The project Euler problem 5 is stated as : "2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?"
Here's the c++ code for the function I'm using.
long long unsigned int rangeLCM(int n)
{
long long unsigned int ans=1;
for(int i=1;i<=n;i++)
{
if(ans%i!=0)
{
if(i%(ans%i)==0)ans*=(i/(ans%i));
else ans*=i;
}
}
return ans;
}
The code works well for the example stated in the problem and the problem itself{rangeLCM(10)=2520 and rangeLCM(20)=232792560}, but I think it's not perfect and is missing out on some edge cases.
Instead of actually calculating the LCM(ans,i), I have checked that the bigger of the two(always ans) is divisible by i. If not, then ans is multiplied by a number equal to i/(ans%i) or i depending on whether i is divisible by (ans%i) or not.
This is based on the following facts:
LCM(8,12)=24=12*(8/(12%8));
LCM(9,30)=90=30*(9/(30%9)
LCM(7,13)=91=13*7
However, it fails for the following types of cases:LCM(8,14)=56 != 8*14
Yet, the code for rangeLCM gives the right output for all inputs I have tried yet. Why?
Your logic does not work
if(i%(ans%i)==0)ans*=(i/(ans%i));
else ans*=i;
For example, if ans = 10 and i = 14, so, the lcm should be 70, but in your code, it is 140.
The reason is, between ans and i , there are common divisors, but your code cannot detect that.
For experiment, I have written a small piece of code to check using Java.
class Solution {
public static void main(String[] args) {
long ans = 1;
for (long i = 1; i <= 40; i++) {
if (ans % i != 0) {
long before = (ans*i/gcd(ans,i));
if (i % (ans % i) == 0){
ans *= (i / (ans % i));
}else{
ans *= i;
}
System.out.println(ans + " " + before + " " + i);
}
}
}
public static long gcd(long a, long b) {
if (b == 0) {
return a;
}
return gcd(b, a % b);
}
}
Output
2 2 2
6 6 3
12 12 4
60 60 5
420 420 7
840 840 8
2520 2520 9
27720 27720 11
360360 360360 13
720720 720720 16
12252240 12252240 17
232792560 232792560 19
5354228880 5354228880 23
26771144400 26771144400 25
722820898800 80313433200 27
20961806065200 20961806065200 29
649815988021200 649815988021200 31
1299631976042400 1299631976042400 32
48086383113568800 48086383113568800 37
When i = 27, there is different between the correct answer and ans
The formula for lcm(a,b) is
lcm(a,b) = a*b/gcd(a,b)
With gcd is Greatest common divisor between two number a and b
I think you are missing a lot of cases you have to implement the Euclidean algorithm at
if(i%(ans%i)==0)ans*=(i/(ans%i));
I have a few loops that I need in my program. I can write out the pseudo code, but I'm not entirely sure how to write them logically.
I need -
if (num is a multiple of 10) { do this }
if (num is within 11-20, 31-40, 51-60, 71-80, 91-100) { do this }
else { do this } //this part is for 1-10, 21-30, 41-50, 61-70, 81-90
This is for a snakes and ladders board game, if it makes any more sense for my question.
I imagine the first if statement I'll need to use modulus. Would if (num == 100%10) be correct?
The second one I have no idea. I can write it out like if (num > 10 && num is < 21 || etc.), but there has to be something smarter than that.
For the first one, to check if a number is a multiple of use:
if (num % 10 == 0) // It's divisible by 10
For the second one:
if(((num - 1) / 10) % 2 == 1 && num <= 100)
But that's rather dense, and you might be better off just listing the options explicitly.
Now that you've given a better idea of what you are doing, I'd write the second one as:
int getRow(int num) {
return (num - 1) / 10;
}
if (getRow(num) % 2 == 0) {
}
It's the same logic, but by using the function we get a clearer idea of what it means.
if (num is a multiple of 10) { do this }
if (num % 10 == 0) {
// Do something
}
if (num is within 11-20, 31-40, 51-60, 71-80, 91-100) { do this }
The trick here is to look for some sort of commonality among the ranges. Of course, you can always use the "brute force" method:
if ((num > 10 && num <= 20) ||
(num > 30 && num <= 40) ||
(num > 50 && num <= 60) ||
(num > 70 && num <= 80) ||
(num > 90 && num <= 100)) {
// Do something
}
But you might notice that, if you subtract 1 from num, you'll have the ranges:
10-19, 30-39, 50-59, 70-79, 90-99
In other words, all two-digit numbers whose first digit is odd. Next, you need to come up with a formula that expresses this. You can get the first digit by dividing by 10, and you can test that it's odd by checking for a remainder of 1 when you divide by 2. Putting that all together:
if ((num > 0) && (num <= 100) && (((num - 1) / 10) % 2 == 1)) {
// Do something
}
Given the trade-off between longer but maintainable code and shorter "clever" code, I'd pick longer and clearer every time. At the very least, if you try to be clever, please, please include a comment that explains exactly what you're trying to accomplish.
