For a game in Gameboy programming, I am using four arrays called top, oldTop, bottom and oldBottom:
struct Point { int x, y; };
struct Rect { struct Point xx, yy; };
Rect top[size], oldTop[size];
Rect bottom[size], oldBottom[i];
where Rect is a struct made of two Struct Points, the top-left and the bottom right corner points.
The idea of the game is to have random-heighted blocks top-down from the ceiling and bottom-up from the floor.
It is similar to the copter-classic game. In my infinite while loop, I shift all of the rectangles down by one pixel using the following code
while (1)
{
for (int i = 0; i < size; i++)
{
//in Struct Rect, xx is the top-left corner point, and yy is the bottom right
top[i].xx.x--;
top[i].yy.x--;
bottom[i].xx.x--;
bottom[i].yy.x--;
if (top[i].xx.x < 0)
{
top[i].xx.x += 240;
top[i].yy.x += 240;
}
if (bottom[i].xx.x < 0)
{
bottom[i].xx.x += 240;
bottom[i].yy.x += 240;
}
}
for (int i = 0; i < size; i++)
{
drawRect(oldTop[i], colorBlack);
drawRect(oldBottom[i], colorBlack);
}
/*call delay function that wait for Vertical Blank*/
for(int i = 0; i < size; i++)
{
drawRect(top[i], colorGreen);
drawRect(bottom[i], colorGreen);
oldTop[i] = top[i];
oldBottom[i] = bottom[i];
}
}
The drawRect method uses DMA to draw the rectangle.
with this code, the code should display the rectangles like this: (drew this up in paint)
But the result I get is
What is odd is that if I don't draw the bottom row at all, then the top row draws fine. The result only messes up when I draw both. This is really weird because I think that the code should be working fine, and the code is not very complicated. Is there a specific reason this is happening, and is there a way to remedy this?
Thanks.
The code that I use to draw the rectangle looks like this:
void drawRect(int row, int col, int width, int height){
int i;
for (i=0; i<height; i++)
{
DMA[3].src = &color;
DMA[3].dst = videoBuffer + (row+r)*240 + col);
DMA[3].cnt = DMA_ON | DMA_FIXED_SOURCE | width;
}
}
Here's a debugging SSCCE (Short, Self-Contained, Correct Example) based on your code. There are assertions in this code that fire; it runs, but is known not to be correct. I've renamed bottom to btm and oldBottom to oldBtm so that the names are symmetric; it makes the code layout more systematic (but is otherwise immaterial).
#include <assert.h>
#include <stdio.h>
typedef struct Point { int x, y; } Point;
typedef struct Rect { struct Point xx, yy; } Rect;
enum { size = 2 };
typedef enum { colourGreen = 0, colourBlack = 1 } Colour;
/*ARGSUSED*/
static void drawRect(Rect r, Colour c)
{
printf(" (%3d)(%3d)", r.xx.x, r.yy.x);
}
int main(void)
{
Rect top[size], oldTop[size];
Rect btm[size], oldBtm[size];
int counter = 0;
for (int i = 0; i < size; i++)
{
top[i].xx.x = 240 - 4 * i;
top[i].xx.y = 0 + 10 + i;
top[i].yy.x = 240 - 14 * i;
top[i].yy.y = 0 + 20 + i;
btm[i].xx.x = 0 + 72 * i;
btm[i].xx.y = 0 + 10 * i;
btm[i].yy.x = 0 + 12 * i;
btm[i].yy.y = 0 + 20 * i;
oldTop[i] = top[i];
oldBtm[i] = btm[i];
}
while (1)
{
if (counter++ > 480) // Limit amount of output!
break;
for (int i = 0; i < size; i++)
{
//in Struct Rect, xx is the top-left corner point, and yy is the bottom right
top[i].xx.x--;
top[i].yy.x--;
btm[i].xx.x--;
btm[i].yy.x--;
if (top[i].xx.x < 0)
{
top[i].xx.x += 240;
top[i].yy.x += 240;
}
if (btm[i].xx.x < 0)
{
btm[i].xx.x += 240;
btm[i].yy.x += 240;
}
}
for (int i = 0; i < size; i++)
{
assert(top[i].xx.x >= 0 && top[i].yy.x >= 0);
assert(btm[i].xx.x >= 0 && btm[i].yy.x >= 0);
}
for (int i = 0; i < size; i++)
{
drawRect(oldTop[i], colourBlack);
drawRect(oldBtm[i], colourBlack);
}
/*call delay function that wait for Vertical Blank*/
for(int i = 0; i < size; i++)
{
drawRect(top[i], colourGreen);
drawRect(btm[i], colourGreen);
oldTop[i] = top[i];
oldBtm[i] = btm[i];
}
putchar('\n');
}
return(0);
}
As noted in a late comment, one big difference between this and your code is that oldBottom in your code is declared as:
Rect top[size], oldTop[size];
Rect bottom[size], oldBottom[i];
using the size i instead of size. This probably accounts for array overwriting issues you see.
