I want to count the number of set bits in a uint in Specman:
var x: uint;
gen x;
var x_set_bits: uint;
x_set_bits = ?;
What's the best way to do this?
One way I've seen is:
x_set_bits = pack(NULL, x).count(it == 1);
pack(NULL, x) converts x to a list of bits.
count acts on the list and counts all the elements for which the condition holds. In this case the condition is that the element equals 1, which comes out to the number of set bits.
I don't know Specman, but another way I've seen this done looks a bit cheesy, but tends to be efficient: Keep a 256-element array; each element of the array consists of the number of bits corresponding to that value. For example (pseudocode):
bit_count = [0, 1, 1, 2, 1, ...]
Thus, bit_count2 == 1, because the value 2, in binary, has a single "1" bit. Simiarly, bit_count[255] == 8.
Then, break the uint into bytes, use the byte values to index into the bit_count array, and add the results. Pseudocode:
total = 0
for byte in list_of_bytes
total = total + bit_count[byte]
EDIT
This issue shows up in the book Beautiful Code, in the chapter by Henry S. Warren. Also, Matt Howells shows a C-language implementation that efficiently calculates a bit count. See this answer.
Related
I was asked this question in a HackerEarth test and I couldn't wrap my head around even forming the algorithm.
The question is -
Count the number of substrings of a string, such that any of their permutations is a palindrome.
So, for aab, the answer is 5 - a, a, b, aa and aab (which can be permuted to form aba).
I feel this is dynamic programming, but I can't find what kind of relations the subproblems might have.
Edit:
So I think the recursive relation might be
dp[i] = dp[i-1] + 1 if str[i] has already appeared before and
substring ending at i-1 has at most 2 characters with odd frequency
else dp[i] = dp[i-1]
No idea if this is right.
I can think of O(n^2) - traverse substrings of length > 1, from indexes (0, 1) up to (0, n-1), then from (1, n-1) down to (1, 3), then from (2, 3) up to (2, n-2), then from (3, n-2) down to (3, 5)...etc.
While traversing, maintain a map of current frequency for each character, as well as totals of the number of characters with odd counts and the number of characters with even counts. Update those on each iteration and add to the total count of palindromic permuted substrings if we are on a substring with (1) odd length and only one character with odd frequency, or (2) even length and no character with odd frequency.
(Add the string length for the count of single character palindromes.)
If I did not misunderstand your question, I tend to believe this is a math problem. Say the length of a string is n, then the answer should be n * (n+1) / 2, the sum of an infinite series. See https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
For example, string abcde, we can get substrings
a, b, c, d, e,
ab, bc, cd, de,
abc, bcd, cde,
abcd, bcde,
abcde .
You may find the answer from the way I listed the substrings.
So here is my solution that may help you.
you can get a list of every possible substring of input by running a nested loop and for every substring you have to check if the substring can form a palindrome or not.
now how to check if a string/substring can form palindrome:
If a substring is having alphabet of odd number of occurance more than 1, them it can't form a palindrome.Here is the code:
bool stringCanbeFormAPalindrome(string s)
{
int oddValues, alphabet[26];
for(int i =0; i< s.length(); i++)
{
alphabet[s[i]-'a']++;
}
for(int i=0; i<26; i++)
{
if(alphabet[i]%2==1)
{
oddValues++;
if(oddValues>1) return FALSE;
}
}
return TRUE;
}
May that helps.
You can do it easily in O(N) time and O(N) space complexity
notice, the only thing that if the permutation of substring is palindrome or not is the parity of odd character in it so just create a mask of parity of every character, now for any valid substring there can be at most 1 bit different to our current mask, let's iterate on which bit is different, and adding the corresponding answer.
