Can this container hold this much liquid?

Question

Can this container hold this much liquid?

Challenge Synopsis

As you most likely know, liquids have an indefinite shape and a definite volume. As such, they always take the shape of their container. They cannot, however, expand to fill their container.

Your job today is to determine whether or not a certain amount of liquid (represented by a certain number of L characters or numbers representing the volume of the part, as per suggestion) can fit into a container of a certain size (represented by a matrix of C characters) with some amount of empty space (represented by space characters) within it. The container will always have C characters all the way around the perimeter.

Your program will return a truthy/falsey value based on whether the liquid will fit into the container. It will only fit if there is an area of connected empty space (made up of spaces adjacent to one another horizontally, diagonally, or vertically) within the container for each part of the liquid that is separated from the rest (either by a space or by two newline characters).

Test Cases

LLL
L
-----    True
CCCCC
C  CC
C  CC
CCCCC

LLL
 LL
------   True
CCCCCC
C C  C
C  CCC
CCCCCC

L L
LLL
-----    False (Not enough space)
CCCCC
CCCCC
C  CC
CCCCC

LL
------   False (Spaces are not connected but liquid is)
CCCCCC
CCCC C
C CCCC
CCCCCC

L L
------   True
CCCCCC
CCCC C
C CCCC
CCCCCC

L L
------   True (There is a pocket of empty space which holds both parts of the liquid)
CCCCCC
CCC  C
CCCCCC
CCCCCC

L

L
------   True (There is a pocket of empty space for each part of the liquid)
CCCCCC
CCCC C
C CCCC
CCCCCC

L L L LL
------   True
CCCCCCCCC
CCCC  C C
C CCCCCCC
CCCCCC CC
CCCCCCCCC

L
L
-----    True
CCCCC
CCCCC
C  CC
CCCCC

Feel free to suggest test cases!

Rules

• This is code-golf, so the shortest answer in bytes wins.
• Standard loopholes are disallowed.

Answer 1

Snails, 58 bytes

Input is taken exactly as in the examples.

t\ t\L{t\L?t\ z!.o=(\ ,\C},!(tz(\L!.!~|\ !.o=(\ ,\C},!(t\L

A 4 bytes longer version is fast enough to instantly complete the test cases (Try this version online):

?^
t\ t\L{t\L`?t\ z!.o=(\ ,\C},!(tz(\L!.!~|\ !.o=(\ ,\C},!(t\L

An indented formatting of the latter:

?^
    t\ 
    t\L
    {
        t\L`?
        t\ 
        z!.
        o=(\ ,\C
    },
    !(tz(
         \L!.!~
         |
         \ !.o=(\ ,\C
},
!(t\L

Answer 2

Clean, 313 bytes

import StdEnv,Data.List
?v=nub[v:[[sum s:k]\\s<-subsequences v|s>[],k<- ?(difference v s)]]
$v m#p=[[(x,y)]\\x<-[0..]&l<-m,y<-[0..]&' '<-l]
=or[and(zipWith(>=)(s++[0,0..])r)\\r<- ?v,s<-permutations(map length(foldl(\p _=nub[sort(nub(e++[(x,y)\\(u,v)<-e,x<-[u-1,u,u+1],y<-[v-1,v,v+1]|(m!!x)!!y<'C']))\\e<-p])p p))]

Try it online!

Defines the function $ :: [Int] [[Char]] -> Bool. TIO link includes a wrapper around STDIN.

? :: [Int] -> [[Int]] is a helper to generate the different ways the volumes can be combined.

Expanded:

$ v m // in function $ of v and m
    # p // define p as
        = [ // a list of
            [(x, y)]    // lists of pairs (x, y)
        \\              // for each
            x <- [0..]  // index x
            & l <- m    // at list l in m
        ,               // for each
            y <- [0..]  // index y
            & ' ' <- l  // at spaces in l
        ]
    = or [ // true if any of the list of
        and (               // true if all of
            zipWith         // element-wise application of
                (>=)            // greater than or equal to
                (s ++ [0, 0..]) // permutation s padded with zeroes
                v               // list v of volumes
        )
    \\                      // for each
        s <- permutations ( // permutation s of
            map length (    // the lengths of
                foldl       // a left-fold of
                    (\p _   // function on p discarding second argument
                        = nub [ // the unique elements of the list of
                            sort (          // sorted versions of
                                nub (       // unique lists composed of
                                    e       // list e of points in a region
                                    ++ [    // prepended to the list of
                                        (x, y)      // pairs (x, y)
                                    \\              // for each
                                        (u, v) <- e // pair (u, v) in list e
                                    ,               // for each
                                        x <- [u-1, u, u+1] // x-coordinate adjacent to u
                                    ,               // for each
                                        y <- [v-1, v, v+1] // y-coordinate adjacent to v
                                    |               // where
                                        (m!!x)!!y < 'C' // the character in m at (x, y) is a space
                                    ]
                                )
                            )
                        \\          // for each
                            e <- p  // region e in p
                        ]
                    )
                    p // applied to a starting argument of p
                    p // recursively, for each element in p
            )
        )
    ]