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I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

Note: this is assuming strings of equal length. instantly reject strings of different length.

example:
A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24
B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? how would one go about proving this. I want it to be true because it would be more space efficient than http://stackoverflow.com/a/2145221/2001647 which also runs in O(n)

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

Note: this is assuming strings of equal length. instantly reject strings of different length.

example:
A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24
B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? how would one go about proving this. I want it to be true because it would be more space efficient than https://stackoverflow.com/a/2145221/2001647 which also runs in O(n)

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

Note: this is assuming strings of equal length. instantly reject strings of different length.

example:
A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24
B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? how would one go about proving this. I want it to be true because it would be more space efficient than http://stackoverflow.com/a/2145221/2001647 which also runs in O(n)

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

Note: this is assuming strings of equal length. instantly reject strings of different length.

example:
A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24
B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? how would one go about proving this. I want it to be true because it would be more space efficient than http://stackoverflow.com/a/2145221/2001647 which also runs in O(n)

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

example: A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24 B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? I want it to be true because it would be more space efficient than http://stackoverflow.com/a/2145221/2001647 which also runs in O(n)

I've come across many coding exercises that require me to determine whether or not two strings are permutations of each other and I've repeatedly wondered if it would be possible to convert each string to char codes and perform mathematical operations on them to determine equivalence.

My idea was to sum up the char values of each and compare. Then multiply the values of each string and compare. If both the sum and product are the same for both strings then the strings are permutations of each other.

Note: this is assuming strings of equal length. instantly reject strings of different length.

example: 
A = "abcd" = [1, 2, 3, 4] -> Sum: 10 -- Product: 24 
B = "bcda" = [2, 3, 4, 1] -> Sum: 10 -- Product: 24

Sum A = Sum B and Product A = Product B therefore A is a permutation of B

Is there a case where this would not hold true? how would one go about proving this. I want it to be true because it would be more space efficient than http://stackoverflow.com/a/2145221/2001647 which also runs in O(n)