There's a second problem though; the assertions in the loop in the middle fire:
(240)(240) ( 0)( 0) (236)(226) ( 72)( 12) (239)(239) (239)(239) (235)(225) ( 71)( 11)
(239)(239) (239)(239) (235)(225) ( 71)( 11) (238)(238) (238)(238) (234)(224) ( 70)( 10)
(238)(238) (238)(238) (234)(224) ( 70)( 10) (237)(237) (237)(237) (233)(223) ( 69)( 9)
(237)(237) (237)(237) (233)(223) ( 69)( 9) (236)(236) (236)(236) (232)(222) ( 68)( 8)
(236)(236) (236)(236) (232)(222) ( 68)( 8) (235)(235) (235)(235) (231)(221) ( 67)( 7)
(235)(235) (235)(235) (231)(221) ( 67)( 7) (234)(234) (234)(234) (230)(220) ( 66)( 6)
(234)(234) (234)(234) (230)(220) ( 66)( 6) (233)(233) (233)(233) (229)(219) ( 65)( 5)
(233)(233) (233)(233) (229)(219) ( 65)( 5) (232)(232) (232)(232) (228)(218) ( 64)( 4)
(232)(232) (232)(232) (228)(218) ( 64)( 4) (231)(231) (231)(231) (227)(217) ( 63)( 3)
(231)(231) (231)(231) (227)(217) ( 63)( 3) (230)(230) (230)(230) (226)(216) ( 62)( 2)
(230)(230) (230)(230) (226)(216) ( 62)( 2) (229)(229) (229)(229) (225)(215) ( 61)( 1)
(229)(229) (229)(229) (225)(215) ( 61)( 1) (228)(228) (228)(228) (224)(214) ( 60)( 0)
Assertion failed: (btm[i].xx.x >= 0 && btm[i].yy.x >= 0), function main, file video.c, line 63.
I think your 'not negative' checks should be revised to:
if (top[i].xx.x < 0)
top[i].xx.x += 240;
if (top[i].yy.x < 0)
top[i].yy.x += 240;
if (btm[i].xx.x < 0)
btm[i].xx.x += 240;
if (btm[i].yy.x < 0)
btm[i].yy.x += 240;
This stops anything going negative. However, it is perfectly plausible that you should simply be checking on the bottom-right x-coordinate (instead of the top-left coordinate) using the original block. Or the wraparound may need to be more complex altogether. That's for you to decipher. But I think that the odd displays occur because you were providing negative values where you didn't intend to and weren't supposed to.
The key points to note here are:
When you're debugging an algorithm, you don't have to use the normal display mechanisms.
When you're debugging, reduce loop sizes where you can (size == 2).
Printing just the relevant information (here, the x-coordinates) helped reduce the output.
Putting the counter code to limit the amount of output simplifies things.
If things are going wrong, look for patterns in what is going wrong early.
I had various versions of the drawRect() function before I got to the design shown, which works well on a wide screen (eg 120x65) terminal window.
Related
I'm trying to implement the Join Five game. It is a game where, given a grid and a starting configuration of dots, you have to add dots in free crossings, so that each dot that you add forms a 5-dot line with those already in the grid. Two lines may only have 1 dot in common (they may cross or touch end to end)
My game grid is an int array that contains 0 or 1. 1 if there is a dot, 0 if there isn't.
I'm doing kinda well in the implementation, but I'd like to display all the possibles moves.
I made a very long and ugly function that is available here : https://pastebin.com/tw9RdNgi (it was way too long for my post i'm sorry)
here is a code snippet :
if(jeu->plat[i][j] == 0) // if we're on a empty spot
{
for(k = 0; k < lineSize; k++) // for each direction
{
//NORTH
if(jeu->plat[i-1-k][j] == 1) // if there is a dot north
{
n++; // we count it
}
else
{
break; //we change direction
}
} //
This code repeats itself 7 other times changing directions and if n or any other variable reaches 4 we count the x and y as a possible move.
And it's not even treating all the cases, if the available spot is between 2 and 2 dots it will not count it. same for 3 and 1 and 1 and 3.
But I don't think the way I started doing it is the best one. I'm pretty sure there is an easier and more optimized way but i can't figure it out.
So my question is: could somebody help me figure out how to find all the possible 5-dot alignments, or tell me if there is a better way of doing it?
Ok, the problem is more difficult than it appears, and a lot of code is required. Everything would have been simpler if you posted all of the necessary code to run it, that is a Minimal, Complete, and Verifiable Example. Anyway, I resorted to putting together a structure for the problem which allows to test it.
