I have a value of 2 bytes. 9C 80
Among them
2 bits in the first byte are the mode values as shown in the picture below,
The next 12bit is the number of steps.
This way, you have a total of 2 bytes.
But I don't know how to calculate it in 16 bits.
The result of extracting 12 bits using 9C 80 bytes is 114.
This is wrong.
The correct answer is 39 steps.
39 steps
Can it come out of the 12bit of the 9C 80?
Help.
Below is the bit position of the byte values passed from c.
struct ble_sync_sport_item
{
uint16_t mode : 2;
uint16_t sport_count : 12;
uint16_t active_time : 4;
uint16_t calories : 10;
uint16_t distance : 12;
};
This is the android code I made to calculate the byte value.
private int bytesToInt(byte[] bytes , String value) {
int binaryToDecimal = 0;
int binaryToDecimal2 = 0;
int binaryToDecimal3 = 0;
int result = 0;
String s1 = "";
String s2 = "";
String s3 = "";
byteLog("5bytes ",bytes);
switch (value) {
case "ACT_STEP":
s1 = String.format("%8s", Integer.toBinaryString(bytes[0] & 0xFF)).replace(' ', '0');
s2 = String.format("%8s", Integer.toBinaryString(bytes[1] & 0xFF)).replace(' ', '0');
Log.d("FASDF ", "s1 == " + s1 + " s2 = " + s2 );
s1 = s1.substring(2, 8).concat(s2.substring(0,2));
s2 = s2.substring(2, 8).concat("00");
Log.d("FASDF ", "s1 == " + s1 + " s2 = " + s2 );
binaryToDecimal = Integer.parseInt(s1, 2);
binaryToDecimal2 = Integer.parseInt(s2, 2);
result = (int) ((int) binaryToDecimal) + ((int) binaryToDecimal2 << 8);
Log.d(tag,"result_step = " + result);
break;
This is the logarithm of the result I calculated.
39 should come out
114 came out.
As the result
The mode value of binary number 10 and
I want to get the sprot_count value of 100111 binary.
D/FASDF: s1 == 10011100 = 0x9C ,, s2 = 10000000 = 0x80
D/SevenHL5ConnectSync: result_step = 114
This could be an issue with bit order in the byte. Please check Big Endian vs Little Endian mode. The result you're getting 114 (1110010) is just the opposite of 39 (0100111) that is a reverse order in the bit.
A top secret message containing uppercase letters from 'A' to 'Z' has been encoded as numbers using the following mapping:
'A' -> 1
'B' -> 2
...
'Z' -> 26
You are an FBI agent and you need to determine the total number of ways that the message can be decoded.
Since the answer could be very large, take it modulo 10^9 + 7.
Example
For message = "123", the output should be
mapDecoding(message) = 3.
"123" can be decoded as "ABC" (1 2 3), "LC" (12 3) or "AW" (1 23), so the total number of ways is 3.
I found these 2 solutions but I cannot understand any of them and the equation used
int mapDecoding(String m) {
for (var e : m.getBytes())
k = v / 49 * 554 / (v * 10 + e) * c + (v = e) / 49 * (c = k %= 1e9 + 7);
return k;
}
int c, v, k = 1;
the second solution
int a, b = 1, c;
int mapDecoding(String m){
for(int d : m.getBytes())
b = 63/(c%49*9+d)*a + (c=d)/49 * (a=b%=1e9+7);
return b;
}
Can anyone help ?
Here is the expression:
class ExpresieUrata
{
public static void main(String[] args)
{
int x = 101;
int y = ( x+= (x *= 3) % ((x++ >> 2 ) - 1) ) ^ 40;
System.out.println(y);
}
}
I I get the output 68 but can't figure out why. I came to the conclusion that before the XOR operation I will get 108, made out of 101 + 7, but can't figure out why - especially the 7.
Can someone tell me the exact order of operation and value of x in storage/used at all steps?
public class Foo {
public static void main(String[] args)
{
int x = 101;
int y = ( x+= (x *= 3) % ((x++ >> 2 ) - 1) );
//int y = ( x+= (x *= 3) % ((x++ >> 2 ) - 1) ) ^ 40;
int z = y ^ 40;
System.out.printf("X: %d Y: %d Z: %d\n", x, y, z);
System.out.printf("303 >> 2 == %d\n", 303 >> 2);
System.out.printf("303 %% 74 == %d\n", (303 % 74));
}
}
Prints:
X: 108 Y: 108 Z: 68
303 >> 2 == 75
303 % 74 == 7
x *= 3 gets you the 303. 303 >> 2 is 75. Now subtract 1 is 74. 303 % 74 is 7. The x+= bit uses the original value of X before all the side effects, so 101 + 7 == 108.
