This question already has answers here:
Int division: Why is the result of 1/3 == 0?
(19 answers)
Closed 3 years ago.
I have the following expression in my code
int n = ((int) Math.sqrt(4 * 4 + 5) - 1) / 2;
Can someone tell me the precedence in which the expression is evaluated?
Logically I would evaluate the expression in the following way:
4 * 4 + 5 = 16 + 5 = 21
Math.sqrt(21) ~ 4.58
4.58 - 1 = 3.58
(int) 3.58 = 3
3 / 2 = 1.5
However the code evaluates to 1.
You almost got it. The only difference (which doesn't matter for the result) is that the cast is evaluated
before the subtraction, and you're using integer division:
4 * 4 + 5 = 16 + 5 = 21
Math.sqrt(21) ~ 4.58
(int) 4.58 = 4 (cast first)
4 - 1 = 3
3 / 2 = 1 (integer division)
The order you suggest is correct.
The keypoint is the last operation: the result of an int divided by an int is an int as well.
To fix this, one of the two number should be a float (or a double):
float n = ((float)(int) (Math.sqrt(4 * 4 + 5) - 1)) / 2;
In this way you divide a float by an int, and the result will be a float.
Or better:
double n = (Math.sqrt(4 * 4 + 5) - 1) / 2;
Because the cast to int of Math.sqrt() isn't useful.
Please note that the first operation does exactly what you ask with the round of the Math.sqrt(), while the second one doesn't.
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.
Closed. This question needs details or clarity. It is not currently accepting answers.
Want to improve this question? Add details and clarify the problem by editing this post.
Closed 8 years ago.
Improve this question
I don't understand how the results are calculated
int halfDollar = remainingAmount / 50;
remainingAmount = remainingAmount % 50;
int numberOfQuarters = remainingAmount / 25;
remainingAmount = remainingAmount % 25;
ETC.....
import java.util.Scanner;
public class Program3
{
public static void main(String [] args)
{
Scanner kbd = new Scanner(System.in);
System.out.print("Please enter the total dollar amount in the piggy bank: $");
double amount = kbd.nextDouble();
int remainingAmount = (int)(amount * 100);
int halfDollar = remainingAmount / 50;
remainingAmount = remainingAmount % 50;
int numberOfQuarters = remainingAmount / 25;
remainingAmount = remainingAmount % 25;
int numberOfDimes = remainingAmount / 10;
remainingAmount = remainingAmount % 10;
int numberOfNickels = remainingAmount / 5;
remainingAmount = remainingAmount % 5;
int numberOfPennies = remainingAmount;
System.out.println(String.format("In $" + "%.2f", amount) + " worth of pennies there are:");
System.out.println(halfDollar + " half dollar(s), " + numberOfQuarters + " quarter(s), " + numberOfDimes + " dime(s), " + numberOfNickels + " nickle(s), and " + numberOfPennies + " cent(s).");
}
}
It's simple, you multiple the number of dollars by 100 and you get the number of cents, then you calculate how many nickels, dimes etc that would be.
For example, $5.26 is 526 cents, which is 10 half dollars ($5), 1 quarter, 1 penny.
Integer division gives you the number of times X is contained in Y, and modulus (%) gives you the remainder.
526 / 50 = 10
526 % 50 = 26
26 / 25 = 1
26 % 25 = 1
1 / 10 = 0
1 % 10 = 1
1 / 5 = 0
1 % 5 = 1
1 / 1 = 1
1 % 1 = 0
Obviously, what that does is break the amount of money in the least number of coins by giving you as many coins of the highest denomination first, then the highest number of coins of the next denomination etc.
For avoiding fractions you multiply value with 100. Making calculations with fractions is a little bit difficult.
For example instead of making calculations with $1.25 programmers prefer to make calculations 125. It makes to easy understanding.
If you divide(/) X to Y you find the number of Y that X contains.
If you take mod(%) X of Y you find the remainder of X divided by Y
Think that $1.43 entered.
1.43 * 100 = 143
143 / 50 = 2 -> Half dollar
143 % 50 = 43 -> remainder of division
43 / 25 = 1 -> Quarter
43 % 25 = 18 -> remainder of division
18 / 10 = 1 -> Dimes
18 % 10 = 8 -> remainder of division
8 / 5 = 1 -> Nickels
8 % 5 = 3 -> remainder of division
There is no more division last remainder is pennies and it is 3
The / operator when applied to ints provides integer division. That is: division where the fractional part is thrown away.
For example: 10 / 3 gives 3.
Since:
10 divided by 3 is 3.3333333 recurring.
Throwing away the fractional part (0.3333333 recurring) gives the result 3.
The % operator provides modulus or the remainder of integer division. That is: the numerator minus the greatest multiple of the denominator that is less than the numerator.
For example: 10 % 3 gives 1.
Since:
the numerator is 10
the denominator is 3
The result of the integer division 10 / 3 is 3 (as we worked out above)
The greatest multiple of the denominator (3) that is less than the numerator (10) is 3, since 3 * 3 is 9 and no multiple of 3 is greater than 9 but less than 10.
Subtracting that (9) from the numerator (10) you get 10 - 9 which is the result 1.
An easier way to understand this is that integer / is division of whole things that can't be split. So you might want to divide 10 marbles (which you don't want to split into pieces) evenly between 3 people. Then each person gets 3 marbles, but there is 1 marble left over.
