如何在SQL中生成所有可能的汇率组合

Question

Given a table of tuples of currency and exchange rate, such as the following:

EUR CHF 1.20
USD EUR 0.80
CHF JPY 1.30

How can I simply generate all the exchange rate between currency (A,B) and also (B,A)?

I would like to have the following:

EUR CHF
CHF EUR

EUR USD
USD EUR

USD CHF
CHF USD

with all the possible combinations, ie a rate can be derived from multiple rates by chaining them

A to B * B to C * C to D = A to D

Answer 1

The only way I can find to do this is using a LOOP, All my queries below use this sample data:

DECLARE @T TABLE (FromCurrency VARCHAR(3), ToCurrency VARCHAR(3), ExchangeRate DECIMAL(10, 5));
INSERT @T VALUES
    ('EUR', 'CHF', 1.20),
    ('USD', 'EUR', 0.80),
    ('CHF', 'JPY', 1.30);

The first step is to get all the reciprocal exchange rates (ie B -> A from the table of A -> B) as these are the easiest to get:

DECLARE @TempExchangeRates TABLE (FromCurrency VARCHAR(3), ToCurrency VARCHAR(3), ExchangeRate DECIMAL(10, 5));

INSERT @TempExchangeRates (FromCurrency, ToCurrency, ExchangeRate)
SELECT  FromCurrency, ToCurrency, ExchangeRate
FROM    @T
UNION
SELECT  ToCurrency, FromCurrency, CAST(1 / ExchangeRate AS DECIMAL(10, 5))
FROM    @T t
WHERE   NOT EXISTS
        (   SELECT  1
            FROM    @T t2
            WHERE   t.FromCurrency = t2.ToCurrency
            AND     t.ToCurrency = t2.FromCurrency
        )

At this point we have:

CHF EUR 0.83333
CHF JPY 1.30000
EUR CHF 1.20000
EUR USD 1.25000
JPY CHF 0.76923
USD EUR 0.80000

So we are still missing

CHF --> USD 
EUR --> JPY 
JPY --> CHF 
JPY --> EUR 
USD --> EUR 

You need to keep performing this join

SELECT  a.FromCurrency, b.ToCurrency, CAST(a.ExchangeRate * b.ExchangeRate AS DECIMAL(10, 5))
FROM    @TempExchangeRates a
        INNER JOIN @TempExchangeRates b
            ON a.ToCurrency = b.FromCurrency
            AND a.FromCurrency != b.ToCurrency
WHERE   NOT EXISTS
        (   SELECT  1
            FROM    @TempExchangeRates c
            WHERE   a.FromCurrency = c.FromCurrency
            AND     b.ToCurrency = c.ToCurrency
        )

And inserting the results until all combinations have been found:

WHILE (1 = 1)
    BEGIN
        INSERT @TempExchangeRates (FromCurrency, ToCurrency, ExchangeRate)
        SELECT  DISTINCT a.FromCurrency, b.ToCurrency, CAST(a.ExchangeRate * b.ExchangeRate AS DECIMAL(10, 5))
        FROM    @TempExchangeRates a
                INNER JOIN @TempExchangeRates b
                    ON a.ToCurrency = b.FromCurrency
                    AND a.FromCurrency != b.ToCurrency
        WHERE   NOT EXISTS
                (   SELECT  1
                    FROM    @TempExchangeRates c
                    WHERE   a.FromCurrency = c.FromCurrency
                    AND     b.ToCurrency = c.ToCurrency
                )

        IF @@ROWCOUNT = 0
            BEGIN
                BREAK;
            END
    END

On the first loop this will retrieve

CHF USD 1.04166
EUR JPY 1.56000
JPY EUR 0.64102
USD CHF 0.96000

Then on the second

JPY USD 0.80128
USD JPY 1.24800

Then all 12 tuples will have been found.

Answer 2

You can do this with a Recursive Common Table Expression

Setup:

Create Table ExchangeRates (
    FromCurrency char(3),
    ToCurrency char(3),
    Rate decimal(10, 2),
    Constraint PK_ExchangeRates Primary Key (FromCurrency, ToCurrency)
);

Create Index IX_ToCurrency On ExchangeRates(ToCurrency, FromCurrency, Rate);

Insert Into ExchangeRates (FromCurrency, ToCurrency, Rate) Values
  ('EUR', 'CHF', 1.20),
  ('USD', 'EUR', 0.80),
  ('CHF', 'JPY', 1.30);

The CTE, which assumes all currency codes are exactly three characters:

With AllExchanges as (
    Select
        FromCurrency,
        ToCurrency,
        Rate
    From
        ExchangeRates
    Union
    Select
        ToCurrency,
        FromCurrency,
        Cast(1.0 / Rate As Decimal(10, 2))
    From
        ExchangeRates
)
, Paths as (
    Select
        FromCurrency,
        cast(FromCurrency as varchar(max)) As ExchangePath,
        ToCurrency,
        Rate
    From
        AllExchanges a
    Union All
    Select
        p.FromCurrency,
        p.ExchangePath + ',' + p.ToCurrency,
        a.ToCurrency,
        Cast(p.Rate * a.Rate as Decimal(10, 2))
    From
        Paths p
            Inner Join
        AllExchanges a
            On p.ToCurrency = a.FromCurrency
    Where
        p.ExchangePath Not Like '%' + a.ToCurrency + '%'
    )
Select
    FromCurrency,
    ExchangePath + ',' + ToCurrency As ExchangePath,
    ToCurrency,
    Rate
From
    Paths

http://sqlfiddle.com/#!3/0fdc5