And OMG, this is freakishly evil, and I would have unkind words if I ever saw code like this.
In my computer science class, I was given an algorithm to multiply two same-length binary numbers. I was instructed to convert it to multiply base 256 numbers and implement it in Java, but I can't seem to get the correct output and I don't know what I'm missing.
The algorithm that I was given:
MULTIPLY(U,V)
define array W[1..2n] for k = 1 to 2n
W[k] = 0 // Initialize result
for j=1 to n
c = 0 // Carry bit
for i = 1 to n
t = U[i]V[ j] + W [i+j] + c
W[i+j] = t mod 2 // lower bit
c= 𝑡/2 // upper bit
k = i+j
while k ≤ 2n and c ≠ 0 // propagate carry bit
t=W[k]+ c
W[k]=tmod2 // lower bit
c=𝑡/2 // upper bit
k++
return W
My attempt:
private static Byte[] bruteMultiply(Byte[] U, Byte[] V) {
Byte[] W = new Byte[U.length * 2];
for (int k = 0; k < W.length; k++) {
W[k] = 0;
}
for (int j = 0; j < U.length; j++) {
int c = 0;
for (int i = 0; i < U.length; i++) {
int t = (U[i] & 0xFF) * (V[j] & 0xFF) + (W[i + j] & 0xFF) + c;
W[i + j] = (byte) (t % 256);
c = t / 256;
}
int k = U.length + j;
while ((k < 2 * U.length) && (c != 0)) {
int t = (W[k] & 0xFF) + c;
W[k] = (byte) (t % 256);
c = t / 256;
k++;
}
}
return W;
}
When I feed it the arrays [197, 33, 151, 79] and [248, 164, 50, 235], I get [216, 234, 132, 91, 206, 122, 31, 73] when [191, 118, 251, 78, 251, 255, 83, 133] was expected.
I don't know what I'm missing or where I went wrong. Any suggestions or pointers would be helpful!
Hint: try to multiply [79, 151,33, 197] and [235, 50, 164, 248] with your code instead and compare the result to the target result.
I believe it is time for you to learn about the endianness. Generally your implementation looks OK but you use different endianness from the one in the example. Once you fix it, I think you'll get the correct answer.
P.S. I see no good reason to use Byte rather than byte in your array. This is another tricky difference that you probably should learn about.
I need to find the number of heavy integers between two integers A and B, where A <= B at all times.
An integer is considered heavy whenever the average of it's digit is larger than 7.
For example: 9878 is considered heavy, because (9 + 8 + 7 + 8)/4 = 8
, while 1111 is not, since (1 + 1 + 1 + 1)/4 = 1.
I have the solution below, but it's absolutely terrible and it times out when run with large inputs. What can I do to make it more efficient?
int countHeavy(int A, int B) {
int countHeavy = 0;
while(A <= B){
if(averageOfDigits(A) > 7){
countHeavy++;
}
A++;
}
return countHeavy;
}
float averageOfDigits(int a) {
float result = 0;
int count = 0;
while (a > 0) {
result += (a % 10);
count++;
a = a / 10;
}
return result / count;
}
Counting the numbers with a look-up table
You can generate a table that stores how many integers with d digits have a sum of their digits that is greater than a number x. Then, you can quickly look up how many heavy numbers there are in any range of 10, 100, 1000 ... integers. These tables hold only 9×d values, so they take up very little space and can be quickly generated.
Then, to check a range A-B where B has d digits, you build the tables for 1 to d-1 digits, and then you split the range A-B into chunks of 10, 100, 1000 ... and look up the values in the tables, e.g. for the range A = 782, B = 4321:
RANGE DIGITS TARGET LOOKUP VALUE
782 - 789 78x > 6 table[1][ 6] 3 <- incomplete range: 2-9
790 - 799 79x > 5 table[1][ 5] 4
800 - 899 8xx >13 table[2][13] 15
900 - 999 9xx >12 table[2][12] 21
1000 - 1999 1xxx >27 table[3][27] 0
2000 - 2999 2xxx >26 table[3][26] 1
3000 - 3999 3xxx >25 table[3][25] 4
4000 - 4099 40xx >24 impossible 0
4100 - 4199 41xx >23 impossible 0
4200 - 4299 42xx >22 impossible 0
4300 - 4309 430x >21 impossible 0
4310 - 4319 431x >20 impossible 0
4320 - 4321 432x >19 impossible 0 <- incomplete range: 0-1
--
48
If the first and last range are incomplete (not *0 - *9), check the starting value or the end value against the target. (In the example, 2 is not greater than 6, so all 3 heavy numbers are included in the range.)
