As the title suggests, I am using the following function to read the parameters of some g-code files present on the SD card:
long parseParameters(String data, char* c){
int offset = data.indexOf(c);
int offset1 = data.lastIndexOf(" ", offset + 1);
return offset1 > 0 ? data.substring(offset + 1, offset + offset1 + 1).toInt() : data.substring(offset + 1).toInt();
}
void setup(){
Serial.begin(9600);
String q = "P3 S255"; // input
Serial.println(parseParameters(p, "S")); // output
}
void loop(){
}
Only today, in an attempt to read the value of S in the string P3 S255 has emerged in a small bug:
INPUT -> OUTPUT
P3 S255 -> 25 (wrong)
A20 P3 S255 -> 255 (Correct)
S255 -> 255 (Correct)
Why? Yet the code would seem correct to me..where did I go wrong?
Thanks in advance to everyone.. :)
Thats the explanation:
int offset = data.indexOf(c); //in your example S
"P3 S255";
^
offset = 3
then you parse for offset1 but take another param namely " " after offset - but there is no " " in the string from offset+1 see above where the index is so it returns -1 why?
myString.lastIndexOf(val, from) The index of val within the String, or -1 if not found. But we find something:
offset = 3;
offset1 = 2 ==> offset1 > 0 ==> data.substring(offset + 1, offset + offset1 + 1).toInt()
which leads to
data.substring(3 + 1, 3 + 2 + 1).toInt()
"P3 S*4*25*6*5"; which results to 25 as you already know
to (optional): the index to end the substring before.
So you have correct for the S in the begin by changing to
data.substring(offset + 1, offset + 1 + offset1 + 1).toInt()
Explanation: You start at offset + 1 this has to be equal in from and to (= same starting point for your calculation)
Related
Let's say I have 15 elements. I want to group them such a way that:
group1 = 1 - 5
group2 = 6 - 9
group3 = 10 - 12
group4 = 13 - 14
group5 = 15
This way I'll get elements in each group as below:
group1 = 5
group2 = 4
group3 = 3
group4 = 2
group5 = 1
As you can see loop interval is decreasing.
I took 15 just for an example. In actual programme it's user driven parameter which can be anything (hopefully few thousand).
Now what I'm looking for is:
Whatever is in group1 should have variable "loop" value 0, group2 should have 1, group3 should have 2 and so on... "loop" is an int variable which is being used to calculate some other stuff.
Let's put in other words too
I have an int variable called "loop". I want to assign value to it such a way that:
First n frames loop value 0 next (n -1) frames loop value 1 then next (n - 2) frames loop value 2 all the way to loop value (n - 1)
Let's say I have 15 frames on my timeline.
So n will be 5 ====>>>>> (5 + 4 + 3 + 2 + 1 = 15; as interval is decreasing by 1)
then
first 5 frames(1 - 5) loop is 0 then next 4 frames(6 - 9) loop is 1 then next 3 frames(10 - 12) loop is 2 then next 2 frames(13 - 14) loop is 3 and for last frame(15) loop is 4.
frames "loop" value
1 - 5 => 0
6 - 9 => 1
10 - 12 => 2
13 - 14 => 3
15 => 4
I've tried with modulo(%). But the issue is on frame 12 loop is 2 so (12 % (5 - 2)) remainder is 0 so it increments loop value.
The following lines are sample code which is running inside a solver. #loop is by default 0 and #Frame is current processing frame number.
int loopint = 5 - #loop;
if (#Frame % loopint == 0)
#loop += 1;
If I understand this correctly, then
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(int argc, char *argv[]) {
int n = atoi(argv[1]);
for(int i = 1; i <= n; ++i) {
printf("%d: %f\n", i, ceil((sqrt(8 * (n - i + 1) + 1) - 1) / 2));
}
}
is an implementation in C.
The math behind this is as follows: The 1 + 2 + 3 + 4 + 5 you have there is a Gauß sum, which has a closed form S = n * (n + 1) / 2 for n terms. Solving this for n, we get
n = (sqrt(8 * S + 1) - 1) / 2
Rounding this upward would give us the solution if you wanted the short stretches at the beginning, that is to say 1, 2, 2, 3, 3, 3, ...
Since you want the stretches to become progressively shorter, we have to invert the order, so S becomes (n - S + 1). Therefore the formula up there.
