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Rearrange and extract values from a data frame to specific columns in R

I have a dataframe df like this

> df <- data.frame(type=c("Id","v1","v2","Id","v1","v1","v2","Id","v1","v2","v3"),num=c(1000,200,500,1001,727,50,800,1002,400,365,865))
> df
   type  num
1    Id 1000
2    v1  200
3    v2  500
4    Id 1001
5    v1  727
6    v1   50
7    v2  800
8    Id 1002
9    v1  400
10   v2  365
11   v3  865

I need to create another data frame with Id, v1, v2, v3 as the column names and corresponding values from df such that the variable below each id belong to that id and when the same variable repeats it has to be mapped with the same id and if the variable is not present NA has to be given. This is the desired output.

    Id  v1  v2  v3
1 1000 200 500  NA
2 1001 727  NA  NA
3 1001  50 800  NA
4 1002 400 365 865

I have thought about a method using for loop. But it seems complicated and difficult to structure it. Is there a way without using for loops.

try to do it this way

   library(tidyverse) 
   df %>% 
      mutate(id = ifelse(type == "Id", num, NA)) %>% 
      fill(id) %>% 
      filter(type != "Id") %>% 
      group_by(id, type) %>% 
      mutate(n = row_number()) %>% 
      pivot_wider(c(id, n), names_from = type, values_from = num) %>% 
      select(-n) %>% 
      ungroup()

# A tibble: 4 x 4
     id    v1    v2    v3
  <dbl> <dbl> <dbl> <dbl>
1  1000   200   500    NA
2  1001   727   800    NA
3  1001    50    NA    NA
4  1002   400   365   865

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