詳細的算法說明可以參考 24 點算法之我見，簡單的窮舉可以把+，-，×，/和()和四個數(shù)進行全排列，但這樣會出現(xiàn)很多無效的表達式，因此我們這里參考“24 點算法之我見”的算法，對表達式做些分析：
“換一種思路，介紹我的 24 點的窮舉法 上面的算法是對數(shù)和運算符進行窮舉和搜索
我的算法是對運算式進行窮舉 無論給什么樣的是 4 個數(shù)，運算式總是不變的，舉例來說：
N+N+N+N=24，這是一種運算式 N*N+N*N=24，這是另一種運算式 N/（N-N/N）=24，這又是另一種運算式
下面這個例子： N+N-（N-N）=24 N+N-N+N=24
上面雖然是兩種不同的運算式，但本質(zhì)是同一種運算式（肯定同時成立或同時不成立），窮舉的時候只要窮舉其中一個就行了
再看下面這個例子 N/(N+N+N)=24 雖然是一個運算式，但是這個運算式是不可能成立的，也就是無解運算式，窮舉的時候是不需要窮舉該運算式的 ” 參考該文章提供的表格，我們可以定義如下兩個 List 對象（去掉無解的表達式）
所有合法的表達式的模板：
val templates=List(
"(N-(N+N))*N",
"(N-(N-N))*N",
"(N*N+N)*N",
"(N*N+N)/N",
"(N*N-N)*N",
"(N*N-N)/N",
"(N/N+N)*N",
"(N/N-N)*N",
"(N+N)*(N+N)",
"(N+N)*(N-N)",
"(N+N)*N*N",
"(N+N)*N/N",
"(N+N)*N+N",
"(N+N)*N-N",
"(N+N)/(N/N)",
"(N+N)/N*N",
"(N+N)/N+N",
"(N+N*N)*N",
"(N+N*N)/N",
"(N+N/N)*N",
"(N+N+N)*N",
"(N+N+N)/N",
"(N+N-N)*N",
"(N-N)*(N+N)",
"(N-N)*(N-N)",
"(N-N)*N*N",
"(N-N)*N/N",
"(N-N)*N+N",
"(N-N)*N-N",
"(N-N)/(N/N)",
"(N-N)/N*N",
"(N-N*N)*N",
"(N-N/N)*N",
"(N-N+N)*N",
"(N-N-N)*N",
"N-(N-N)*N",
"N-(N-N)+N",
"N-(N-N-N)",
"N*(N-(N+N))",
"N*(N-(N-N))",
"N*(N*N+N)",
"N*(N*N-N)",
"N*(N/N+N)",
"N*(N/N-N)",
"N*(N+N)*N",
"N*(N+N)/N",
"N*(N+N)+N",
"N*(N+N)-N",
"N*(N+N*N)",
"N*(N+N/N)",
"N*(N+N+N)",
"N*(N+N-N)",
"N*(N-N)*N",
"N*(N-N)/N",
"N*(N-N)+N",
"N*(N-N)-N",
"N*(N-N*N)",
"N*(N-N/N)",
"N*(N-N+N)",
"N*(N-N-N)",
"N*N-(N+N)",
"N*N-(N-N)",
"N*N*(N+N)",
"N*N*(N-N)",
"N*N*N*N",
"N*N*N/N",
"N*N*N+N",
"N*N*N-N",
"N*N/(N*N)",
"N*N/(N/N)",
"N*N/(N+N)",
"N*N/(N-N)",
"N*N/N*N",
"N*N/N/N",
"N*N/N+N",
"N*N/N-N",
"N*N+N*N",
"N*N+N/N",
"N*N+N+N",
"N*N+N-N",
"N*N-N*N",
"N*N-N/N",
"N*N-N+N",
"N*N-N-N",
"N/((N+N)/N)",
"N/((N-N)/N)",
"N/(N*N)*N",
"N/(N*N/N)",
"N/(N/(N+N))",
"N/(N/(N-N))",
"N/(N/N)*N",
"N/(N/N)/N",
"N/(N/N*N)",
"N/(N/N/N)",
"N/(N/N-N)",