EDIT: Note that unless the number of elements in your data set fits the n * (n+1) / 2 pattern precisely, you will have shorter stretches either at the beginning or in the end. This implementation places the irregular stretch at the beginning. If you want them at the end,
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(int argc, char *argv[]) {
int n = atoi(argv[1]);
int n2 = (int) ceil((sqrt(8 * n + 1) - 1) / 2);
int upper = n2 * (n2 + 1) / 2;
for(int i = 1; i <= n; ++i) {
printf("%d: %f\n", i, n2 - ceil((sqrt(8 * (upper - i + 1) + 1) - 1) / 2));
}
}
does it. This calculates the next such number beyond your element count, then calculates the numbers you would have if you had that many elements.
int sum_down(int x)
{
if (x >= 0)
{
x = x - 1;
int y = x + sum_down(x);
return y + sum_down(x);
}
else
{
return 1;
}
}
What is this smallest integer value of the parameter x, so that the returned value is greater than 1.000.000 ?
Right now I am just doing it by trial and error and since this question is asked via a paper format. I don't think I will have enough time to do trial and error. Question is, how do you guys visualise this quickly such that it can be solved easily. Thanks guys and I am new to programming so thanks in advance!
The recursion logic:
x = x - 1;
int y = x + sum_down(x);
return y + sum_down(x);
can be simplified to:
x = x - 1;
int y = x + sum_down(x) + sum_down(x);
return y;
which can be simplified to:
int y = (x-1) + sum_down(x-1) + sum_down(x-1);
return y;
which can be simplified to:
return (x-1) + 2*sum_down(x-1);
Put in mathematical form,
f(N) = (N-1) + 2*f(N-1)
with the recursion terminating when N is -1. f(-1) = 1.
Hence,
f(0) = -1 + 2*1 = 1
f(1) = 0 + 2*1 = 2
f(2) = 1 + 2*2 = 5
...
f(18) = 17 + 2*f(17) = 524269
f(19) = 18 + 2*524269 = 1048556
Your program can be written this way (sorry about c#):
public static void Main()
{
int i = 0;
int j = 0;
do
{
i++;
j = sum_down(i);
Console.Out.WriteLine("j:" + j);
} while (j < 1000000);
Console.Out.WriteLine("i:" + i);
}
static int sum_down(int x)
{
if (x >= 0)
{
return x - 1 + 2 * sum_down(x - 1);
}
else
{
return 1;
}
}
So at first iteration you'll get 2, then 5, then 12... So you can neglect the x-1 part since it'll stay little compared to the multiplication.
So we have:
i = 1 => sum_down ~= 4 (real is 2)
i = 2 => sum_down ~= 8 (real is 5)
i = 3 => sum_down ~= 16 (real is 12)
i = 4 => sum_down ~= 32 (real is 27)
i = 5 => sum_down ~= 64 (real is 58)
So we can say that sum_down(x) ~= 2^x+1. Then it's just basic math with 2^x+1 < 1 000 000 which is 19.
A bit late, but it's not that hard to get an exact non-recursive formula.
Write it up mathematically, as explained in other answers already:
f(-1) = 1
f(x) = 2*f(x-1) + x-1
This is the same as
f(-1) = 1
f(x+1) = 2*f(x) + x
(just switched from x and x-1 to x+1 and x, difference 1 in both cases)
The first few x and f(x) are:
x: -1 0 1 2 3 4
f(x): 1 1 2 5 12 27
And while there are many arbitrary complicated ways to transform this into a non-recursive formula, with easy ones it often helps to write up what the difference is between each two elements:
x: -1 0 1 2 3 4
f(x): 1 1 2 5 12 27
0 1 3 7 15
So, for some x
f(x+1) - f(x) = 2^(x+1) - 1
f(x+2) - f(x) = (f(x+2) - f(x+1)) + (f(x+1) - f(x)) = 2^(x+2) + 2^(x+1) - 2
f(x+n) - f(x) = sum[0<=i<n](2^(x+1+i)) - n
With eg. a x=0 inserted, to make f(x+n) to f(n):
f(x+n) - f(x) = sum[0<=i<n](2^(x+1+i)) - n
f(0+n) - f(0) = sum[0<=i<n](2^(0+1+i)) - n
f(n) - 1 = sum[0<=i<n](2^(i+1)) - n
f(n) = sum[0<=i<n](2^(i+1)) - n + 1
f(n) = sum[0<i<=n](2^i) - n + 1
f(n) = (2^(n+1) - 2) - n + 1
f(n) = 2^(n+1) - n - 1
No recursion anymore.
