R 根据组中第一个值的条件替换 df 中的后续值

我在有序的R数据框中有这种类型的数据

set.seed(25)

date <- sort(as.Date(sample( as.numeric(as.Date("2019-01-01")): as.numeric(as.Date("2021-03-31")), 10, 
                             replace = T), 
                     origin = '1970-01-01'))

type <- c("Football", "Football", "Rugby", "Football", "Hockey", "Tennis", "Hockey", "Basketball", "Basketball", "Rugby")

id <- c("1","1","1","1","2","2","3","4","4","5")

df <- data.frame(date,id, type)



      date id       type
  2019-04-09  1   Football
  2019-04-13  1   Football
  2019-04-20  1      Rugby
  2019-04-21  1   Football
  2019-05-31  2     Hockey
  2020-02-09  2     Tennis
  2020-03-08  3     Hockey
  2020-03-24  4 Basketball
  2020-08-18  4   Football
  2020-11-01  5      Rugby

我想得到的结果是

    date id       type     type_2
  2019-04-09  1   Football   Football
  2019-04-13  1   Football   Football
  2019-04-20  1      Rugby      Multi
  2019-04-21  1   Football      Multi
  2019-05-31  2     Hockey     Hockey
  2020-02-09  2     Tennis      Multi
  2020-03-08  3     Hockey     Hockey
  2020-03-24  4 Basketball Basketball
  2020-08-18  4 Basketball Basketball
  2020-11-01  5      Rugby      Rugby

基本上，如果一个id练习的下一项运动与前一项相同，那么他练习的第一项运动保持不变，类型_2保持不变，但他以后一旦改变运动，他以后的其他价值观就会改变为多值.

我试着用dplyr分的lag()分、lead()分和if_else()分来做这件事，但结果从来都不是我想要的

欢迎有任何见解