Here's a C++ code (assuming unordered_map is O(1) per query)
string s;
cin>>s;
int n=s.length();
int ans=0;
unordered_map<int,int>um;
um[0]=1;
int mask=0;
for(int i=0;i<n;++i){
mask^=1<<(s[i]-'a');
ans+=um[mask];
for(int j=27;j>=0;--j){
ans+=um[mask^(1<<j)];
}
um[mask]++;
}
cout<<ans;
take care of integer overflow.
Given that a number can contain only digits from 1 to 8 (with no repetition), and is of length 8, how can we hash such numbers without using a hashSet?
We can't just directly use the value of the number of the hashing value, as the stack size of the program is limited. (By this, I mean that we can't directly make the index of an array, represent our number).
Therefore, this 8 digit number needs to be mapped to, at maximum, a 5 digit number.
I saw this answer. The hash function returns a 8-digit number, for a input that is an 8-digit number.
So, what can I do here?
There's a few things you can do. You could subtract 1 from each digit and parse it as an octal number, which will map one-to-one every number from your domain to the range [0,16777216) with no gaps. The resulting number can be used as an index into a very large array. An example of this could work as below:
function hash(num) {
return parseInt(num
.toString()
.split('')
.map(x => x - 1), 8);
}
const set = new Array(8**8);
set[hash(12345678)] = true;
// 12345678 is in the set
Or if you wanna conserve some space and grow the data structure as you add elements. You can use a tree structure with 8 branches at every node and a maximum depth of 8. I'll leave that up to you to figure out if you think it's worth the trouble.
Edit:
After seeing the updated question, I began thinking about how you could probably map the number to its position in a lexicographically sorted list of the permutations of the digits 1-8. That would be optimal because it gives you the theoretical 5-digit hash you want (under 40320). I had some trouble formulating the algorithm to do this on my own, so I did some digging. I found this example implementation that does just what you're looking for. I've taken inspiration from this to implement the algorithm in JavaScript for you.
function hash(num) {
const digits = num
.toString()
.split('')
.map(x => x - 1);
const len = digits.length;
const seen = new Array(len);
let rank = 0;
for(let i = 0; i < len; i++) {
seen[digits[i]] = true;
rank += numsBelowUnseen(digits[i], seen) * fact(len - i - 1);
}
return rank;
}
// count unseen digits less than n
function numsBelowUnseen(n, seen) {
let count = 0;
for(let i = 0; i < n; i++) {
if(!seen[i]) count++;
}
return count;
}
// factorial fuction
function fact(x) {
return x <= 0 ? 1 : x * fact(x - 1);
}
kamoroso94 gave me the idea of representing the number in octal. The number remains unique if we remove the first digit from it. So, we can make an array of length 8^7=2097152, and thus use the 7-digit octal version as index.
If this array size is bigger than the stack, then we can use only 6 digits of the input, convert them to their octal values. So, 8^6=262144, that is pretty small. We can make a 2D array of length 8^6. So, total space used will be in the order of 2*(8^6). The first index of the second dimension represents that the number starts from the smaller number, and the second index represents that the number starts from the bigger number.
I'm in the process of getting comfortable passing unnamed functions as arguments and I am using this to practice with, based off of the examples in the Swift Programming Guide.
So we have an array of Ints:
var numbers: Int[] = [1, 2, 3, 4, 5, 6, 7]
And I apply a transform like so: (7)
func transformNumber(number: Int) -> Int {
let result = number * 3
return result
}
numbers = numbers.map(transformNumber)
Which is equal to: (7)
numbers = numbers.map({(number: Int) -> Int in
let result = number * 3
return result;
})
Which is equal to: (8)
numbers = numbers.map({number in number * 3})
Which is equal to: (8)
numbers = numbers.map({$0 * 3})
Which is equal to: (8)
numbers = numbers.map() {$0 * 3}
As you can see in the following graphic, the iteration count in the playground sidebar shows that in the furthest abstraction of a function declaration, it has an 8 count.
Question
Why is it showing as 8 iterations for the last two examples?
It's not showing 8 iterations, really. It's showing that 8 things executed on that line. There were 7 executions as part of the map function, and an 8th to do the assignment back into the numbers variable.