The piece which answers your question is the following one:
typedef struct board {
int side_;
char **dots_;
} board;
void board_set_possible_moves(board *b)
{
/* Directions
012
7 3
654 */
static int dr[8] = { -1,-1,-1, 0, 1, 1, 1, 0 };
static int dc[8] = { -1, 0, 1, 1, 1, 0,-1,-1 };
int side_ = b->side_;
char **dots_ = b->dots_;
for (int r = 0; r < side_; ++r) {
for (int c = 0; c < side_; ++c) {
// The place already has a dot
if (dots_[r][c] == 1)
continue;
// Count up to 4 dots in the 8 directions from current position
int ndots[8] = { 0 };
for (int d = 0; d < 8; ++d) {
for (int i = 1; i <= 4; ++i) {
int nr = r + dr[d] * i;
int nc = c + dc[d] * i;
if (nr < 0 || nc < 0 || nr >= side_ || nc >= side_ || dots_[nr][nc] != 1)
break;
++ndots[d];
}
}
// Decide if the position is a valid one
for (int d = 0; d < 4; ++d) {
if (ndots[d] + ndots[d + 4] >= 4)
dots_[r][c] = 2;
}
}
}
}
Note that I defined a square board with a pointer to pointers to chars, one per place. If there is a 0 in one of the places, then there is no dot and the place is not a valid move; if there is a 1, then there is a dot; if there is a 2, then the place has no dot, but it is a valid move. Valid here means that there are at least 4 dots aligned with the current one.
You can model the directions with a number from 0 to 7 (start from NW, move clockwise). Each direction has an associated movement expressed as dr and dc. Moving in every direction I count how many dots are there (up to 4, and stopping as soon as I find a non dot), and later I can sum opposite directions to obtain the total number of aligned points.
Of course these move are not necessarily valid, because we are missing the definition of lines already drawn and so we cannot check for them.
Here you can find a test for the function.
#include <stdio.h>
#include <stdlib.h>
board *board_init(board *b, int side) {
b->side_ = side;
b->dots_ = malloc(side * sizeof(char*));
b->dots_[0] = calloc(side*side, 1);
for (int r = 1; r < side; ++r) {
b->dots_[r] = b->dots_[r - 1] + side;
}
return b;
}
board *board_free(board *b) {
free(b->dots_[0]);
free(b->dots_);
return b;
}
void board_cross(board *b) {
board_init(b, 18);
for (int i = 0; i < 4; ++i) {
b->dots_[4][7 + i] = 1;
b->dots_[7][4 + i] = 1;
b->dots_[7][10 + i] = 1;
b->dots_[10][4 + i] = 1;
b->dots_[10][10 + i] = 1;
b->dots_[13][7 + i] = 1;
b->dots_[4 + i][7] = 1;
b->dots_[4 + i][10] = 1;
b->dots_[7 + i][4] = 1;
b->dots_[7 + i][13] = 1;
b->dots_[10 + i][7] = 1;
b->dots_[10 + i][10] = 1;
}
}
void board_print(const board *b, FILE *f)
{
int side_ = b->side_;
char **dots_ = b->dots_;
for (int r = 0; r < side_; ++r) {
for (int c = 0; c < side_; ++c) {
static char map[] = " oX";
fprintf(f, "%c%s", map[dots_[r][c]], c == side_ - 1 ? "" : " - ");
}
fprintf(f, "\n");
if (r < side_ - 1) {
for (int c = 0; c < side_; ++c) {
fprintf(f, "|%s", c == side_ - 1 ? "" : " ");
}
fprintf(f, "\n");
}
}
}
int main(void)
{
board b;
board_cross(&b);
board_set_possible_moves(&b);
board_print(&b, stdout);
board_free(&b);
return 0;
}
I have made a (pretty bad) line follower.
Here is a sketch to roughly know the shape of the robot and location of the treads and sensors
[-] 0 0 [-] // 0 = color sensor
[-]------[-] // - = robot body
[-]------[-] // [-] = tank tread
[-] [-]
Here's what it does:
get Red, Green & Blue, make average of sensor 1 readings, do the same for 2
subtract to get value
this value will go through the PID part
steer with calculated steering
repeat (all of this is in a loop)
I use RGB and not reflected intensity (which is what is commonly used), because sometimes I need to detect if there's green color under the sensor (if there is, turn).
The real problem comes with the steering part. Unfortunately, it only accelerates a motor, meaning that in very tight turns we just lose the line.
Optimally, it should compensate a bit with the other motor (maybe going in the other direction?), but I am not sure how to calculate the speed of the motor, nor how to enforce this very strict line following policy.
Here is the code (I am also very grateful for any kind of tips on how to clean up the code! This is my first project in C :D ). I am not asking to read it all (it is pretty long), you could also just look at the steering function, and work your way back to rawFollowLine, this should hopefully shorten the code.
