How to select the columns of a dataframe based on a vector of strings, matching for exact coincidence?

I have a dataframe with the followign column names:

NewYork_10
NewYork_20
NewYork3_10
NewYork3_20
NewYork4_10
NewYork4_20
HongKong_10
HongKong_20
SanFrancisco_10
SanFrancisco_20

And I have a vector:

list <- c("NewYork", "SanFrancisco")

I want a script that creates a new dataframe, selecting those columns that have the exact same string before the underscore.
In the example given above, you would get a new dataframe with the following columns.
NewYork_10
NewYork_20
SanFrancisco_10
SanFrancisco_20

I did several tries with grep:

dplyr::select(matches(list_cities))

dplyr::select(matches(paste0(list_cities), "_"))

And even using anchors for a vector, which I'm not sure is possible.

dplyr::select(matches(paste0("^",list_cities, "_.*")))

But in every case it's capturing all the values of the vector that start with the given substring.

You can try:

df[grep("^(NewYork|SanFrancisco)_", names(df))]
#df[grep(paste0("^(", paste0(name_list, collapse="|"), ")_"), names(df))] #Alternative using the name_list
#  NewYork_10 NewYork_20 SanFrancisco_10 SanFrancisco_20
#1          1          1               1               1

or using dplyr::select

library(tidyverse)
df %>% select(matches("^(NewYork|SanFrancisco)_"))
#  NewYork_10 NewYork_20 SanFrancisco_10 SanFrancisco_20
#1          1          1               1               1

Where ^ is the start of the string, (NewYork|SanFrancisco) matches NewYork or SanFrancisco followed by _.

Or using startsWith:

df[Reduce(`|`, lapply(paste0(name_list, "_"), startsWith, x=names(df)))]
#  NewYork_10 NewYork_20 SanFrancisco_10 SanFrancisco_20
#1          1          1               1               1

Data (taken from @benson23)

df <- data.frame(NewYork_10 = 1,
           NewYork_20 = 1,
           NewYork3_10 = 1,
           NewYork3_20 = 1,
           NewYork4_10 = 1,
           NewYork4_20 = 1,
           HongKong_10 = 1,
           HongKong_20 = 1,
           SanFrancisco_10 = 1,
           SanFrancisco_20 = 1)

name_list <- c("NewYork", "SanFrancisco")

We can also use matches

df %>%
    select(matches("(NewYork)|(SanFrancisco)_.*")

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