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authorSyndamia <kamen.d.mladenov@protonmail.com>2021-09-15 15:53:59 +0300
committerSyndamia <kamen.d.mladenov@protonmail.com>2021-09-15 15:53:59 +0300
commit4b88d354f628182beeb25ad76f57e8a616ff30c1 (patch)
treef9419e4c72ecd2ffbf41c743031bc7e9cc4e2840 /C++
parent65c04eaad8fbcce98c3c11054ee52b5277c82402 (diff)
downloadalgorithms-4b88d354f628182beeb25ad76f57e8a616ff30c1.tar
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Renamed C++ folder to accomodate C files
Diffstat (limited to 'C++')
-rw-r--r--C++/FindSpiralNumber.cpp179
-rw-r--r--C++/FindSpiralNumberCoord.cpp147
-rw-r--r--C++/LeibnizPI.cpp26
-rw-r--r--C++/QuadraticEquationGrapher.cpp63
4 files changed, 0 insertions, 415 deletions
diff --git a/C++/FindSpiralNumber.cpp b/C++/FindSpiralNumber.cpp
deleted file mode 100644
index 78e1681..0000000
--- a/C++/FindSpiralNumber.cpp
+++ /dev/null
@@ -1,179 +0,0 @@
-#include <iostream>
-
-using namespace std;
-
-int main()
-{
- int x, y;
- cout << "x = ";
- cin >> x;
- cout << "y = ";
- cin >> y;
-
- int n, v = max(abs(x), abs(y)), g = 8 * (v * (v + 1) / 2);
-
- if (y == v || x == v) { // Top row or right column
- n = g - x + y - 6 * v;
- }
- else { // Left column or bottom row
- n = g + x - y - 2 * v;
- }
-
- printf("n = %d", n);
-
- return 0;
-}
-
-/* --------------
- * Task condition
- * --------------
- * You have a spiral of whole numbers, starting from 0, like this:
- *
- * 36 < 35 < 34 < 33 < 32 < 31 < 30
- * V ^
- * 37 16 < 15 < 14 < 13 < 12 29
- * V V ^ ^
- * 38 17 4 < 3 < 2 11 28
- * V V V ^ ^ ^
- * 39 18 5 0 > 1 10 27 ...
- * V V V ^ ^ ^
- * 40 19 6 > 7 > 8 > 9 26 51
- * V V ^ ^
- * 41 20 > 21 > 22 > 23 > 24 > 25 50
- * V ^
- * 42 > 43 > 44 > 45 > 46 > 47 > 48 > 49
- *
- * The distance between two neighbouring numbers is 1, meaning 0 is at (0;0), 1 is at (1;0), 38 is at (-3;1).
- * You are given the coordinates of a number and you have to find the actual number.
- *
- * --------------------------
- * Explanation of my solution
- * --------------------------
- *
- * My solution is a very mathematical one. First, I divide the spiral into squares,
- * depending on the offset of 0;0.
- * Example:
- * - Square 1 (because x and y are between -1 and 1 (one of them is always 1 or -1)):
- * 4 < 3 < 2
- * V ^
- * 5 1
- * V
- * 6 > 7 > 8
- *
- * - Square 2 (because x and y are between -2 and 2 (one of them is always 2 or -2)):
- * 16 < 15 < 14 < 13 < 12
- * V ^
- * 17 11
- * V ^
- * 18 10
- * V ^
- * 19 9
- * V
- * 20 > 21 > 22 > 23 > 24
- *
- * - Square 3 (because x and y are between -3 and 3 (one of them is always 3 or -3)):
- * 36 < 35 < 34 < 33 < 32 < 31 < 30
- * V ^
- * 37 29
- * V ^
- * 38 28
- * V ^
- * 39 27
- * V ^
- * 40 26
- * V ^
- * 41 25
- * V
- * 42 > 43 > 44 > 45 > 46 > 47 > 48
- *
- * And so on. I call the number of the square "v".
- * We can find it by getting the absolute value of both coordinates and get the biggest number.
- *
- * Then there is the biggest number in the square, the one in the bottom right corner, I call that "g".
- * g for square 1 (v = 1) is 8, for v = 2: g = 24, for v = 3: g = 48 and so on.
- * We can see that each g is divisble by 8, but the multiplier is slightly tricky to find.
- * The multiplier is the sum of all whole number from 1 up until v.
- *
- * Example:
- * v = 2
- * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2) = 8 * 3 = 24
- *
- * v = 3
- * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2 + 3) = 8 * 6 = 48
- *
- * Then, we divide the whole square into two corners. We take the diagonal from top left to bottom right, and check in which part the coordinates are.
- * We do that because we have two formulas. In brief, what they do is tranform the coordinates into the number from which we'll subtract from g.
- *
- * Example:
- * v = 3, g = 48
- *
- * Lets take a look at the formula for the bottom of the square. We aren't interested in g, so the important part is "x - y - 2*v".
- * What it does is make the coordinates for x and y correspond to a number from -12 to 0.
