A15646. Wonderful Jump
编程题
普及/提高-
知识点
题目描述
You are given an array of positive integers $a_1,a_2,\ldots,a_n$ of length $n$ .
In one operation you can jump from index $i$ to index $j$ ( $1 \le i \le j \le n$ ) by paying $\min(a_i, a_{i + 1}, \ldots, a_j) \cdot (j - i)^2$ eris.
For all $k$ from $1$ to $n$ , find the minimum number of eris needed to get from index $1$ to index $k$ .
In one operation you can jump from index $i$ to index $j$ ( $1 \le i \le j \le n$ ) by paying $\min(a_i, a_{i + 1}, \ldots, a_j) \cdot (j - i)^2$ eris.
For all $k$ from $1$ to $n$ , find the minimum number of eris needed to get from index $1$ to index $k$ .
输入格式
The first line contains a single integer $n$ ( $2 \le n \le 4 \cdot 10^5$ ).
The second line contains $n$ integers $a_1,a_2,\ldots a_n$ ( $1 \le a_i \le n$ ).
The second line contains $n$ integers $a_1,a_2,\ldots a_n$ ( $1 \le a_i \le n$ ).
输出格式
Output $n$ integers — the $k$ -th integer is the minimum number of eris needed to reach index $k$ if you start from index $1$ .
输入输出样例
输入 #1
3 2 1 3
输出 #1
0 1 2
输入 #2
6 1 4 1 6 3 2
输出 #2
0 1 2 3 6 8
输入 #3
2 1 2
输出 #3
0 1
输入 #4
4 1 4 4 4
输出 #4
0 1 4 8
说明/提示
In the first example:
- From $1$ to $1$ : the cost is $0$ ,
- From $1$ to $2$ : $1 \rightarrow 2$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2=1$ ,
- From $1$ to $3$ : $1 \rightarrow 2 \rightarrow 3$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2 + \min(1, 3) \cdot (3 - 2) ^ 2 = 1 + 1 = 2$ .
In the fourth example from $1$ to $4$ : $1 \rightarrow 3 \rightarrow 4$ — the cost is $\min(1, 4, 4) \cdot (3 - 1) ^ 2 + \min(4, 4) \cdot (4 - 3) ^ 2 = 4 + 4 = 8$ .
- From $1$ to $1$ : the cost is $0$ ,
- From $1$ to $2$ : $1 \rightarrow 2$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2=1$ ,
- From $1$ to $3$ : $1 \rightarrow 2 \rightarrow 3$ — the cost is $\min(2, 1) \cdot (2 - 1) ^ 2 + \min(1, 3) \cdot (3 - 2) ^ 2 = 1 + 1 = 2$ .
In the fourth example from $1$ to $4$ : $1 \rightarrow 3 \rightarrow 4$ — the cost is $\min(1, 4, 4) \cdot (3 - 1) ^ 2 + \min(4, 4) \cdot (4 - 3) ^ 2 = 4 + 4 = 8$ .