March of the Penguins

Question

Problem Description
Somewhere near the south pole, a number of penguins are standing on a number of ice floes. Being social animals, the penguins would like to get together, all on the same floe. The penguins do not want to get wet, so they have use their limited jump distance to get together by jumping from piece to piece. However, temperatures have been high lately, and the floes are showing cracks, and they get damaged further by the force needed to jump to another floe. Fortunately the penguins are real experts on cracking ice floes, and know exactly how many times a penguin can jump off each floe before it disintegrates and disappears. Landing on an ice floe does not damage it. You have to help the penguins find all floes where they can meet.

A sample layout of ice floes with 3 penguins on them.

Input
On the first line one positive number: the number of testcases, at most 100. After that per testcase:

One line with the integer N (1 ≤ N ≤ 100) and a floating-point number D (0 ≤ D ≤ 100 000), denoting the number of ice pieces and the maximum distance a penguin can jump.

N lines, each line containing xi, yi, ni and mi, denoting for each ice piece its X and Y coordinate, the number of penguins on it and the maximum number of times a penguin can jump off this piece before it disappears (−10 000 ≤ xi, yi ≤ 10 000, 0 ≤ ni ≤ 10, 1 ≤ mi ≤ 200).

Output
Per testcase:

One line containing a space-separated list of 0-based indices of the pieces on which all penguins can meet. If no such piece exists, output a line with the single number −1.

Sample Input
2
5 3.5
1 1 1 1
2 3 0 1
3 5 1 1
5 1 1 1
5 4 0 1
3 1.1
-1 0 5 10
0 0 3 9
2 0 1 1

Sample Output
1 2 4
-1

Answer 1

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# 读取数据
input_file <- "penguins.txt"
data <- readLines(input_file)

# 解析数据
n_cases <- as.integer(substr(data[1], 1, 1))
x <- rep(NA, n_cases)
y <- rep(NA, n_cases)
m <- rep(NA, n_cases)
d <- rep(NA, n_cases)
for(i in 2:n_cases+1){
    x[i-1] <- as.numeric(strsplit(data[i], ", ")[1])
    y[i-1] <- as.numeric(strsplit(data[i], ", ")[2])
    m[i-1] <- as.numeric(strsplit(data[i], ", ")[3])
    d[i-1] <- as.numeric(strsplit(data[i], ", ")[4])
}

# 计算每个冰块的最小距离和最大跳跃次数
min_dist <- min(d)
max_jump <- max(m)
jump_table <- expand.grid(x=x, y=y, d=d, m=m)
jump_table[, 2] <- jump_table[, 2]/min_dist * max_jump
jump_table[, 3] <- jump_table[, 3] + 1 # 跳跃次数加上1是为了跳到相邻的冰块上

# 检查所有冰块是否都满足条件
valid_cases <- apply(jump_table, 1, function(row) {
    all(apply(row[m], 1, function(col) col <= row[d]) & 
         any(apply(row[m], 1, function(col) col >= row[d])))
})

# 输出结果
output <- ifelse(valid_cases, paste(sort(unique(unlist(grep(" ", paste(jump_table[valid_cases, ], collapse=" "))))), "\n", sep = ""), "-1\n")
cat(output)

这个脚本首先读取输入文件的内容，并解析出冰块的位置、数量以及它们可以跳跃的最大次数。然后，它计算了每个冰块的最小距离和最大跳跃次数，以便检查它们是否都满足条件。最后，如果所有的冰块都能满足条件，输出一个包含所有满足条件的冰块位置的列表；否则，输出“-1”。