Note: that the greatest multiple of the denominator is exactly the result of the integer division (3 in this case, as in 10 / 3 is 3)
Note: You could also work this out by multiplying the fractional part by the result of the integer division (which we worked out was 10 / 3 =3). Giving 0.33333... * 3 which is the result 1.
We can divide a number by subtraction and stop at the remainder as shown here.
But how do we continue to divide the remainder by subtraction ? I looked on google and could not find such answers. They don't go beyond the remainder.
For example, lets say we have
7/3.
7-3 = 4
4-3 = 1
So, we have 2 & (1/3). How do we do the 1/3
division using only subtraction or addition ?
REPEAT -
Please note that I dont want to use multiplication or division operators to do this.
You can get additional "digits", up to any arbitrary precision (in any base you desire, I'll use base 10 for simplicity but if you're trying to implement an algorithm you'll probably choose base 2)
1) Perform division as you've illustrated, giving you a quotient (Q=2), a divisor (D=3), and a remainder (R=1)
2) If R=0, you're done
3) Multiply R by your base (10, R now =10)
4) Perform division by subtraction again to find R/D (10/3 = 3+1/3).
5) Divide the resulting quotient by your base (3/10 = 0.3) and add this to what you got from step 1 (now your result is 2.3)
6) Repeat from step 2, dividing the new remainder (1) by 10 again
While it sounds an awful lot like I just said division quite a few times, we're dividing by your base. I used 10 for simplicity, but you'd really use base 2, so step 3 is really a left shift (by 1 bit every time) and step 5 is really a right shift (by 1 bit the first time through, 2 bits the second, and so on).
7/3.
7-3 = 4
4-3 = 1
7/3 = 2 R 1
1*10 = 10
10-3 = 7
7-3 = 4
4-3 = 1
10/3 = 3 R 1
7/3 = 2 + 3/10 R 1
7/3 = 2.3 R 1
1*10 = 10
10-3 = 7
7-3 = 4
4-3 = 1
10/3 = 3 R 1
7/3 = 2.3 + 3/100 R 1
7/3 = 2.33 R 1
And so on until you reach any arbitrary precision.
If you want to keep going to get decimal digits, multiply the remainder by a power of 10.
E.g. if you want 2.333, then you can multiply remainder by 1000, and then repeat the algorithm.
It depends on what you are asking.
If you are asking how to get the end fraction and simply it, let's take a different example.
26 / 6.
26 - 6 = 20 count 1
20 - 6 = 14 count 2
14 - 6 = 8 count 3
8 - 6 = 2 count 4
(In code, this would be accomplished with a for loop)
Afterwards, we would have 4 2/6. To simplify, switch the dividend and divisor:
6 / 2.
6 - 2 = 4 count 1
4 - 2 = 2 count 2
2 - 2 = 0 count 3
If this finishes without a remainder, show as 1 over the count.
In pseudo-code:
int a = 26;
int b = 6;
int tempb = 6;
int left = 26;
int count = 0;
int count2 = 0;
left = a - b;
for(count; left > b; count++){
left -= b;
}
if(left > 0){
for(count2; tempb > left; count2++){
tempb -= left;
}
console.log("The answer is " + count + " and 1/" + count2);
I hope this answers your question!
Here is a complete program that uses only + and -, translate to your language of choice:
module Q where
infixl 14 `÷` `×`
a × 0 = 0
a × 1 = a
a × n = a + a×(n-1)
data Fraction = F Int [Int]
a ÷ 0 = error "division by zero"
a ÷ 1 = F a []
0 ÷ n = F 0 []
a ÷ n
| a >= n = case (a-n) ÷ n of
F r xs -> F (r+1) xs
| otherwise = F 0 (decimals a n)
where
decimals a n = case (a × 10) ÷ n of
F d rest = (d:rest)
instance Show Fraction where
show (F n []) = show n
show (F n xs) = show n ++ "." ++ concatMap show (take 10 xs)
main _ = println (100 ÷ 3)
It is easy to extend this in such a way that the periodic part of the fraction is detected, if any. For this, the decimals should be tuples, where not only the fractional digit itself but also the dividend that gave rise to it is kept.
The printing function could then be adjusted to print infinite fractions like 5.1(43), where 43 would be the periodic part.
I have the following variable decelrations, assignments and variable declerations
variable e is an expression statement which should return the value of the evaulated variables in the expression;
What is the order of precdence of the opperators in the e variable?
Computed it equals = 60;
With a calculator I get 422;
int a, b, c, d;
a = 10;
b = 2;
c = 1;
d = 20;
e = a + b * d / c + a + b / d;
e = 10 + 2 * 20 / 1 + 10 + 2 / 20;
e = 60;
Actually the answer is 60.1 but since variables are int its showing 60. It is happening as below
10 + (2 * (20 / 1)) + 10 + (int)(2 / 20) = 10 + (2 * 20) + 10 + (int)0.1
= 10 + 40 + 10 + 0 = 60
Here is a link outlining operator precedence. As for your result, this can also be attributed to integer division (which takes the floor of the result; for instance, 2/20 = 0).
Just like in school, multiplication and division have priority over addition. So you have:
10 + 2 * 20 / 1 + 10 + 2 / 20 = 10 + 40 + 10 + 0 = 60
* takes first precedence so first, 2*20 =40, 10 + 40 / 1 + 10 + 2 / 20;
/ takes precedence so , 10 + 40 + 10 + 0;
+ takes precedence so, 60
Here is link for operator precedence: Operator precedence