How about this :
int x = 0;
while (sum_down(x) <= 1000000)
{
x++;
}
The loop increments x until the result of sum_down(x) is superior to 1.000.000.
Edit : The result would be 19.
While trying to understand and simplify the recursion logic behind the sum_down() function is enlightening and informative, this snippet tend to be logical and pragmatic in that it does not try and solve the problem in terms of context, but in terms of results.
Two lines of Python code to answer your question:
>>> from itertools import * # no code but needed for dropwhile() and count()
Define the recursive function (See R Sahu's answer)
>>> f = lambda x: 1 if x<0 else (x-1) + 2*f(x-1)
Then use the dropwhile() function to remove elements from the list [0, 1, 2, 3, ....] for which f(x)<=1000000, resulting in a list of integers for which f(x) > 1000000. Note: count() returns an infinite "list" of [0, 1, 2, ....]
The dropwhile() function returns a Python generator so we use next() to get the first value of the list:
>>> next(dropwhile(lambda x: f(x)<=1000000, count()))
19
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I have a problem:
I have a N (N <= 40). N is a length of sequence of zeroz and ones. How to find the number of sequences of zeros and ones in which there are no three "1" together?
Example:
N = 3, answer = 7
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
Here's a solution using a recursive function :
(PHP code here, but it's really simple)
$seq = '';
function tree ($node, $flag, $seq)
{
if ($flag == 3) { return 0; }
if ($node == 0) { echo $seq, ' '; return 0;}
$seq1 = $seq.'1';
$seq2 = $seq.'0';
tree($node-1, $flag+1, $seq1);
tree($node-1, 0, $seq2);
}
tree(8, 0, $seq);
I use a tree to go through all the possible sequences, and a flag to check how many 1 in a row.
If there is two 1 in a row, then the flag reaches 3, and the function is stopped for this branch.
If we reach a leaf of the tree (ie. $node = 0), then the sequence is displayed, and the function ends.
Else, the function explores the two sub-trees starting from the current node.
void tree ( int node, int flag, std::string seq)
{
std::string seq1 = seq;
std::string seq2 = seq;
if(flag ==3) { return; }
if(node ==0) { printf("%s\n",seq.c_str()); return;}
seq1 += '1';
seq2 += '0';
tree(node-1, flag+1, seq1);
tree(node-1, 0, seq2);
}
You can write a grammar for the (non-empty) strings of this language. It's designed so that each string appears exactly once.
S := 0 | 1 | 11 | 10 | 110 | 0S | 10S | 110S
Let a_i be the total number of strings of length i in S.
First, look at the number of strings of length 1 on both sides of the grammar rule. There's a_1 in S by definition which deals with the left-hand-side.
a_1 = 2
For a_2, on the right-hand-side we immediately get two strings of length 2 (11 and 10), plus another two from the 0S rule (00 and 01). This gives us:
a_2 = 2 + a_1 = 4
Similarly, for a_3, we get:
a_3 = 1 + a_2 + a_1 = 7
(So far so good, we've got the right solution 7 for the case where the strings are length three).
For i > 3, consider the number of strings of length i on both sides.
a_i = a_{i-1} + a_{i-2} + a_{i-3}
Now we've got a recurrence we can use. A quick check for a_4...
a_4 = a_1 + a_2 + a_3 = 2 + 4 + 7 = 13.
There's 16 strings of length 4 and three containing 111: 1110, 0111, 1111. So 13 looks right!
Here's some code in Python for the general case, using this recurrence.
def strings_without_111(n):
if n == 0: return 1
a = [2, 4, 7]
for _ in xrange(n - 1):
a = [a[1], a[2], a[0] + a[1] + a[2]]
return a[0]
This is a dp problem. I will explain the solution in a way so that it is easy to modify it to count the number of sequences having no sequence a0a1a2 in them(where ai is arbitrary binary value).
I will use 4 helper variables each counting the sequence up to a given length that are valid and end with 00, 01, 10, and 11 respectively. Name those c00, c01, c10, c11. It is pretty obvious that for length N = 2, those numbers are all 1:
int c00 = 1;
int c01 = 1;
int c10 = 1;
int c11 = 1;
Now assuming we have counted the sequences up to a given length k we count the sequences in the four groups for length k + 1 in the following manner:
int new_c00 = c10 + c00;
int new_c01 = c10 + c00;
int new_c10 = c01 + c11;
int new_c11 = c01;
The logic above is pretty simple - if we append a 0 to either a sequence of length k ending at 0 0 or ending at 1 0 we end up with a new sequence of length k + 1 and ending with 0 0 and so on for the other equations above.
