Trying to construct a certain function from set of strings to real numbers…
$begingroup$
Given the set $S$ of all strings of alphabet $Sigma={a,b,c,...,z}$, I want to construct a function $f : S rightarrow mathbb{R}$ such that $$f(s_1)=f(s_2) Leftrightarrow areAnagrams(s_1,s_2) $$
My first step to this is that $f(s)=[len(s)].d_1d_2...d_n$. Having the length of the string in the mapped number helps preventing two unequal length strings having the same $f$ value. However, I am now stuck trying to construct the $d_1...d_n$ portion so that is specific to the letters in $s$.
For example, if I index each of $a,b,...,z$ with $0,1,...,25$ and then have $$f(s)=[len(s)].[text{sum index of each character in s]} $$ there could be a case like $az$ and $by$ mapping to the same number of $2.25$. I'm not sure what formula would work such that:
$f(s_1)=f(s_2)$ if $areAnagrams(s_1,s_2)$
$f(s_1)neq f(s_2)$ if $neg areAnagrams(s_1,s_2)$
functions proof-writing computer-science
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
$endgroup$
add a comment |
$begingroup$
Given the set $S$ of all strings of alphabet $Sigma={a,b,c,...,z}$, I want to construct a function $f : S rightarrow mathbb{R}$ such that $$f(s_1)=f(s_2) Leftrightarrow areAnagrams(s_1,s_2) $$
My first step to this is that $f(s)=[len(s)].d_1d_2...d_n$. Having the length of the string in the mapped number helps preventing two unequal length strings having the same $f$ value. However, I am now stuck trying to construct the $d_1...d_n$ portion so that is specific to the letters in $s$.
For example, if I index each of $a,b,...,z$ with $0,1,...,25$ and then have $$f(s)=[len(s)].[text{sum index of each character in s]} $$ there could be a case like $az$ and $by$ mapping to the same number of $2.25$. I'm not sure what formula would work such that:
$f(s_1)=f(s_2)$ if $areAnagrams(s_1,s_2)$
$f(s_1)neq f(s_2)$ if $neg areAnagrams(s_1,s_2)$
functions proof-writing computer-science
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
$endgroup$
add a comment |
$begingroup$
Given the set $S$ of all strings of alphabet $Sigma={a,b,c,...,z}$, I want to construct a function $f : S rightarrow mathbb{R}$ such that $$f(s_1)=f(s_2) Leftrightarrow areAnagrams(s_1,s_2) $$
My first step to this is that $f(s)=[len(s)].d_1d_2...d_n$. Having the length of the string in the mapped number helps preventing two unequal length strings having the same $f$ value. However, I am now stuck trying to construct the $d_1...d_n$ portion so that is specific to the letters in $s$.
For example, if I index each of $a,b,...,z$ with $0,1,...,25$ and then have $$f(s)=[len(s)].[text{sum index of each character in s]} $$ there could be a case like $az$ and $by$ mapping to the same number of $2.25$. I'm not sure what formula would work such that:
$f(s_1)=f(s_2)$ if $areAnagrams(s_1,s_2)$
$f(s_1)neq f(s_2)$ if $neg areAnagrams(s_1,s_2)$
functions proof-writing computer-science
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
$endgroup$
Given the set $S$ of all strings of alphabet $Sigma={a,b,c,...,z}$, I want to construct a function $f : S rightarrow mathbb{R}$ such that $$f(s_1)=f(s_2) Leftrightarrow areAnagrams(s_1,s_2) $$
My first step to this is that $f(s)=[len(s)].d_1d_2...d_n$. Having the length of the string in the mapped number helps preventing two unequal length strings having the same $f$ value. However, I am now stuck trying to construct the $d_1...d_n$ portion so that is specific to the letters in $s$.
For example, if I index each of $a,b,...,z$ with $0,1,...,25$ and then have $$f(s)=[len(s)].[text{sum index of each character in s]} $$ there could be a case like $az$ and $by$ mapping to the same number of $2.25$. I'm not sure what formula would work such that:
$f(s_1)=f(s_2)$ if $areAnagrams(s_1,s_2)$
$f(s_1)neq f(s_2)$ if $neg areAnagrams(s_1,s_2)$
functions proof-writing computer-science
functions proof-writing computer-science
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
asked Dec 29 '18 at 16:27
Hisoka MorohHisoka Moroh
420110
420110
add a comment |
add a comment |
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