It looks like this could probably provide more helpful diagnostics. I would highly encourage you to provide feedback via https://bugreport.apple.com.
Slightly rewriting your experiment to use only closures, the call counts still differ by one:
Case 1: Explicitly specifying argument types (visit count is 7)
var f1 = {(number: Int) -> Int in
let result = number * 3
return result
}
numbers.map(f1)
Case 2: Implicit argument types (visit count is 8)
var f2 = {$0 * 3}
numbers.map(f2)
If the (x times) count reported by the REPL does indeed represent a count of visits to that code location, and noting that the count is greater by one in cases where the closure type arguments are not explicitly specified (e.g. f2), my guess is that at least in the playground REPL, the extra visit is to establish actual parameter types and fill that gap in the underlying AST.
I am looking for to take one particular number or range of numbers from a set of number?
Example
A = [-10,-2,-3,-8, 0 ,1, 2, 3, 4 ,5,7, 8, 9, 10, -100];
How can I just take number 5 from the set of above number and
How can I take a range of number for example from -3 to 4 from A.
Please help.
Thanks
I don't know what you are trying to accomplish by this. But you could check each entry of the set and test it it's in the specified range of numbers. The test for a single number could be accomplished by testing each number explicitly or as a special case of range check where the lower and the upper bound are the same number.
looping and testing, no matter what the programming language is, although most programming languages have builtin methods for accomplishing this type of task (so you may want to specify what language are you supposed to use for your homework):
procfun get_element:
index=0
for element in set:
if element is 5 then return (element,index)
increment index
your "5" is in element and at set[index]
getting a range:
procfun getrange:
subset = []
index = 0
for element in set:
if element is -3:
push element in subset
while index < length(set)-1:
push set[index] in subset
if set[index] is 4:
return subset
increment index
#if we met "-3" but we didn't met "4" then there's no such range
return None
#keep searching for a "-3"
increment index
return None
if ran against A, subset would be [-3,-8, 0 ,1, 2, 3, 4]; this is a "first matched, first grabbed" poorman's algorithm. on sorted sets the algorithms can get smarter and faster.
I want to convert the decimal number 27 into binary such a way that , first the digit 2 is converted and its binary value is placed in an array and then the digit 7 is converted and its binary number is placed in that array. what should I do?
thanks in advance
That's called binary-coded decimal. It's easiest to work right-to-left. Take the value modulo 10 (% operator in C/C++/ObjC) and put it in the array. Then integer-divide the value by 10 (/ operator in C/C++/ObjC). Continue until your value is zero. Then reverse the array if you need most-significant digit first.
If I understand your question correctly, you want to go from 27 to an array that looks like {0010, 0111}.
If you understand how base systems work (specifically the decimal system), this should be simple.
First, you find the remainder of your number when divided by 10. Your number 27 in this case would result with 7.
Then you integer divide your number by 10 and store it back in that variable. Your number 27 would result in 2.
How many times do you do this?
You do this until you have no more digits.
How many digits can you have?
Well, if you think about the number 100, it has 3 digits because the number needs to remember that one 10^2 exists in the number. On the other hand, 99 does not.
The answer to the previous question is 1 + floor of Log base 10 of the input number.
Log of 100 is 2, plus 1 is 3, which equals number of digits.
Log of 99 is a little less than 2, but flooring it is 1, plus 1 is 2.
In java it is like this:
int input = 27;
int number = 0;
int numDigits = Math.floor(Log(10, input)) + 1;
int[] digitArray = new int [numDigits];
for (int i = 0; i < numDigits; i++) {
number = input % 10;
digitArray[numDigits - i - 1] = number;
input = input / 10;
}
return digitArray;
Java doesn't have a Log function that is portable for any base (it has it for base e), but it is trivial to make a function for it.
double Log( double base, double value ) {
return Math.log(value)/Math.log(base);
}
Good luck.