king-army-riddle.R

library(dplyr)
library(ggplot2)

length_army <- 60

army_front <- function(x) (length_army * x) + length_army
army_back <- function(x) (length_army * x)

velocity_king <- length_army + length_army * sqrt(2)

king_1 <- function(x) length_army - (velocity_king * x)
x_t <- length_army / (length_army + velocity_king)
  
king_2 <- function(x, c) (velocity_king * x) + length_army * (length_army - velocity_king) / (length_army + velocity_king)

x <- seq(0, 1, 0.01)

data <- data_frame(x = x) %>% 
  mutate(army_front = army_front(x),
         army_back = army_back(x),
         k1 = king_1(x),
         k2 = king_2(x),
         king = ifelse(x < x_t, k1, k2)) 

data %>% # head()
  ggplot(aes(x = x)) +
  geom_ribbon(aes(ymin = army_back,
                  ymax = army_front),
              alpha = 0.5) +
  geom_line(aes(y = k1), colour = "blue") +
  geom_line(aes(y = k2), colour = "red") +
  geom_line(aes(y = king)) +
  theme_minimal()