Generating the look-up table
For 1-digit decimal integers, the number of integers n that is greater than value x is:
x: 0 1 2 3 4 5 6 7 8 9
n: 9 8 7 6 5 4 3 2 1 0
As you can see, this is easily calculated by taking n = 9-x.
For 2-digit decimal integers, the number of integers n whose sum of digits is greater than value x is:
x: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
n: 99 97 94 90 85 79 72 64 55 45 36 28 21 15 10 6 3 1 0
For 3-digit decimal integers, the number of integers n whose sum of digits is greater than value x is:
x: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
n: 999 996 990 980 965 944 916 880 835 780 717 648 575 500 425 352 283 220 165 120 84 56 35 20 10 4 1 0
Each of these sequences can be generated from the previous one: start with value 10d and then subtract from this value the previous sequence in reverse (skipping the first zero). E.g. to generate the sequence for 3 digits from the sequence for 2 digits, start with 103 = 1000, and then:
0. 1000 - 1 = 999
1. 999 - 3 = 996
2. 996 - 6 = 990
3. 990 - 10 = 980
4. 980 - 15 = 965
5. 965 - 21 = 944
6. 944 - 28 = 916
7. 916 - 36 = 880
8. 880 - 45 = 835
9. 835 - 55 = 780
10. 780 - 64 + 1 = 717 <- after 10 steps, start adding the previous sequence again
11. 717 - 72 + 3 = 648
12. 648 - 79 + 6 = 575
13. 575 - 85 + 10 = 500
14. 500 - 90 + 15 = 425
15. 425 - 94 + 21 = 352
16. 352 - 97 + 28 = 283
17. 283 - 99 + 36 = 220
18. 220 - 100 + 45 = 165 <- at the end of the sequence, keep subtracting 10^(d-1)
19. 165 - 100 + 55 = 120
20. 120 - 100 + 64 = 84
21. 84 - 100 + 72 = 56
22. 56 - 100 + 79 = 35
23. 35 - 100 + 85 = 20
24. 20 - 100 + 90 = 10
25. 10 - 100 + 94 = 4
26. 4 - 100 + 97 = 1
27. 1 - 100 + 99 = 0
By the way, you can use the same tables if "heavy" numbers are defined with a value other than 7.
Code example
Below is a Javascript code snippet (I don't speak Java) that demonstrates the method. It is very much unoptimised, but it does the 0→100,000,000 example in less than 0.07ms. It also works for weights other than 7. Translated to Java, it should easily beat any algorithm that actually runs through the numbers and checks their weight.
function countHeavy(A, B, weight) {
var a = decimalDigits(A), b = decimalDigits(B); // create arrays
while (a.length < b.length) a.push(0); // add leading zeros
var digits = b.length, table = weightTable(); // create table
var count = 0, diff = B - A + 1, d = 0; // calculate range
for (var i = digits - 1; i >= 0; i--) if (a[i]) d = i; // lowest non-0 digit
while (diff) { // increment a until a=b
while (a[d] == 10) { // move to higher digit
a[d++] = 0;
++a[d]; // carry 1
}
var step = Math.pow(10, d); // value of digit d
if (step <= diff) {
diff -= step;
count += increment(d); // increment digit d
}
else --d; // move to lower digit
}
return count;
function weightTable() { // see above for details
var t = [[],[9,8,7,6,5,4,3,2,1,0]];
for (var i = 2; i < digits; i++) {
var total = Math.pow(10, i), final = total / 10;
t[i] = [];
for (var j = 9 * i; total > 0; --j) {
if (j > 9) total -= t[i - 1][j - 10]; else total -= final;
if (j < 9 * (i - 1)) total += t[i - 1][j];
t[i].push(total);
}
}
return t;
}
function increment(d) {
var sum = 0, size = digits;
for (var i = digits - 1; i >= d; i--) {
if (a[i] == 0 && i == size - 1) size = i; // count used digits
sum += a[i]; // sum of digits
}
++a[d];
var target = weight * size - sum;
if (d == 0) return (target < 0) ? 1 : 0; // if d is lowest digit
if (target < 0) return table[d][0] + 1; // whole range is heavy
return (target > 9 * d) ? 0 : table[d][target]; // use look-up table
}
function decimalDigits(n) {
var array = [];
do {array.push(n % 10);
n = Math.floor(n / 10);
} while (n);
return array;
}
}
document.write("0 → 100,000,000 = " + countHeavy(0, 100000000, 7) + "<br>");
document.write("782 → 4321 = " + countHeavy(782, 4321, 7) + "<br>");
document.write("782 → 4321 = " + countHeavy(782, 4321, 5) + " (weight: 5)");
I really liked the post of #m69 so I wrote implementation inspired by it. The table creation is not that elegant, but works. For n+1 digits long integer I sum (at most) 10 values from n digits long integer, one for every digit 0-9.
