Glass Beads 问题求解

Question

Description

Once upon a time there was a famous actress. As you may expect, she played mostly Antique Comedies most of all. All the people loved her. But she was not interested in the crowds. Her big hobby were beads of any kind. Many bead makers were working for her and they manufactured new necklaces and bracelets every day. One day she called her main Inspector of Bead Makers (IBM) and told him she wanted a very long and special necklace.

The necklace should be made of glass beads of different sizes connected to each other but without any thread running through the beads, so that means the beads can be disconnected at any point. The actress chose the succession of beads she wants to have and the IBM promised to make the necklace. But then he realized a problem. The joint between two neighbouring beads is not very robust so it is possible that the necklace will get torn by its own weight. The situation becomes even worse when the necklace is disjoined. Moreover, the point of disconnection is very important. If there are small beads at the beginning, the possibility of tearing is much higher than if there were large beads. IBM wants to test the robustness of a necklace so he needs a program that will be able to determine the worst possible point of disjoining the beads.

The description of the necklace is a string A = a1a2 ... am specifying sizes of the particular beads, where the last character am is considered to precede character a1 in circular fashion.

The disjoint point i is said to be worse than the disjoint point j if and only if the string aiai+1 ... ana1 ... ai-1 is lexicografically smaller than the string ajaj+1 ... ana1 ... aj-1. String a1a2 ... an is lexicografically smaller than the string b1b2 ... bn if and only if there exists an integer i, i <= n, so that aj=bj, for each j, 1 <= j < i and ai < bi
Input

The input consists of N cases. The first line of the input contains only positive integer N. Then follow the cases. Each case consists of exactly one line containing necklace description. Maximal length of each description is 10000 characters. Each bead is represented by a lower-case character of the english alphabet (a--z), where a < b ... z.
Output

For each case, print exactly one line containing only one integer -- number of the bead which is the first at the worst possible disjoining, i.e.\ such i, that the string A[i] is lexicographically smallest among all the n possible disjoinings of a necklace. If there are more than one solution, print the one with the lowest i.
Sample Input

4
helloworld
amandamanda
dontcallmebfu
aaabaaa
Sample Output

10
11
6
5

Answer 1

以下回答参考 皆我百晓生、券券喵儿 等免费微信小程序相关内容作答，并由本人整理回复。

# read data
data <- readLines()

# split into list
list_data <- lapply(data, as.character)

# convert to numeric
numeric_list <- sapply(list_data, function(x) {strsplit(x, "")[[1]][[1]]})

# convert to matrix
matrix_data <- as.matrix(numeric_list)

# find max length
max_len <- length(unique(matrix_data))

# create empty matrix for results
results <- matrix(NA, nrow(max_len), ncol(max_len))

# loop over lengths
for(i in 1:max_len){
  # extract current length
  cur_len <- matrix_data[, i]

  # create temporary matrix
  temp_matrix <- matrix(cur_len, nrow(length(unique(cur_len))))

  # sort rows
  sorted_rows <- apply(temp_matrix, 2, sort)

  # find index of minimum element in sorted rows
  min_index <- which(sorted_rows == rowMin(sorted_rows))
  
  # add result to matrix
  results[i, ] <- min_index + 1
  
}

# output results
write.table(results, file="output.txt", sep="\t")

这个脚本使用 R 语言来解决 Glass Beads 问题。首先读取输入数据，并将其转换为数字格式。然后，它计算字符串的最大长度，并创建一个空的矩阵以存储结果。接下来，它遍历每个长度，并对每个长度进行操作：提取当前长度、创建临时矩阵、排序行、找到最小元素在排序后的行中的索引并添加结果到结果矩阵中。

最后，将结果写入文本文件 "output.txt"。