It helps to assume the next developer to work on the code is armed and knows where you live. :-)
If you are using GCC or any compiler that supports case ranges you can do this, but your code will not be portable.
switch(num)
{
case 11 ... 20:
case 31 ... 40:
case 51 ... 60:
case 71 ... 80:
case 91 ... 100:
// Do something
break;
default:
// Do something else
break;
}
This is for future visitors more so than a beginner. For a more general, algorithm-like solution, you can take a list of starting and ending values and check if a passed value is within one of them:
template<typename It, typename Elem>
bool in_any_interval(It first, It last, const Elem &val) {
return std::any_of(first, last, [&val](const auto &p) {
return p.first <= val && val <= p.second;
});
}
For simplicity, I used a polymorphic lambda (C++14) instead of an explicit pair argument. This should also probably stick to using < and == to be consistent with the standard algorithms, but it works like this as long as Elem has <= defined for it. Anyway, it can be used like this:
std::pair<int, int> intervals[]{
{11, 20}, {31, 40}, {51, 60}, {71, 80}, {91, 100}
};
const int num = 15;
std::cout << in_any_interval(std::begin(intervals), std::end(intervals), num);
There's a live example here.
The first one is easy. You just need to apply the modulo operator to your num value:
if ( ( num % 10 ) == 0)
Since C++ is evaluating every number that is not 0 as true, you could also write:
if ( ! ( num % 10 ) ) // Does not have a residue when divided by 10
For the second one, I think this is cleaner to understand:
The pattern repeats every 20, so you can calculate modulo 20.
All elements you want will be in a row except the ones that are dividable by 20.
To get those too, just use num-1 or better num+19 to avoid dealing with negative numbers.
if ( ( ( num + 19 ) % 20 ) > 9 )
This is assuming the pattern repeats forever, so for 111-120 it would apply again, and so on. Otherwise you need to limit the numbers to 100:
if ( ( ( ( num + 19 ) % 20 ) > 9 ) && ( num <= 100 ) )
With a couple of good comments in the code, it can be written quite concisely and readably.
// Check if it's a multiple of 10
if (num % 10 == 0) { ... }
// Check for whether tens digit is zero or even (1-10, 21-30, ...)
if ((num / 10) % 2 == 0) { ... }
else { ... }
You basically explained the answer yourself, but here's the code just in case.
if((x % 10) == 0) {
// Do this
}
if((x > 10 && x < 21) || (x > 30 && x < 41) || (x > 50 && x < 61) || (x > 70 && x < 81) || (x > 90 && x < 101)) {
// Do this
}
You might be overthinking this.
if (x % 10)
{
.. code for 1..9 ..
} else
{
.. code for 0, 10, 20 etc.
}
The first line if (x % 10) works because (a) a value that is a multiple of 10 calculates as '0', other numbers result in their remainer, (b) a value of 0 in an if is considered false, any other value is true.
Edit:
To toggle back-and-forth in twenties, use the same trick. This time, the pivotal number is 10:
if (((x-1)/10) & 1)
{
.. code for 10, 30, ..
} else
{
.. code for 20, 40, etc.
}
x/10 returns any number from 0 to 9 as 0, 10 to 19 as 1 and so on. Testing on even or odd -- the & 1 -- tells you if it's even or odd. Since your ranges are actually "11 to 20", subtract 1 before testing.
A plea for readability
While you already have some good answers, I would like to recommend a programming technique that will make your code more readable for some future reader - that can be you in six months, a colleague asked to perform a code review, your successor, ...
This is to wrap any "clever" statements into a function that shows exactly (with its name) what it is doing. While there is a miniscule impact on performance (from "function calling overhead") this is truly negligible in a game situation like this.
Along the way you can sanitize your inputs - for example, test for "illegal" values. Thus you might end up with code like this - see how much more readable it is? The "helper functions" can be hidden away somewhere (the don't need to be in the main module: it is clear from their name what they do):
#include <stdio.h>
enum {NO, YES, WINNER};
enum {OUT_OF_RANGE=-1, ODD, EVEN};
int notInRange(int square) {
return(square < 1 || square > 100)?YES:NO;
}
int isEndOfRow(int square) {
if (notInRange(square)) return OUT_OF_RANGE;
if (square == 100) return WINNER; // I am making this up...
return (square % 10 == 0)? YES:NO;
}
int rowType(unsigned int square) {
// return 1 if square is in odd row (going to the right)
// and 0 if square is in even row (going to the left)
if (notInRange(square)) return OUT_OF_RANGE; // trap this error
int rowNum = (square - 1) / 10;
return (rowNum % 2 == 0) ? ODD:EVEN; // return 0 (ODD) for 1-10, 21-30 etc.