Note that c11 is not added to the number of sequences ending with 1 1 and with length k + 1. That is because if we append 1 to a sequence ending with 1 1 we will end up with an invalid sequence( ending at 1 1 1).
Here is a complete solution for your case:
int c00 = 1;
int c01 = 1;
int c10 = 1;
int c11 = 1;
for (int i = 0; i < n - 2; ++i) {
int new_c00 = c10 + c00;
int new_c01 = c10 + c00;
int new_c10 = c01 + c11;
int new_c11 = c01;
c00 = new_c00;
c01 = new_c01;
c10 = new_c10;
c11 = new_c11;
}
// total valid sequences of length n
int result = c00 + c01 + c10 + c11;
cout << result << endl;
Also you will have to take special care for the case when N < 2, because the above solution does not handle that correctly.
To find a number of all possible sequences for N bits are easy. It is 2^N.
To find all sequences contains 111 a bit harder.
Assume N=3 then Count = 1
111
Assume N=4 then Count = 3
0111
1110
1111
Assume N=5 then Count = 8
11100
11101
11110
11111
01110
01111
00111
10111
If you write simple simulation program it yields 1 3 8 20 47 107 ...
Subtract 2^n - count(n) = 2 4 7 13 24 44 81 149...
Google it and it gives OEIS sequence, known as tribonacci numbers. Solved by simple recurrent equation:
a(n) = a(n - 1) + a(n - 2) + a(n - 3)
Given stack pointer value, is it possible to determine the value of the passed arguments to the function? Where are the arguments stored in the stack frame.
Lets say, executing gcc compiled ELF binary on x86 architecture on Linux platform:
int foo(int a, int b)
{
...
}
foo(a,b) is called from main() and I know the stack pointer(SP) value which is pointing to foo() now. How can I retrive the value of arguments a and b?
EDIT: If stack grows from smaller address to larger address, and arguments are passed right to left using cdecl, can I obtain args value like this:
b = *(SP + 1);
a = *(SP + 2);
EDIT: The following program prints the value of functions args a, b using above arch and specifications.
void foo(int a, int b)
{
int i;
register int stackptr asm("sp");
int *sp = (int *)stackptr;
printf("\n\ta=%d b=%d\n", a, b);
for (i=0; i<16; i++) {
printf("*(sp + %d) = %d\n", i, *(sp +i));
}
}
int main()
{
foo(3, 8);
foo(9, 2);
foo(1, 4);
return 0;
}
The output of above code is:
a=3 b=8
*(sp + 0) = 134514016
*(sp + 1) = 0
*(sp + 2) = 0
*(sp + 3) = 134513373
*(sp + 4) = 8239384
*(sp + 5) = 134513228
*(sp + 6) = 6
*(sp + 7) = -1076716032
*(sp + 8) = 134513456
*(sp + 9) = 0
*(sp + 10) = -1076715960
*(sp + 11) = 134513759
*(sp + 12) = 3 //value of arg a
*(sp + 13) = 8 //value of arg b
*(sp + 14) = 134513817
*(sp + 15) = 10612724
a=9 b=2
*(sp + 0) = 134514016
*(sp + 1) = 0
*(sp + 2) = 0
*(sp + 3) = 134513373
*(sp + 4) = 8239384
*(sp + 5) = 134513228
*(sp + 6) = 6
*(sp + 7) = -1076716032
*(sp + 8) = 134513456
*(sp + 9) = 0
*(sp + 10) = -1076715960
*(sp + 11) = 134513779
*(sp + 12) = 9 //value of arg a
*(sp + 13) = 2 //value of arg b
*(sp + 14) = 134513817
*(sp + 15) = 10612724
a=1 b=4
*(sp + 0) = 134514016
*(sp + 1) = 0
*(sp + 2) = 0
*(sp + 3) = 134513373
*(sp + 4) = 8239384
*(sp + 5) = 134513228
*(sp + 6) = 6
*(sp + 7) = -1076716032
*(sp + 8) = 134513456
*(sp + 9) = 0
*(sp + 10) = -1076715960
*(sp + 11) = 134513799
*(sp + 12) = 1 //value of arg a
*(sp + 13) = 4 //value of arg b
*(sp + 14) = 134513817
*(sp + 15) = 10612724
Why function arguments are stored from offset 12 of SP? Also notice values at offset 0 to 10 are always same, and value at offset 11 increases by 20 on each invocation of function foo().
