310659: CF1866J. Jackets and Packets
Description
Pak Chanek has $N$ jackets that are stored in a wardrobe. Pak Chanek's wardrobe has enough room for two stacks of jackets, namely the left stack and the right stack. Initially, all $N$ jackets are in the left stack, while the right stack is empty. Initially, the $i$-th jacket from the top of the left stack has colour $C_i$.
Pak Chanek wants to pack all of those jackets into some packets, such that the jackets in the same packet has the same colour. However, it is possible for two jackets with the same colour to be in different packets.
Pak Chanek can do two kinds of operations:
- Pak Chanek can pick any number of jackets from the top from one stack as long as the colour is the same, then take those jackets out of the stack and pack them into a packet. This packing operation takes $X$ minutes, no matter how many jackets are packed.
- Pak Chanek can move one topmost jacket from one stack to the top of the other stack (possibly right to left or left to right). This moving operation takes $Y$ minutes.
Determine the minimum time to pack all jackets!
InputThe first line contains three integers $N$, $X$, and $Y$ ($1 \leq N \leq 400$; $1\leq X,Y\leq10^9$) — the number of jackets, the time to do a packing operation, and the time to do a movement operation.
The second line contains $N$ integers $C_1, C_2, C_3, \ldots, C_N$ ($1 \leq C_i \leq N$) — the colour of each jacket.
OutputAn integer representing the minimum time to pack all jackets.
ExampleInput8 7 2 4 4 2 4 1 2 2 1Output
38Note
Let's denote the contents of the two stacks using arrays that represent the colours of the jackets in the stack from top to bottom. Initially, the two stacks form $[4, 4, 2, 4, 1, 2, 2, 1]$ and $[]$.
Pak Chanek can do the following sequence of operations:
- Movement from left to right. The two stacks become $[4, 2, 4, 1, 2, 2, 1]$ and $[4]$.
- Movement from left to right. The two stacks become $[2, 4, 1, 2, 2, 1]$ and $[4, 4]$.
- Packing for $1$ jacket from the top of the left stack. The two stacks become $[4, 1, 2, 2, 1]$ and $[4, 4]$.
- Movement from left to right. The two stacks become $[1, 2, 2, 1]$ and $[4, 4, 4]$.
- Movement from left to right. The two stacks become $[2, 2, 1]$ and $[1, 4, 4, 4]$.
- Packing for $2$ jackets from the top of the left stack. The two stacks become $[1]$ and $[1, 4, 4, 4]$.
- Movement from right to left. The two stacks become $[1, 1]$ and $[4, 4, 4]$.
- Packing for $3$ jackets from the top of the right stack. The two stacks become $[1, 1]$ and $[]$.
- Packing for $2$ jackets from the top of the left stack. The two stacks become $[]$ and $[]$.
In total, it requires a time of $2+2+7+2+2+7+2+7+7=38$ minutes to pack all jackets. It can be proven that there are no other ways that are faster.
Output
Pak Chanek有N件夹克，它们都存放在衣柜的左堆中，右堆初始为空。每件夹克都有一种颜色C_i。Pak Chanek想将这些夹克打包成一些包裹，使得同一包裹中的夹克颜色相同。Pak Chanek可以进行两种操作：
1. 从任一堆的顶部取出相同颜色的任意数量的夹克，将它们打包成一个包裹，此操作耗时X分钟。
2. 将一堆中最顶部的夹克移动到另一堆的顶部，此操作耗时Y分钟。
求打包所有夹克所需的最短时间。
输入数据格式：
第一行包含三个整数N、X和Y，分别表示夹克的数量、打包操作所需时间和移动操作所需时间。
第二行包含N个整数C_1, C_2, ..., C_N，表示每件夹克的颜色。
输出数据格式：
一个整数，表示打包所有夹克所需的最短时间。
示例：
输入：
8 7 2
4 4 2 4 1 2 2 1
输出：
38题目大意： Pak Chanek有N件夹克，它们都存放在衣柜的左堆中，右堆初始为空。每件夹克都有一种颜色C_i。Pak Chanek想将这些夹克打包成一些包裹，使得同一包裹中的夹克颜色相同。Pak Chanek可以进行两种操作： 1. 从任一堆的顶部取出相同颜色的任意数量的夹克，将它们打包成一个包裹，此操作耗时X分钟。 2. 将一堆中最顶部的夹克移动到另一堆的顶部，此操作耗时Y分钟。 求打包所有夹克所需的最短时间。 输入数据格式： 第一行包含三个整数N、X和Y，分别表示夹克的数量、打包操作所需时间和移动操作所需时间。 第二行包含N个整数C_1, C_2, ..., C_N，表示每件夹克的颜色。 输出数据格式： 一个整数，表示打包所有夹克所需的最短时间。 示例： 输入： 8 7 2 4 4 2 4 1 2 2 1 输出： 38