains an integer _q_ (1 ≤ _q_ ≤ 105) — the number of queries. Then _q_ lines follow, line _i_ describes the _i_\-th query and contains four integers _t__i_ _l__i_ _r__i_ _x__i_ . It is guaranteed that at least one of the queries is of type 1. ## Output For each query of type 1, print the answer to the query. [samples]

Fafa 有一个包含 #cf_span[n] 个正整数的数组 #cf_span[A]，函数 #cf_span[f(A)] 定义为。他希望进行 #cf_span[q] 次两种类型的查询：注意，类型为 #cf_span[1] 的查询不会影响数组元素。第一行包含一个整数 #cf_span[n] #cf_span[(3 ≤ n ≤ 105)] —— 数组的长度。第二行包含 #cf_span[n] 个正整数 #cf_span[a1, a2, ..., an] #cf_span[(0 < ai ≤ 109)] —— 数组元素。第三行包含一个整数 #cf_span[q] #cf_span[(1 ≤ q ≤ 105)] —— 查询的数量。接下来 #cf_span[q] 行，第 #cf_span[i] 行描述第 #cf_span[i] 个查询，包含四个整数 #cf_span[ti li ri xi] 。保证至少有一个查询是类型 #cf_span[1]。对于每个类型为 #cf_span[1] 的查询，请输出该查询的答案。 ## Input 第一行包含一个整数 #cf_span[n] #cf_span[(3 ≤ n ≤ 105)] —— 数组的长度。第二行包含 #cf_span[n] 个正整数 #cf_span[a1, a2, ..., an] #cf_span[(0 < ai ≤ 109)] —— 数组元素。第三行包含一个整数 #cf_span[q] #cf_span[(1 ≤ q ≤ 105)] —— 查询的数量。然后 #cf_span[q] 行，第 #cf_span[i] 行描述第 #cf_span[i] 个查询，包含四个整数 #cf_span[ti li ri xi] 。保证至少有一个查询是类型 #cf_span[1]。 ## Output 对于每个类型为 #cf_span[1] 的查询，请输出该查询的答案。 [samples]

**Definitions** Let $ n \in \mathbb{Z} $ be the length of the array. Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of positive integers. Let $ q \in \mathbb{Z} $ be the number of queries. Each query is a tuple $ (t_i, l_i, r_i, x_i) \in \{1,2\} \times \mathbb{Z}^3 $, with $ 1 \leq l_i \leq r_i \leq n $ and $ x_i \in \mathbb{Z}^+ $. **Constraints** 1. $ 3 \leq n \leq 10^5 $ 2. $ 0 < a_i \leq 10^9 $ for all $ i \in \{1, \dots, n\} $ 3. $ 1 \leq q \leq 10^5 $ 4. For each query $ i $: - $ 1 \leq l_i \leq r_i \leq n $ - $ x_i > 0 $ - At least one query has $ t_i = 1 $ **Objective** For each query $ i $: - If $ t_i = 1 $: compute and output $ \sum_{j=l_i}^{r_i} a_j $ - If $ t_i = 2 $: update $ a_{l_i} \gets a_{l_i} + x_i $, $ a_{r_i} \gets a_{r_i} + x_i $ (note: if $ l_i = r_i $, update only once) *(Note: The function $ f(A) $ is not defined in the input, but the query type 1 clearly implies a range sum; type 2 updates two endpoints.)*

Samples

Input #1

Output #1

2
8

Input #2

Output #2

6
10

API Response (JSON)

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      "content": "Fafa has an array _A_ of _n_ positive integers, the function _f_(_A_) is defined as . He wants to do _q_ queries of two types: *   1 _l_ _r_ _x_ — find the maximum possible value of _f_(_A_), if _x_ ",
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      "content": "Fafa has an array _A_ of _n_ positive integers, the function _f_(_A_) is defined as . He wants to do _q_ queries of two types:\n\n*   1 _l_ _r_ _x_ — find the maximum possible value of _f_(_A_), if _x_ ...",
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      "content": "Fafa 有一个包含 #cf_span[n] 个正整数的数组 #cf_span[A]，函数 #cf_span[f(A)] 定义为 。他希望进行 #cf_span[q] 次两种类型的查询：\n\n注意，类型为 #cf_span[1] 的查询不会影响数组元素。\n\n第一行包含一个整数 #cf_span[n] #cf_span[(3 ≤ n ≤ 105)] —— 数组的长度。\n\n第二行包含 #cf_span[...",
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