UPDATE: I found that gcc has in-build function to retrieve frame pointer address
void * __builtin_frame_address (unsigned int level)
When I print values at offsets starting from __builtin_frame_address(0) the function arguments start from offset 2. How can I confirm that this behavior is always consistent?
You must know the calling convention to know what order the arguments are pushed onto the stack, or even if they are on the stack. Many pass the first few arguments in registers. Even on x86, you have fastcall, pascal, register, stdcall and cdecl, just to name a few.
EDIT: Don't forget that printf is also a function, and local variables also go on the stack. So, in your sample app, you have your parameters (since it's cdecl), then your locals, then your function saved state and return address, then parameters to printf (maybe, not sure if it's cdecl or fastcall), then printf's locals by the time anything actually makes it to the screen.
There's no easy way and certainly there's no portable way (for the same source file this could even change between gcc 4.1 and gcc 4.2) but gdb sure can do it. Using gcc, you can probably find all you need analyzing the DWARF info.
gdb also uses prologue analysis to detect how local variables are assigned in the stack (among other things) but I'm not sure if something like a "calling analysis" exists in gdb's source. May be reading prologue-value.h in gdb's source could help you.
The local variables are allocated on the stack, thus variables i, stackptr and sp are allocated on the call stack. So, if we print all the stack records we will find these variables, then the return pointer, then the saved frame pointer (if saved) and then the function parameters. Hence, in example above the args start at 12.
If you want to access immediately to the function call parameters you should start from the frame pointer address obtained using __builtin_frame_address(unsigned int level). Arguments are pushed on the stack before the saved frame pointer, thus you have to add an offset equal to the frame pointer address size if you start from the beginning of the saved frame pointer record on the stack. Hence, in example above, args start at offset 2.
How does this code concatenate the data from the string buffer? What is the * 10 doing? I know that by subtracting '0' you are subtracting the ASCII so turn into an integer.
char *buf; // assume that buf is assigned a value such as 01234567891234567
long key_num = 0;
someFunction(&key_num);
...
void someFunction(long *key_num) {
for (int i = 0; i < 18; i++)
*key_num = *key_num * 10 + (buf[i] - '0')
}
(Copied from my memory of code that I am working on recently)
It's basically an atoi-type (or atol-type) function for creating an integral value from a string. Consider the string "123".
Before starting, key_num is set to zero.
On the first iteration, that's multiplied by 10 to give you 0, then it has the character value '1' added and '0' subtracted, effectively adding 1 to give 1.
On the second iteration, that's multiplied by 10 to give you 10, then it has the character value '2' added and '0' subtracted, effectively adding 2 to give 12.
On the third iteration, that's multiplied by 10 to give you 120, then it has the character value '3' added and '0' subtracted, effectively adding 3 to give 123.
Voila! There you have it, 123.
If you change the code to look like:
#include <iostream>
char buf[] = "012345678901234567";
void someFunction(long long *key_num) {
std::cout << *key_num << std::endl;
for (int i = 0; i < 18; i++) {
*key_num = *key_num * 10 + (buf[i] - '0');
std::cout << *key_num << std::endl;
}
}
int main (void) {
long long x = 0;
someFunction (&x);
return 0;
}
then you should see it in action (I had to change your value from the 17-character array you provided in your comment to an 18-character one, otherwise you'd get some problems when you tried to use the character beyond the end; I also had to change to a long long because my longs weren't big enough):
0
0
1
12
123
1234
12345
123456
1234567
12345678
123456789
1234567890
12345678901
123456789012
1234567890123
12345678901234
123456789012345
1234567890123456
12345678901234567
As a shorter example with the number 1234, that can be thought of as:
1000 * 1 + 100 * 2 + 10 * 3 + 4
Or:
10 * (10 * (10 * 1 + 2) + 3) + 4
The first time through the loop, *key_num would be 1. The second time it is multiplied by 10 and 2 added (ie 12), the third time multiplied by 10 and 3 added (ie 123), the fourth time multiplied by 10 and 4 added (ie 1234).
It just multiples the current long value (*key_num) by 10, adds the digit value, then stores the result again.
EDIT: It's not bit-shifting anything. It's just math. You can imagine it as shifting decimal digits, but it's binary internally.
key_num = 0 (0)
key_num = key_num * 10 + ('0' - '0') (0)
key_num = key_num * 10 + ('1' - '0') (1)
key_num = key_num * 10 + ('2' - '0') (12)