I use this simplification to avoid arbitrary range calculation:
countHeavy(A, B) = countHeavy(0, B) - countHeavy(0, A-1)
The result is calculated in two loops. One for numbers shorter than the given number and one for the rest. I was not able to merge them easily. getResultis just lookup into the tablewith range checking, the rest of the code should be quite obvious.
public class HeavyNumbers {
private static int maxDigits = String.valueOf(Long.MAX_VALUE).length();
private int[][] table = null;
public HeavyNumbers(){
table = new int[maxDigits + 1][];
table[0] = new int[]{1};
for (int s = 1; s < maxDigits + 1; ++s) {
table[s] = new int[s * 9 + 1];
for (int k = 0; k < table[s].length; ++k) {
for (int d = 0; d < 10; ++d) {
if (table[s - 1].length > k - d) {
table[s][k] += table[s - 1][Math.max(0, k - d)];
}
}
}
}
}
private int[] getNumberAsArray(long number) {
int[] tmp = new int[maxDigits];
int cnt = 0;
while (number != 0) {
int remainder = (int) (number % 10);
tmp[cnt++] = remainder;
number = number / 10;
}
int[] ret = new int[cnt];
for (int i = 0; i < cnt; ++i) {
ret[i] = tmp[i];
}
return ret;
}
private int getResult(int[] sum, int digits, int fixDigitSum, int heavyThreshold) {
int target = heavyThreshold * digits - fixDigitSum + 1;
if (target < sum.length) {
return sum[Math.max(0, target)];
}
return 0;
}
public int getHeavyNumbersCount(long toNumberIncl, int heavyThreshold) {
if (toNumberIncl <= 0) return 0;
int[] numberAsArray = getNumberAsArray(toNumberIncl);
int res = 0;
for (int i = 0; i < numberAsArray.length - 1; ++i) {
for (int d = 1; d < 10; ++d) {
res += getResult(table[i], i + 1, d, heavyThreshold);
}
}
int fixDigitSum = 0;
int fromDigit = 1;
for (int i = numberAsArray.length - 1; i >= 0; --i) {
int toDigit = numberAsArray[i];
if (i == 0) {
toDigit++;
}
for (int d = fromDigit; d < toDigit; ++d) {
res += getResult(table[i], numberAsArray.length, fixDigitSum + d, heavyThreshold);
}
fixDigitSum += numberAsArray[i];
fromDigit = 0;
}
return res;
}
public int getHeavyNumbersCount(long fromIncl, long toIncl, int heavyThreshold) {
return getHeavyNumbersCount(toIncl, heavyThreshold) -
getHeavyNumbersCount(fromIncl - 1, heavyThreshold);
}
}
It is used like this:
HeavyNumbers h = new HeavyNumbers();
System.out.println( h.getHeavyNumbersCount(100000000,7));
prints out 569484, the repeated calculation time without initialization of the table is under 1us
I looked at the problem differently than you did. My perception is that the problem is based on the base-10 representation of a number, so the first thing you should do is to put the number into a base-10 representation. There may be a nicer way of doing it, but Java Strings represent Integers in base-10, so I used those. It's actually pretty fast to turn a single character into an integer, so this doesn't really cost much time.
Most importantly, your calculations in this matter never need to use division or floats. The problem is, at its core, about integers only. Do all the digits (integers) in the number (integer) add up to a value greater than or equal to seven (integer) times the number of digits (integer)?
Caveat - I don't claim that this is the fastest possible way of doing it, but this is probably faster than your original approach.