void rawFollowLine(int speed, float Kp, float Ki, float Kd){
_checkInit();
set_sensor_mode(sn_lx_color, "RGB-RAW");
set_sensor_mode(sn_rx_color, "RGB-RAW");
//printAllSensors();
int wasBlackCounter = 0;
int wasBlack = 0;
int lastBlack = 0;
for (int i = 0; i < 2000; i++)
{
if (isTerminating == 1)
{
killMotors(0);
break;
}
int greenCheck = rawGreenCheck(&wasBlack, &wasBlackCounter, &lastBlack);
if (wasBlack == 1){
wasBlackCounter++;
if (wasBlackCounter > 50){
wasBlackCounter = 0;
wasBlack = 0;
}
}
if (greenCheck == 1)
{
// lx is green
killMotors(1);
usleep(400 * 1000);
drive(200, 70);
waitIfMotorIsRunning();
killMotors(1);
pivotTurn(-90);
}
else if (greenCheck == 2)
{
// rx is green
killMotors(1);
usleep(400 * 1000);
drive(200, 70);
waitIfMotorIsRunning();
killMotors(1);
pivotTurn(90);
}
else if (greenCheck == 3)
{
// both rx and lx are green
killMotors(1);
turn(180);
}
else if (greenCheck == 5)
{
if(lastBlack == 2)
{
lastBlack = 0;
drive(100, -200);
//pivotTurn(50);
}
else if (lastBlack == 1)
{
lastBlack = 0;
drive(100, -200);
//pivotTurn(-50);
} else {
pidLineRaw(speed, Kp, Ki, Kd, &lastBlack);
}
}
else
{
pidLineRaw(speed, Kp, Ki, Kd, &lastBlack);
}
}
killMotors(1);
}
int rawGreenCheck(int *wasBlack, int *wasBlackCounter, int *lastBlack)
{
// Some documentation
// return nums:
// 3 = double green
// 2 = right green
// 1 = left green
// 0 = no green
int lx_red;
int lx_green;
int lx_blue;
int rx_red;
int rx_green;
int rx_blue;
get_sensor_value(0, sn_lx_color, &lx_red);
get_sensor_value(0, sn_rx_color, &rx_red);
get_sensor_value(1, sn_lx_color, &lx_green);
get_sensor_value(1, sn_rx_color, &rx_green);
get_sensor_value(2, sn_lx_color, &lx_blue);
get_sensor_value(2, sn_rx_color, &rx_blue);
//printf("rx_red %d\n", rx_red);
rx_red = (rx_red * rx_ratio_r);
rx_green = (rx_green * rx_ratio_g);
rx_blue = (rx_blue * rx_ratio_b);
//printf("rx_red (again) %d\n", rx_red);
if(
lx_red < 55 &&
lx_green > 90 &&
lx_blue < 55 &&
rx_red < 55 &&
rx_green > 90 &&
rx_blue < 55
)
{
// rx and lx see green
if (*wasBlack == 1)
{
// Apparently we crossed an intersection!
printf("Apparently we crossed an intersection!\n");
// We need to go straight.
*wasBlack = 0;
*wasBlackCounter = 0;
return 0;
}
else
{
return 3;
}
}
else if(lx_red < 55 && lx_green > 90 && lx_blue < 55)
{
// lx sees green
return 1;
}
else if(rx_red < 55 && rx_green > 90 && rx_blue < 55)
{
// rx sees green
return 2;
}
else if(rx_red < 50 && rx_green < 50 && rx_blue < 50 && lx_red < 50 && lx_green < 50 && lx_blue < 50)
{
// rx and lx see black
// this is needed if the intersection has the green tiles after the black line
printf("We are on the line? Is this an intersection?\n");
*wasBlack = 1;
return 0;
}
else if(lx_red < 55 && lx_green < 55 && lx_blue < 55)
{
// lx = right sees black
// this is needed if the intersection has the green tiles after the black line
//printf("We are on the line? Is this an intersection?\n");
killMotor(1, motor[R]);
rotateTillBlack(motor[L], sn_rx_color);
//printf("ASS2\n");
return 0;
}
else if(rx_red < 55 && rx_green < 55 && rx_blue < 55)
{
// rx = left sees black
killMotor(1, motor[L]);
rotateTillBlack(motor[R], sn_lx_color);
//printf("ASS1\n");
return 0;
}
//*lx_color_status = 0;
//*rx_color_status = 0;
*lastBlack = 0;
return 0;
}
void pidLineRaw(int speed, float Kp, float Ki, float Kd, int *lastBlack)
{
int red_lx_color;
int red_rx_color;
int green_lx_color;
int green_rx_color;
int blue_lx_color;
int blue_rx_color;
int lx_color;
int rx_color;
int last_error = 0;
int integral = 0;
int derivative = 0;
//float Kp = 0.1;
//float Ki = 0;
//float Kd = 0;
//set_sensor_mode(sn_lx_color, "COL-REFLECT");
//set_sensor_mode(sn_rx_color, "COL-REFLECT");
get_sensor_value(0, sn_lx_color, &red_lx_color);
get_sensor_value(0, sn_rx_color, &red_rx_color);
get_sensor_value(1, sn_lx_color, &green_lx_color);
get_sensor_value(1, sn_rx_color, &green_rx_color);
get_sensor_value(2, sn_lx_color, &blue_lx_color);
get_sensor_value(2, sn_rx_color, &blue_rx_color);
lx_color = (red_lx_color + green_lx_color+ blue_lx_color)/3;
rx_color = ( (red_rx_color*rx_ratio_r) + (green_rx_color*rx_ratio_g) + (blue_rx_color*rx_ratio_b))/3;
if(*lastBlack == 0)
{
int error = lx_color - rx_color;
integral = integral + error;
derivative = error - last_error;
last_error = error;
int steering_val = (error * Kp) + (integral * Ki) + (derivative * Kd);
// printf("error: %d\nsteering: %d\n",error, steering_val);
move_steering(-steering_val, speed, 1, 0);
} else if (*lastBlack == 1)
{
printf("lx_color_status\n");
move_steering(35, speed, 1, 0);
move_steering(-2, speed, 1, 0);
}
else if (*lastBlack == 2)
{
printf("rx_color_status\n");
move_steering(-35, speed, 1, 0);
move_steering(2, speed, 1, 0);
}
else
{
printf("HMMM: %d\n", *lastBlack);
exit(666);
}
}
static void _getSteeringSpeed(int speed, int *lx_speed, int *rx_speed, int steering)
{
if(steering > 100 || steering < -100)
{
printf("Yo wtf steering is %d\n", steering);
}
else
{
int speed_factor = (50 - abs(steering)) / 50;
*lx_speed = speed;
*rx_speed = speed;
if(steering >= 0)
{
*rx_speed = *rx_speed * speed_factor;
}
else
{
*lx_speed = *lx_speed * speed_factor;
}
}
}
Some parts are omitted, yes, they are not required to solve the problem.