- * So this:
- * 36
- * V
- * 37
- * V
- * 38
- * V
- * 39
- * V
- * 40
- * V
- * 41
- * V
- * 42 > 43 > 44 > 45 > 46 > 47 > 48
- * Becomes:
- * -12
- * V
- * -11
- * V
- * -10
- * V
- * -9
- * V
- * -8
- * V
- * -7
- * V
- * -6 > -5 > -4 > -3 > -2 > -1 > 0
- *
- * "- 2 * v" is -6, the number in the bottom left corner. Then, if we increase Y (meaning we want to go up the left column),
- * we want the number to also decrease (make it further away from 0). We also have to account for X, because there it's always -3.
- * So, we need them to sum up to 0 when we're on the bottom left corner, so we can just subtract Y from X. As we said,
- * X is always -3 on the left column, so by increasing Y, we also increase the negative number.
- *
- * Ok, here are some example numbers:
- * X | Y | X - Y
- * ---|----|------
- * -3 | -3 | 0
- * -3 | -2 | -1
- * -3 | 0 | -3
- *
- * This actually works out for us just fine when we're traversing the bottom row. There, Y is always -3, and
- * when increasing X we want to increase our number (make it close to 0). So, X - Y become a positive number,
- * which summed up with the negative number ("-2*v") makes the result number closer to 0, which is what we want.
- *
- * Here are more example numbers:
- * X | Y | X - Y
- * ---|----|------
- * -3 | -3 | 0
- * -2 | -3 | 1
- * 0 | -3 | 3
- *
- * The formula for the top of the square (top row and right column) works the same , but there our corner number isn't "-2*v" but "-6*v",
- * and we want the reverse effect: increase number (make smaller) on increasing X and decerease number on incrasing Y,
- * so we make "X - Y" to be "Y - X"
- *
- * -13 < -14 < -15 < -16 < -17 < -18 < -19
- * ^
- * -20
- * ^
- * -21
- * ^
- * -22
- * ^
- * -23
- * ^
- * -24
- */
diff --git a/C++/FindSpiralNumberCoord.cpp b/C++/FindSpiralNumberCoord.cpp
deleted file mode 100644
index 07b2071..0000000
--- a/C++/FindSpiralNumberCoord.cpp
+++ /dev/null
@@ -1,147 +0,0 @@
-#include <iostream>
-
-using namespace std;
-
-int main()
-{
- int n, v, g, x, y;
- cout << "n = ";
- cin >> n;
-
- while (g < n) {
- v++;
- g = 8 * (v * (v + 1) / 2);
- }
-
- if (n >= g - 2 * v) { // Bottom row
- y = -v;
- x = v - (g - n);
- }
- else if (n >= g - 4 * v) { // Left column
- x = -v;
- y = ((g - 2 * v) - n) - v;
- }
- else if (n >= g - 6 * v) { // Top row
- y = v;
- x = ((g - 4 * v) - n) - v;
- }
- else { // Right column
- x = v;
- y = v - ((g - 6 * v) - n);
- }
-
- printf("(%d;%d)\n", x, y);
-
- return 0;
-}
-
-/* --------------
- * Task condition
- * --------------
- * You have a spiral of whole numbers, starting from 0, like this:
- *
- * 36 < 35 < 34 < 33 < 32 < 31 < 30
- * V ^
- * 37 16 < 15 < 14 < 13 < 12 29
- * V V ^ ^
- * 38 17 4 < 3 < 2 11 28
- * V V V ^ ^ ^
- * 39 18 5 0 > 1 10 27 ...
- * V V V ^ ^ ^
- * 40 19 6 > 7 > 8 > 9 26 51
- * V V ^ ^
- * 41 20 > 21 > 22 > 23 > 24 > 25 50
- * V ^
- * 42 > 43 > 44 > 45 > 46 > 47 > 48 > 49
- *
- * You are given a number n and your goal is to find the coordinates of the number.
- * The distance between two neighbouring numbers is 1, meaning 0 is at (0;0), 1 is at (1;0), 38 is at (-3;1).
- *
- * --------------------------
- * Explanation of my solution
- * --------------------------
- *
- * My solution is a very mathematical one. First, I divide the spiral into squares,
- * depending on the offset of 0;0.
- * Example:
- * - Square 1 (because x and y are between -1 and 1 (one of them is always 1 or -1)):
- * 4 < 3 < 2
- * V ^
- * 5 1
- * V
- * 6 > 7 > 8
- *
- * - Square 2 (because x and y are between -2 and 2 (one of them is always 2 or -2)):
- * 16 < 15 < 14 < 13 < 12
- * V ^
- * 17 11
- * V ^
- * 18 10
- * V ^
- * 19 9
- * V
- * 20 > 21 > 22 > 23 > 24
- *
- * - Square 3 (because x and y are between -3 and 3 (one of them is always 3 or -3)):
- * 36 < 35 < 34 < 33 < 32 < 31 < 30
- * V ^
- * 37 29
- * V ^
- * 38 28
- * V ^
- * 39 27
- * V ^
- * 40 26
- * V ^
- * 41 25
- * V
- * 42 > 43 > 44 > 45 > 46 > 47 > 48
- *
- * And so on. I call the number of the square "v".