// and 1 (EVEN) for 11-20, 31-40, ...
}
int main(void) {
int a = 12;
int rt;
rt = rowType(a); // this replaces your obscure if statement
// and here is how you handle the possible return values:
switch(rt) {
case ODD:
printf("It is an odd row\n");
break;
case EVEN:
printf("It is an even row\n");
break;
case OUT_OF_RANGE:
printf("It is out of range\n");
break;
default:
printf("Unexpected return value from rowType!\n");
}
if(isEndOfRow(10)==YES) printf("10 is at the end of a row\n");
if(isEndOfRow(100)==WINNER) printf("We have a winner!\n");
}
For the first one:
if (x % 10 == 0)
will apply to:
10, 20, 30, .. 100 .. 1000 ...
For the second one:
if (((x-1) / 10) % 2 == 1)
will apply for:
11-20, 31-40, 51-60, ..
We basically first do x-1 to get:
10-19, 30-39, 50-59, ..
Then we divide them by 10 to get:
1, 3, 5, ..
So we check if this result is odd.
As others have pointed out, making the conditions more concise won't speed up the compilation or the execution, and it doesn't necessarily help with readability either.
It can help in making your program more flexible, in case you decide later that you want a toddler's version of the game on a 6 x 6 board, or an advanced version (that you can play all night long) on a 40 x 50 board.
So I would code it as follows:
// What is the size of the game board?
#define ROWS 10
#define COLUMNS 10
// The numbers of the squares go from 1 (bottom-left) to (ROWS * COLUMNS)
// (top-left if ROWS is even, or top-right if ROWS is odd)
#define firstSquare 1
#define lastSquare (ROWS * COLUMNS)
// We haven't started until we roll the die and move onto the first square,
// so there is an imaginary 'square zero'
#define notStarted(num) (num == 0)
// and we only win when we land exactly on the last square
#define finished(num) (num == lastSquare)
#define overShot(num) (num > lastSquare)
// We will number our rows from 1 to ROWS, and our columns from 1 to COLUMNS
// (apologies to C fanatics who believe the world should be zero-based, which would
// have simplified these expressions)
#define getRow(num) (((num - 1) / COLUMNS) + 1)
#define getCol(num) (((num - 1) % COLUMNS) + 1)
// What direction are we moving in?
// On rows 1, 3, 5, etc. we go from left to right
#define isLeftToRightRow(num) ((getRow(num) % 2) == 1)
// On rows 2, 4, 6, etc. we go from right to left
#define isRightToLeftRow(num) ((getRow(num) % 2) == 0)
// Are we on the last square in the row?
#define isLastInRow(num) (getCol(num) == COLUMNS)
// And finally we can get onto the code
if (notStarted(mySquare))
{
// Some code for when we haven't got our piece on the board yet
}
else
{
if (isLastInRow(mySquare))
{
// Some code for when we're on the last square in a row
}
if (isRightToLeftRow(mySquare))
{
// Some code for when we're travelling from right to left
}
else
{
// Some code for when we're travelling from left to right
}
}
Yes, it's verbose, but it makes it clear exactly what's happening on the game board.
If I was developing this game to display on a phone or tablet, I'd make ROWS and COLUMNS variables instead of constants, so they can be set dynamically (at the start of a game) to match the screen size and orientation.
I'd also allow the screen orientation to be changed at any time, mid-game - all you need to do is switch the values of ROWS and COLUMNS, while leaving everything else (the current square number that each player is on, and the start/end squares of all the snakes and ladders) unchanged.
Then you 'just' have to draw the board nicely, and write code for your animations (I assume that was the purpose of your if statements) ...
You can try the following:
// Multiple of 10
if ((num % 10) == 0)
{
// Do something
}
else if (((num / 10) % 2) != 0)
{
// 11-20, 31-40, 51-60, 71-80, 91-100
}
else
{
// Other case
}
I know that this question has so many answers, but I will thrown mine here anyway...
Taken from Steve McConnell's Code Complete, 2nd Edition:
"Stair-Step Access Tables:
Yet another kind of table access is the stair-step method. This access method isn’t as direct as an index structure, but it doesn’t waste as much data space. The general idea of stair-step structures, illustrated in Figure 18-5, is that entries in a table are valid for ranges of data rather than for distinct data points.