I am also extremely sorry as there might be unused variables and such. I am working on refactoring the project, I'll update the post when I'm done.
So, summing everything up, I need to make sure that the steering part properly turns and follows the line. How do I do that? Is the code that I wrote even suitable? I'm guessing the steering itself might need some sort of feedback loop, to check if it's on the line?
I am writing maze generator and at the some point I have to choose random unvisited neighbour of a cell. The first idea was just to enumerate neighbours such as left = 0, top = 1, right = 2, bottom = 3 and use rand() % 4 to generate random number and choose appropriate cell. However, not all cells features 4 neighbours, so that I had to write following code:
Cell* getRandomNeighbour(const Maze* const maze, const Cell* const currentCell) {
int randomNumb = rand() % 4;
int timer = 1;
while(timer > 0) {
if (randomNumb == 0 && currentCell->x < maze->width-1 && maze->map[currentCell->y][currentCell->x+1].isUnvisited)
return &maze->map[currentCell->y][currentCell->x+1];
if (randomNumb == 1 && currentCell->x > 0 && maze->map[currentCell->y][currentCell->x-1].isUnvisited)
return &maze->map[currentCell->y][currentCell->x-1];
if (randomNumb == 2 && currentCell->y < maze->height-1 && maze->map[currentCell->y+1][currentCell->x].isUnvisited)
return &maze->map[currentCell->y+1][currentCell->x];
if (randomNumb == 3 && currentCell->y > 0 && maze->map[currentCell->y-1][currentCell->x].isUnvisited)
return &maze->map[currentCell->y-1][currentCell->x];
timer--;
randomNumb = rand() % 4;
}
if (currentCell->x < maze->width-1 && maze->map[currentCell->y][currentCell->x+1].isUnvisited)
return &maze->map[currentCell->y][currentCell->x+1];
if (currentCell->x > 0 && maze->map[currentCell->y][currentCell->x-1].isUnvisited)
return &maze->map[currentCell->y][currentCell->x-1];
if (currentCell->y < maze->height-1 && maze->map[currentCell->y+1][currentCell->x].isUnvisited)
return &maze->map[currentCell->y+1][currentCell->x];
if (currentCell->y > 0 && maze->map[currentCell->y-1][currentCell->x].isUnvisited)
return &maze->map[currentCell->y-1][currentCell->x];
return NULL;
}
So, if after 10 iterations the right decision isn't chosen, it will be picked by brute force. This approach seems to be good for the reason that varying of variable timer changes the complexity of maze: the less timer is, the more straightforward maze is. Nevertheless, if my only purpose is to generate completely random maze, it takes a lot of execution time and look a little bit ugly. Is there any pattern(in C language) or way of refactoring that could enable me to deal with this situation without long switches and a lot of if-else constructions?
As #pat and #Ivan Gritsenko suggested, you can limit your random choice to the valid cells only, like this:
Cell* getRandomNeighbour(const Maze* const maze, const Cell* const currentCell)
{
Cell *neighbours[4] = {NULL};
int count = 0;
// first select the valid neighbours
if ( currentCell->x < maze->width - 1
&& maze->map[currentCell->y][currentCell->x + 1].isUnvisited ) {
neighbours[count++] = &maze->map[currentCell->y][currentCell->x + 1];
}
if ( currentCell->x > 0
&& maze->map[currentCell->y][currentCell->x - 1].isUnvisited ) {
neighbours[count++] = &maze->map[currentCell->y][currentCell->x - 1];
}
if ( currentCell->y < maze->height - 1
&& maze->map[currentCell->y + 1][currentCell->x].isUnvisited ) {
neighbours[count++] = &maze->map[currentCell->y + 1][currentCell->x];
}
if ( currentCell->y > 0
&& maze->map[currentCell->y - 1][currentCell->x].isUnvisited ) {
neighbours[count++] = &maze->map[currentCell->y - 1][currentCell->x];
}
// then choose one of them (if any)
int chosen = 0;
if ( count > 1 )
{
int divisor = RAND_MAX / count;
do {
chosen = rand() / divisor;
} while (chosen >= count);
}
return neighbours[chosen];
}
The rationale behind the random number generation part (as opposed to the more common rand() % count) is well explained in this answer.