- *
- * Then there is the biggest number in the square, the one in the bottom right corner, I call that "g".
- * g for square 1 (v = 1) is 8, for v = 2: g = 24, for v = 3: g = 48 and so on.
- * We can see that each g is divisble by 8, but the multiplier is slightly tricky to find.
- * The multiplier is the sum of all whole number from 1 up until v.
- *
- * Example:
- * v = 2
- * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2) = 8 * 3 = 24
- *
- * v = 3
- * g = 8 * (Sum of numbers from 1 to v) = 8 * (1 + 2 + 3) = 8 * 6 = 48
- *
- * After we've found g and v, we start looking at the numbers in the corners.
- * The bottom right corner is g by definition, the bottom left corner is g - 2 * v,
- * the top left is g - 4 * v and the top right is g - 6 * v.
- * By comparing the values in the corners we can determine where the number is:
- * top row, bottom row, left column or right column.
- *
- * Example:
- * v = 2, g = 24, n = 11
- *
- * if (n > bottom left corner) number is on bottom row (between 20 and 24)
- * else if (n > top left corner) number is on left column (between 16 and 20)
- * else if (n > top right corner) number is on top row (between 16 and 12)
- * else number is on right column (between 12 and 9)
- *
- * After we find on which side the number is, we can immediately determine the x or y coordinate,
- * as it will be +v or -v.
- * The final step is to determine the other coordinate. The formula differs slightly depending on a side,
- * but the gist of it is that we look at the difference between a corner number and our number, which gives
- * us distance from the corner number and we offset the searched coordinate.
- *
- * Example:
- * v = 2, g = 24, n = 11
- * We have determined that our number is in the right column.
- * This means we know for sure that the X coordinate of n is 2.
- *
- * offset = corner number - n = (g - 6 * v) - 11 = 12 - 11 = 1
- *
- * The Y coordinate of the corner number is 2 (12 is located at (2;2)).
- * In our case, we want to subtract our offset from that coordinate, so
- *
- * Y coordinate of n = Y coordinate of corner number - offset = 2 - 1 = 1.
- *
- * And so we found that n is located at (2;1)
- */
diff --git a/C++/LeibnizPI.cpp b/C++/LeibnizPI.cpp
deleted file mode 100644
index 2243f61..0000000
--- a/C++/LeibnizPI.cpp
+++ /dev/null
@@ -1,26 +0,0 @@
-#include <iostream>
-
-using namespace std;
-
-int main()
-{
- cout << "n = ";
- unsigned int n = 1;
- cin >> n;
- long double pid4 = 1;
-
- for(unsigned int i = 0, dvsr = 3; i < n; i++, dvsr += 2) {
- pid4 += ((i % 2) ? 1.0 : -1.0) / dvsr;
- }
-
- cout.precision(64);
- cout << endl << pid4 * 4.0 << endl;
-
- return 0;
-}
-
-/* This is a quick implementation of of the Leibniz formula for PI
- * https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
- *
- * Fun fact: you need around 100 million iterations for 7 correct decimal places
- */
diff --git a/C++/QuadraticEquationGrapher.cpp b/C++/QuadraticEquationGrapher.cpp
deleted file mode 100644
index 7dfbe64..0000000
--- a/C++/QuadraticEquationGrapher.cpp
+++ /dev/null
@@ -1,63 +0,0 @@
-#include <iostream>
-#include <math.h>
-
-using namespace std;
-
-/* Program that graphs a quadratic equation on the standard output */
-
-/* Equation precision - how precise the quadratic equation result should be
- * - higher values are more precise, but they could not show up on the graph
- * - needs to be balanced with step
- * Step - size of each unit (character)
- */
-const int eqPrec = 1;
-const double step = 1;
-
-const char line = '*';
-const char verLine = '|';
-const char horLine = '-';
-const char empty = ' ';
-
-double quadr(double x, double a, double b, double c) {
- return double( round( ( (a*pow(x, 2)) + (b*x) + c) * eqPrec ) / eqPrec);
-}
-
-void printQadr(int startx, int endx, int starty, int endy, double a, double b, double c) {
- double currY, currX;
- for (int y = max(starty, endy); y >= min(starty, endy); y--) {
- for (int x = startx; x <= endx; x++) {
- currY = y * step;
- currX = x * step;
-
- if (quadr(currX, a, b, c) == currY
- || ((quadr(currX, a, b, c) < currY
- || (quadr(currX - step, a, b, c) == 0 || quadr(currX + step, a, b, c) == 0)) // Wide lines
- && (quadr(currX + step, a, b, c) > currY != quadr(currX - step, a, b, c) > currY)) // Long lines
- ) {
- cout << line;
- } else if (x == 0) {
- cout << verLine;
- } else if (y == 0) {
- cout << horLine;
- } else {
- cout << empty;
- }
- }
- cout << endl;
- }
-}
-
-void printQadr(int start, int end, double a, double b, double c) {
- printQadr(start, end, start, end, a, b, c);
-}
-
-int main()
-{
- double a = 0.2;
- double b = 2;
- double c = -10;
-
- printQadr(-25, 15, 20, -15, a, b, c);
-
- return 0;
-}