Java hashcode reverse calculation

Question

I am trying to test out how String hashcode works by adding a new character and do the reverse to subtract it out, however it didn't give me the right answer when i did the calculation.

For example

int PRIME = 31;

//this will print 1687846330 
System.out.println("mlkjihgfedcb".hashCode());   

//this will print 783628775 which equals to "mlkjihgfedcba".hashCode();
System.out.println(("mlkjihgfedcb".hashCode() * PRIME + (int) 'a')); 

//this will print 25278344 which doesn't equals to "mlkjihgfedcb".hashCode()
System.out.println(("mlkjihgfedcba".hashCode() - (int) 'a') / PRIME); 

I am wondering did i do the math right on my last step above ? overflow shouldn't matter for the calculation right ?

Answer 1

Hash functions are not reversible functions. As proof, consider the Pigeonhole principle, you can only store values in the integer range in a hashCode but there are an infinite number of Strings. Therefore, there must be multiple strings with the same hashCode (and there are).