Factoring repeated code, and a more disciplined way of picking the order of directions to try yields this:
// in_maze returns whether x, y is a valid maze coodinate.
int in_maze(const Maze* const maze, int x, int y) {
return 0 <= x && x < maze->width && 0 <= y && y < maze->height;
}
Cell *get_random_neighbour(const Maze* const maze, const Cell* const c) {
int dirs[] = {0, 1, 2, 3};
// Randomly shuffle dirs.
for (int i = 0; i < 4; i++) {
int r = i + rand() % (4 - i);
int t = dirs[i];
dirs[i] = dirs[r];
dirs[r] = t;
}
// Iterate through the shuffled dirs, returning the first one that's valid.
for (int trial=0; trial<4; trial++) {
int dx = (dirs[trial] == 0) - (dirs[trial] == 2);
int dy = (dirs[trial] == 1) - (dirs[trial] == 3);
if (in_maze(maze, c->x + dx, c->y + dy)) {
const Cell * const ret = &maze->map[c->y + dy][c->x + dx];
if (ret->isUnvisited) return ret;
}
}
return NULL;
}
(Disclaimer: untested -- it probably has a few minor issues, for example const correctness).
I have a simple (brute-force) recursive solver algorithm that takes lots of time for bigger values of OpxCnt variable. For small values of OpxCnt, no problem, works like a charm. The algorithm gets very slow as the OpxCnt variable gets bigger. This is to be expected but any optimization or a different algorithm ?
My final goal is that :: I want to read all the True values in the map array by
executing some number of read operations that have the minimum operation
cost. This is not the same as minimum number of read operations.
At function completion, There should be no True value unread.
map array is populated by some external function, any member may be 1 or 0.
For example ::
map[4] = 1;
map[8] = 1;
1 read operation having Adr=4,Cnt=5 has the lowest cost (35)
whereas
2 read operations having Adr=4,Cnt=1 & Adr=8,Cnt=1 costs (27+27=54)
#include <string.h>
typedef unsigned int Ui32;
#define cntof(x) (sizeof(x) / sizeof((x)[0]))
#define ZERO(x) do{memset(&(x), 0, sizeof(x));}while(0)
typedef struct _S_MB_oper{
Ui32 Adr;
Ui32 Cnt;
}S_MB_oper;
typedef struct _S_MB_code{
Ui32 OpxCnt;
S_MB_oper OpxLst[20];
Ui32 OpxPay;
}S_MB_code;
char map[65536] = {0};
static int opx_ListOkey(S_MB_code *px_kod, char *pi_map)
{
int cost = 0;
char map[65536];
memcpy(map, pi_map, sizeof(map));
for(Ui32 o = 0; o < px_kod->OpxCnt; o++)
{
for(Ui32 i = 0; i < px_kod->OpxLst[o].Cnt; i++)
{
Ui32 adr = px_kod->OpxLst[o].Adr + i;
// ...
if(adr < cntof(map)){map[adr] = 0x0;}
}
}
for(Ui32 i = 0; i < cntof(map); i++)
{
if(map[i] > 0x0){return -1;}
}
// calculate COST...
for(Ui32 o = 0; o < px_kod->OpxCnt; o++)
{
cost += 12;
cost += 13;
cost += (2 * px_kod->OpxLst[o].Cnt);
}
px_kod->OpxPay = (Ui32)cost; return cost;
}
static int opx_FindNext(char *map, int pi_idx)
{
int i;
if(pi_idx < 0){pi_idx = 0;}
for(i = pi_idx; i < 65536; i++)
{
if(map[i] > 0x0){return i;}
}
return -1;
}
static int opx_FindZero(char *map, int pi_idx)
{
int i;
if(pi_idx < 0){pi_idx = 0;}
for(i = pi_idx; i < 65536; i++)
{
if(map[i] < 0x1){return i;}
}
return -1;
}
static int opx_Resolver(S_MB_code *po_bst, S_MB_code *px_wrk, char *pi_map, Ui32 *px_idx, int _min, int _max)
{
int pay, kmax, kmin = 1;
if(*px_idx >= px_wrk->OpxCnt)
{
return opx_ListOkey(px_wrk, pi_map);
}
_min = opx_FindNext(pi_map, _min);
// ...