Here is my code:
package heavyNum;
public class HeavyNum
{
public static void main(String[] args)
{
HeavyNum hn = new HeavyNum();
long startTime = System.currentTimeMillis();
hn.countHeavy(100000000, 1);
long endTime = System.currentTimeMillis();
System.out.println("Time elapsed: "+(endTime- startTime));
}
private void countHeavy(int A, int B)
{
int heavyFound = 0;
for(int i = B+1; i < A; i++)
{
if(isHeavy(i))
heavyFound++;
}
System.out.println("Found "+heavyFound+" heavy numbers");
}
private boolean isHeavy(int i)
{
String asString = Integer.valueOf(i).toString();
int length = asString.length();
int dividingLine = length * 7, currTotal = 0, counter = 0;
while(counter < length)
{
currTotal += Character.getNumericValue(asString.charAt(counter++));
}
return currTotal > dividingLine;
}
}
Credit goes to this SO Question for how I get the number of digits in an integer and this SO Question for how to quickly convert characters to integers in java
Running on a powerful computer with no debugger for numbers between one and 100,000,000 resulted in this output:
Found 569484 heavy numbers
Time elapsed: 6985
EDIT: I initially was looking for numbers whose digits were greater than or equal to 7x the number of digits. I previously had results of 843,453 numbers in 7025 milliseconds.
Here's a pretty barebones recursion with memoization that enumerates the digit possibilities one by one for a fixed-digit number. You may be able to set A and B by controlling the range of i when calculating the corresponding number of digits.
Seems pretty fast (see the result for 20 digits).
JavaScript code:
var hash = {}
function f(k,soFar,count){
if (k == 0){
return 1;
}
var key = [k,soFar].join(",");
if (hash[key]){
return hash[key];
}
var res = 0;
for (var i=Math.max(count==0?1:0,7*(k+count)+1-soFar-9*(k-1)); i<=9; i++){
res += f(k-1,soFar+i,count+1);
}
return hash[key] = res;
}
// Output:
console.log(f(3,0,0)); // 56
hash = {};
console.log(f(6,0,0)); // 12313
hash = {};
console.log(f(20,0,0)); // 2224550892070475
You can indeed use strings to get the number of digits and then add the values of the individual digits to see if their sum > 7 * length, as Jeutnarg seems to do. I took his code and added my own, simple isHeavyRV(int):
private boolean isHeavyRV(int i)
{
int sum = 0, count = 0;
while (i > 0)
{
sum += i % 10;
count++;
i = i / 10;
}
return sum >= count * 7;
}
Now, instead of
if(isHeavy(i))
I tried
if(isHeavyRV(i))
I actually first tested his implementation of isHeavy(), using strings, and that ran in 12388 milliseconds on my machine (an older iMac), and it found 843453 heavy numbers.
Using my implementation, I found exactly the same number of heavy numbers, but in a time of a mere 5416 milliseconds.
Strings may be fast, but they can't beat a simple loop doing basically what Integer.toString(i, 10) does as well, but without the string detour.
When you add 1 to a number, you are incrementing one digit, and changing all the smaller digits to zero. If incrementing changes from a heavy to a non-heavy number, its because too many low-order digits were zeroed. In this case, it's pretty easy to find the next heavy number without checking all the numbers in between:
public class CountHeavy
{
public static void main(String[] args)
{
long startTime = System.currentTimeMillis();
int numHeavy = countHeavy(1, 100000000);
long endTime = System.currentTimeMillis();
System.out.printf("Found %d heavy numbers between 1 and 100000000\n", numHeavy);
System.out.println("Time elapsed: "+(endTime- startTime)+" ms");
}
static int countHeavy(int from, int to)
{
int numdigits=1;
int maxatdigits=9;
int numFound = 0;
if (from<1)
{
from=1;
}
for(int i = from; i < to;)
{
//keep track of number of digits in i
while (i > maxatdigits)
{
long newmax = 10L*maxatdigits+9;
maxatdigits = (int)Math.min(Integer.MAX_VALUE, newmax);
++numdigits;
}
//get sum of digits
int digitsum=0;
for(int digits=i;digits>0;digits/=10)
{
digitsum+=(digits%10);
}
//calculate a step size that increments the first non-zero digit
int step=1;
int stepzeros=0;
while(step <= (Integer.MAX_VALUE/10) && to-i >= step*10 && i%(step*10) == 0)
{
step*=10;
stepzeros+=1;
}
//step is a 1 followed stepzeros zeros
//how much is our sum too small by?
int need = numdigits*7+1 - digitsum;
if (need <= 0)
{
//already have enough. All the numbers between i and i+step are heavy
numFound+=step;
}
else if (need <= stepzeros*9)
{
//increment to the smallest possible heavy number. This puts all the
//needed sum in the lowest-order digits
step = need%9;
for(;need >= 9;need-=9)
{
step = step*10+9;
}
}
//else there are no heavy numbers between i and i+step
i+=step;
}
return numFound;
}
}
Found 569484 heavy numbers between 1 and 100000000
Time elapsed: 31 ms
Note that the answer is different from #JeutNarg's, because you asked for average > 7, not average >= 7.