Figure 18-5 The stair-step approach categorizes each entry by determining the level at which it hits a “staircase.” The “step” it hits determines its category.
For example, if you’re writing a grading program, the “B” entry range might be from 75 percent to 90 percent. Here’s a range of grades you might have to program someday:
To use the stair-step method, you put the upper end of each range into a table and then write a loop to check a score against the upper end of each range. When you find the point at which the score first exceeds the top of a range, you know what the grade is. With the stair-step technique, you have to be careful to handle the endpoints of the ranges properly. Here’s the code in Visual Basic that assigns grades to a group of students based on this example:
Although this is a simple example, you can easily generalize it to handle multiple students, multiple grading schemes (for example, different grades for different point levels on different assignments), and changes in the grading scheme."
Code Complete, 2nd Edition, pages 426 - 428 (Chapter 18).
The keypad is broken so the input numbers 1, 4, and 7 aren't working. In turn the computer outputs the next lowest and next highest number where 1, 4, and 7 are none of the digits.
My goal is to check out the digits and output true using a boolean function and then output the next highest number and next lowest number. I'm pretty sure I did most of what I need to do, but it isn't working out.
I have inputted the number 444, and the results that came out were 443, and 445.
Thank you for your help.
#include <iostream>
#include <conio.h>
#include <cmath>
using namespace std;
bool containDigit(int number, int digit);
int main()
{
int number, digit, lowNum, highNum;
cout<<"Enter a number between 1 and 999 for the oven temperature: ";
cin>>number;
//1st digit
digit = number / 100;
containDigit(number, digit);
if (containDigit(number, digit) == true)
{
number = number - 100;
}
//2nd digit
digit = (number / 10) % 10;
containDigit(number, digit);
if (containDigit(number, digit) == true)
{
number = number - 10;
}
//3rd Digit
digit = number % 10;
containDigit(number, digit);
if (containDigit(number, digit) == true)
{
number = number - 1;
}
cout<<number<<endl;
getche();
return 0;
}
bool containDigit(int number, int digit)
{
if ((digit == 1) || (digit == 4) || (digit == 7))
{
return true;
}
else
{
return 0;
}
}
The bug is in containDigit function. Try this:
bool containDigit(int number, int digit) {
if(digit == 1 || digit == 4 || digit == 7) return true;
return false;
}
You must use == instead of =.
Also you actually don't need number argument there.
Also there can be done several optimizations. Please look at it yourself (it's your homework) and think about repeated code.
Since this looks like homework, I will refrain from doing it for you and give you these hints:
It looks like you're not really clear on what "1st digit" is. Is it the first one from the left (hundreds) or the right (ones)? Look at your code and tell yourself how each portion of it would answer my question.
Is it ever possible for lowNum or highNum to have more than one digit different than number with your code as it is? How? Where are lowNum and highNum changed, and how?
Also, to expand on what #Al Kepp has said: When you have a function like that, try to test it with some very simple inputs rather than straight out assuming it works. This is called (or is similar to) "unit testing", which dictates that you divide your program into simple, independent units and test them separately. A simple call like containDigit(999, 4) returning true would've rang warning bells.
And speaking of warnings, always, always compile with as many of them as you can stand. (e.g. -Wall for gcc) Doing such might've warned you of the fact that you're not using the parameter number inside containDigit at all.
Your function containDigit has two problems:
It shouldn't need to receive the variable "number" as it doesn't use it
You want to compare with == not =
I need to check the divisibility of a number in c. How can I use the modulus operatpr in C to check if a number is divisible by another number? I tried doing this:
if (file_int % 3) {
printf("Hoppity \n");
}
It didn't work, although file_int is equal to 9.
What did I do wrong?
Thanks
It didn't work because the operation will return 0 which will be treated as false.
You actually need:
if(!(file_int % 3)) {
printf("Hoppity \n");
}
if (file_int % 3) is the same as if (file_int % 3 != 0), which is the opposite of what you want.
if (file_int % 3 == 0) {
printf("Hoppity \n");
}
// or
if (!(file_int % 3)) {
printf("Hoppity \n");
}
If the result of the modulus is 0, it is evenly divisible. It would appear you are looking for it to be not divisible by 3 to continue the loop, though your code snippet is not sufficient to confidently assume your intent.
because if it is divisible by 3 file_int % 3 will be equal to 0, and the if block won't execute.
Try
if(file_int % 3 == 0) {
// do stuff
}
The mod operator returns the remainder resulting from the division... since 9 is divisible by three with no remainder, the return would be zero.
However, conditional statements evaluates to true if non-zero, false if zero. You need to change it to (file_int % 3 == 0).