if(_min < 0){return -1;}
kmax = (_max - _min) + 1;
// must be less than 127 !
if(kmax > 127){kmax = 127;}
// is this recursion the last one ?
if(*px_idx >= (px_wrk->OpxCnt - 1))
{
kmin = kmax;
}
else
{
int zero = opx_FindZero(pi_map, _min);
// ...
if(zero > 0)
{
kmin = zero - _min;
// enforce kmax limit !?
if(kmin > kmax){kmin = kmax;}
}
}
for(int _cnt = kmin; _cnt <= kmax; _cnt++)
{
px_wrk->OpxLst[*px_idx].Adr = (Ui32)_min;
px_wrk->OpxLst[*px_idx].Cnt = (Ui32)_cnt;
(*px_idx)++;
pay = opx_Resolver(po_bst, px_wrk, pi_map, px_idx, (_min + _cnt), _max);
(*px_idx)--;
if(pay > 0)
{
if((Ui32)pay < po_bst->OpxPay)
{
memcpy(po_bst, px_wrk, sizeof(*po_bst));
}
}
}
return (int)po_bst->OpxPay;
}
int main()
{
int _max = -1, _cnt = 0;
S_MB_code best = {0};
S_MB_code work = {0};
// SOME TEST DATA...
map[ 4] = 1;
map[ 8] = 1;
/*
map[64] = 1;
map[72] = 1;
map[80] = 1;
map[88] = 1;
map[96] = 1;
*/
// SOME TEST DATA...
for(int i = 0; i < cntof(map); i++)
{
if(map[i] > 0)
{
_max = i; _cnt++;
}
}
// num of Opx can be as much as num of individual bit(s).
if(_cnt > cntof(work.OpxLst)){_cnt = cntof(work.OpxLst);}
best.OpxPay = 1000000000L; // invalid great number...
for(int opx_cnt = 1; opx_cnt <= _cnt; opx_cnt++)
{
int rv;
Ui32 x = 0;
ZERO(work); work.OpxCnt = (Ui32)opx_cnt;
rv = opx_Resolver(&best, &work, map, &x, -42, _max);
}
return 0;
}
You can use dynamic programming to calculate the lowest cost that covers the first i true values in map[]. Call this f(i). As I'll explain, you can calculate f(i) by looking at all f(j) for j < i, so this will take time quadratic in the number of true values -- much better than exponential. The final answer you're looking for will be f(n), where n is the number of true values in map[].
A first step is to preprocess map[] into a list of the positions of true values. (It's possible to do DP on the raw map[] array, but this will be slower if true values are sparse, and cannot be faster.)
int pos[65536]; // Every position *could* be true
int nTrue = 0;
void getPosList() {
for (int i = 0; i < 65536; ++i) {
if (map[i]) pos[nTrue++] = i;
}
}
When we're looking at the subproblem on just the first i true values, what we know is that the ith true value must be covered by a read that ends at i. This block could start at any position j <= i; we don't know, so we have to test all i of them and pick the best. The key property (Optimal Substructure) that enables DP here is that in any optimal solution to the i-sized subproblem, if the read that covers the ith true value starts at the jth true value, then the preceding j-1 true values must be covered by an optimal solution to the (j-1)-sized subproblem.
So: f(i) = min(f(j) + score(pos(j+1), pos(i)), with the minimum taken over all 1 <= j < i. pos(k) refers to the position of the kth true value in map[], and score(x, y) is the score of a read from position x to position y, inclusive.
int scores[65537]; // We effectively start indexing at 1
scores[0] = 0; // Covering the first 0 true values requires 0 cost
// Calculate the minimum score that could allow the first i > 0 true values
// to be read, and store it in scores[i].
// We can assume that all lower values have already been calculated.
void calcF(int i) {
int bestStart, bestScore = INT_MAX;
for (int j = 0; j < i; ++j) { // Always executes at least once
int attemptScore = scores[j] + score(pos[j + 1], pos[i]);
if (attemptScore < bestScore) {
bestStart = j + 1;
bestScore = attemptScore;
}
}
scores[i] = bestScore;
}
int score(int i, int j) {
return 25 + 2 * (j + 1 - i);
}
int main(int argc, char **argv) {
// Set up map[] however you want
getPosList();
for (int i = 1; i <= nTrue; ++i) {
calcF(i);
}
printf("Optimal solution has cost %d.\n", scores[nTrue]);
return 0;
}
Extracting a Solution from Scores
Using this scheme, you can calculate the score of an optimal solution: it's simply f(n), where n is the number of true values in map[]. In order to actually construct the solution, you need to read back through the table of f() scores to infer which choice was made:
void printSolution() {
int i = nTrue;
while (i) {
for (int j = 0; j < i; ++j) {
if (scores[i] == scores[j] + score(pos[j + 1], pos[i])) {
// We know that a read can be made from pos[j + 1] to pos[i] in
// an optimal solution, so let's make it.
printf("Read from %d to %d for cost %d.\n", pos[j + 1], pos[i], score(pos[j + 1], pos[i]));
i = j;
break;
}
}
}
}
There may be several possible choices, but all of them will produce optimal solutions.