"N/(N+N)*N",
"N/(N-N)*N",
"N/(N-N/N)",
"N/N*(N+N)",
"N/N*(N-N)",
"N/N*N*N",
"N/N*N/N",
"N/N*N+N",
"N/N*N-N",
"N/N/(N/N)",
"N/N/N*N",
"N/N+N*N",
"N/N+N+N",
"N+(N+N)*N",
"N+(N+N)/N",
"N+(N-N)*N",
"N+N-(N-N)",
"N+N*(N+N)",
"N+N*(N-N)",
"N+N*N*N",
"N+N*N/N",
"N+N*N+N",
"N+N*N-N",
"N+N/(N/N)",
"N+N/N*N",
"N+N/N+N",
"N+N+N*N",
"N+N+N/N",
"N+N+N+N",
"N+N+N-N",
"N+N-N+N",
"N+N-N-N",
"N-N*(N-N)",
"N-N+N*N",
"N-N+N+N"
)等價表達式的定義：
val equivalence = List(
"N+N-N+N,N+N+N-N",
"N+N-(N-N),N+N-N+N,N+N+N-N",
"N+N*(N+N),(N+N)*N+N",
"N+N*(N-N),N+(N-N)*N",
"N+N/N*N,N+N*N/N",
"(N+N)/N*N,(N+N)*N/N",
"N+N/(N/N),N+N/N*N,N+N*N/N",
"(N+N)/(N/N),(N+N)/N*N,(N+N)*N/N",
"N-N+N+N,N+N+N-N",
"N-N+N*N,N+N*N-N",
"(N-N+N)*N,(N+N-N)*N",
"(N-(N+N))*N,(N-N-N)*N",
"N-(N-N)+N,N-N+N+N,N+N+N-N",
"N+N-N-N,N-N+N+N,N+N+N-N",
"N-(N-N-N),N-N+N+N,N+N+N-N",
"N-(N-N)*N,N+(N-N)*N",
"(N-(N-N))*N,(N-N+N)*N,(N+N-N)*N",
"(N-N)*N+N,N+(N-N)*N",
"(N-N)*(N+N),(N+N)*(N-N)",
"N-N*(N-N),N+N*(N-N),N+(N-N)*N",
"(N-N)/N*N,(N-N)*N/N",
"(N-N)/(N/N),(N-N)/N*N,(N-N)*N/N",
"N*N+N+N,N+N+N*N",
"N*(N+N)+N,N+(N+N)*N",
"N*(N+N+N),(N+N+N)*N",
"N*N+N-N,N-N+N*N",
"N*(N+N)-N,(N+N)*N-N",
"N*(N+N-N),(N+N-N)*N",
"N*(N+N)*N,(N+N)*N*N",
"(N*N+N)*N,(N+N*N)*N",
"N*(N+N*N),(N+N*N)*N",
"N*(N+N)/N,(N+N)*N/N",
"(N*N+N)/N,(N+N*N)/N",
"N*(N+N/N),(N+N/N)*N",
"N*N-N+N,N-N+N*N",
"N*(N-N)+N,N+(N-N)*N",
"N*(N-N+N),(N+N-N)*N",
"N*N-(N+N),N*N-N-N",
"N*(N-(N+N)),N*(N-N-N),(N-N-N)*N",
"N*(N-N)-N,(N-N)*N-N",
"N*(N-N-N),(N-N-N)*N",
"N*N-(N-N),N*N-N+N,N-N+N*N",
"N*(N-(N-N)),N*(N-N+N),(N+N-N)*N",
"N*(N-N)*N,(N-N)*N*N",
"N*(N-N*N),(N-N*N)*N",
"N*(N-N)/N,(N-M2)*N/N",
"N*(N-N/N),(N-N/N)*N",
"N*N*N+N,N+N*N*N",
"N*N*(N+N),(N+N)*N*N",
"N*(N*N+N),(N+N*N)*N",
"N*N*(N-N),(N-N)*N*N",
"N*(N*N-N),(N*N-N)*N",
"N*N/N+N,N+N*N/N",
