Problem I
Sine Wave
Let us attempt to draw a sine wave using whitespace and the X character. Sine waves are usually drawn horizontally, but standard program output is ordered from top to bottom. We will therefore draw our wave vertically.
Our program shall accept two arguments:
-
$N$, which controls how many waves should be drawn
-
$L$, which controls how many lines are used to print the waves
Most programming languages have a built in function to compute the sine of a value. For example, Python has a built in math.sin function that we could leverage. Alas, the sine function takes radians, distance travelled along the perimeter of a unit circle, as input. How will we figure out the value to input for each line?
A circle is $2 \pi $ radians. Since we wish to draw $N$ waves, the total distance in radians is given by $2 \pi N$. Therefore, the distance travelled from one line to the next will be $\frac{2 \pi N}{L}$. We can then see that for the $i$th line, where $0 \leq i < L$, the distance travelled in radians up to that line is $r_i = i \cdot \frac{2 \pi N}{L}$.
We are not done yet, as $\sin (x)$ will return a real number between $-1.0$ and $1.0$, inclusive. We cannot print a negative number of Xs, and to make sure the wave is clearly visible, we still need an appropriate number of Xs. Let us use $40$ for the full width, or peak-to-peak amplitude, of the waves. In other words, an amplitude of $20$, also called semi-amplitude. Then we need to linearly transform the return value of the sine function to a real number between $0$ and $40$, and round that number to figure out how many X characters to print. See the table below for examples.
|
Sine value |
Number of X characters to print |
|
$-1.0$ |
$0$ |
|
$0.0$ |
$20$ |
|
$1.0$ |
$40$ |
|
$0.8414709848078$ |
$37$ |
Input
Input consists of two lines. The first line contains the integer $N$, the number of waves to draw, where $1 \leq N \leq 10$. The second line contains the integer $L$, the number of lines used to draw the waves, where $1 \leq L \leq 1\, 000$.
Output
Draw the sine wave as described above. Exactly one newline character (\n) should immediately follow the last X on each line. If your program outputs additional whitespace, it will be considered incorrect.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 20 |
XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXX XXXX X X XXXX XXXXXXXX XXXXXXXXXXXXXX |
| Sample Input 2 | Sample Output 2 |
|---|---|
2 12 |
XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXX XXX XXX XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXX XXX XXX |
| Sample Input 3 | Sample Output 3 |
|---|---|
1 40 |
XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXXXXX XXXXXXXX XXXXXX XXXX XX X X XX XXXX XXXXXX XXXXXXXX XXXXXXXXXXX XXXXXXXXXXXXXX XXXXXXXXXXXXXXXXX |