"N*(N/N+N),(N+N/N)*N",
"N*N/N*N,N*N*N/N",
"N*N/(N*N),N*N/N/N",
"N*N/(N/N),N*N/N*N,N*N*N/N",
"N/N+N+N,N+N+N/N",
"N/N+N*N,N*N+N/N",
"N/(N+N)*N,N*N/(N+N)",
"(N/N+N)*N,(N+N/N)*N",
"N/((N+N)/N),N/(N+N)*N,N*N/(N+N)",
"N/(N-N)*N,N*N/(N-N)",
"N/((N-N)/N),N/(N-N)*N,N*N/(N-N)",
"N/N*N+N,N+N*N/N",
"N/N*(N+N),(N+N)*N/N",
"N/N*N-N,N*N/N-N",
"N/N*(N-N),N*(N-N)/N",
"N/N*N*N,N*N*N/N",
"N/(N*N)*N,N/N/N*N,N*N/N/N",
"N/N*N/N,N*N/N/N",
"N/(N*N/N),N/N/N*N,N*N/N/N",
"N/(N/(N+N)),N/N*(N+N),(N+N)*N/N",
"N/(N/(N-N)),N/N*(N-N),(N-N)*N/N",
"N/N/N*N,N*N/N/N",
"N/(N/N)*N,N/N*N*N,N*N*N/N",
"N/(N/N*N),N/N*N/N,N*N/N/N",
"N/N/(N/N),N/N/N*N,N*N/N/N",
"N/(N/N)/N,N/N*N/N,N*N/N/N",
"N/(N/N/N),N/N*N/N,N*N/N/N"
) 通過這兩個 List 對象，我們?nèi)サ舻葍r的表達式，得出最終的合法表達式只有 73 種，大大縮小了需要窮舉的表達式的數(shù)目：
val templates=List(
"N*N-N+N",
"(N-N)*N*N",
"N*N+N*N",
"(N+N)*N*N",
"N*N*N*N",
"(N+N*N)*N",
"(N*N-N)*N",
"N*N+N+N",
"(N/N-N)*N",
"(N-(N-N))*N",
"N-(N-N-N)",
"N+N-(N-N)",
"N*(N/N-N)",
"(N-N*N)*N",
"N*(N-N)+N",
"N+N+N/N",
"(N-N)*(N-N)",
"N+N*N/N",
"N*N/(N-N)",
"(N+N)*(N+N)",
"(N-N)*N/N",
"N+(N+N)/N",
"N*N/(N+N)",
"(N+N)*N/N",
"(N*N+N)*N",
"(N*N-N)/N",
"(N/N+N)*N",
"N*N/N/N",
"N+N+N-N",
"N-(N-N)+N",
"N/(N-N/N)",
"N+(N-N)*N",
"(N+N+N)*N",
"N+N*N-N",
"N*N-N/N",
"(N+N)*N-N",
"(N+N)*(N-N)",
"(N-N/N)*N",
"N*(N+N)+N",
"N*N+N/N",
"N*N/N-N",
"(N+N/N)*N",
"N*N*N/N",
"(N+N*N)/N",
"N+N*N+N",
"N-(N-N)*N",
"(N-(N+N))*N",
"N*N-N-N",
"N+N/N+N",
"(N-N)*N-N",
"(N+N)/N+N",
"N*N+N-N",
"N/N+N+N",
"N*N*N-N",
"(N*N+N)/N",
"N+N+N*N",
"N*(N-N)/N",
"N/N*N+N",
"N+N*N*N",
"N+N+N+N",
"N*N/(N*N)",
"N+(N+N)*N",
"(N-N)*N+N",
"(N+N+N)/N",
"(N+N)*N+N",
"N*N*N+N",
"N*N-(N-N)",
"N*N-(N+N)",
"(N-N-N)*N",
"N*N/N+N",
"(N+N-N)*N",
"N/(N/N-N)",
"N*N-N*N"
)
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