Further Speedups
The solution above will work for an arbitrary scoring function. Because your scoring function has a simple structure, it may be that even faster algorithms can be developed.
For example, we can prove that there is a gap width above which it is always beneficial to break a single read into two reads. Suppose we have a read from position x-a to x, and another read from position y to y+b, with y > x. The combined costs of these two separate reads are 25 + 2 * (a + 1) + 25 + 2 * (b + 1) = 54 + 2 * (a + b). A single read stretching from x-a to y+b would cost 25 + 2 * (y + b - x + a + 1) = 27 + 2 * (a + b) + 2 * (y - x). Therefore the single read costs 27 - 2 * (y - x) less. If y - x > 13, this difference goes below zero: in other words, it can never be optimal to include a single read that spans a gap of 12 or more.
To make use of this property, inside calcF(), final reads could be tried in decreasing order of start-position (i.e. in increasing order of width), and the inner loop stopped as soon as any gap width exceeds 12. Because that read and all subsequent wider reads tried would contain this too-large gap and therefore be suboptimal, they need not be tried.
How do I find the vertices of the broken line that surrounds the silhouette in this image?
A possible input for the example above is:
WIDTH HEIGHT POSITION
3 9 17
5 9 9
12 4 8
3 11 3
10 7 1
2 3 19
So for this example the solution would be
[(1, 0), (1, 7), (3, 7), (3, 11), (6, 11), (6, 7),
(9, 7), (9, 9), (14, 9), (14, 4), (17, 4), (17, 9),
(20, 9), (20, 3), (21, 3), (21, 0)]
This is pretty simple. Make an array that is the length of the X axis, initialize to 0. As you read in the inputs, write the heights into this array if the height is >= the current value at that location in the array.
Then just loop over the array, and every time the value changes it is a vertex.
Basically:
int heights[SIZE] = {0};
int i, width, pos, height, prev = -1;
while (scanf("%d %d %d", &width, &height, &pos) == 3) {
for (i = 0; i < width; ++i) {
if (heights[pos+i] < height)
heights[pos+i] = height;
}
}
for (i = 0; i < SIZE; ++i) {
if (heights[i] != prev) {
printf("(%d,%d) ", i+1, heights[i]);
prev = heights[i];
}
}
printf("\n");
In the naive case, this doesn't seem like a very difficult algorithm. Do you know if the input size will get large/how large?
My initial attempt: Try to move from left to right. First pick the block with the leftmost edge that exists on the origin line. Climb to its top. Find all blocks with a left edge between the current point and the upper right point of the current block. Of that set, pick the closest (but check for edge cases, pun not intended). If the set is empty, start working your way down the right side of the block, looking for other blocks you may intercept.
Basically this is just how you'd trace it with your eye.
You can do some simple optimization by keeping sorted lists and then searching the lists rather than finding sets and digging around. For example, you might keep 4 sorted lists of the blocks, each sorted by the x or y coordinate of one of the sides.
If you have many, many blocks, you could consider using a multi-dimensional data structure to further organize the information.
I solved this problem using the sweep-line algorithm. This is a python class solution.
there two keys:
1) using the variable "points" to save all the left and right points and their heights and the sign of the height to indicate whether the points are left or right.
2) the variable "active" is used to save all the active lines that has been scanned.
class Solution:
# #param {integer[][]} buildings
# #return {integer[][]}
def getSkyline(self, buildings):
if len(buildings)==0: return []
if len(buildings)==1: return [[buildings[0][0], buildings[0][2]], [buildings[0][1], 0]]
points=[]
for building in buildings:
points+=[[building[0],building[2]]]
points+=[[building[1],-building[2]]] # the negative sign means this point is a right point
points=sorted(points, key=lambda x: x[0])
moving, active, res, current=0, [0], [],-1
while moving<len(points):
i=moving
while i<=len(points):
if i<len(points) and points[i][0]==points[moving][0]:
if points[i][1]>0:
active+=[points[i][1]]
if points[i][1]>current:
current=points[i][1]
if len(res)>0 and res[-1][0]==points[i][0]:
res[-1][1]=current
else:
res+=[[points[moving][0], current]]
else:
active.remove(-points[i][1]) #remove height of the lines than have been finished with scanning
i+=1
else:
break
if max(active)<current:
current=max(active)
res+=[[points[moving][0], current]]
moving=i
return res
I made a Java class to try and solve this. The class includes methods for generating, solving and printing data-sets. I haven't tested extensively, there may be a few bugs remaining. Also, my solution may be needlessly complicated, but it's designed to work (in theory) for non-discrete height and coordinate values.
import java.util.Random;
public class Skyline {
private int[][] buildings;
private int[][] skyline;
private int maxLength;
private int maxHeight;
public Skyline(int buildings, int maxLength, int maxHeight) {
this.maxLength = maxLength;
this.maxHeight = maxHeight;
makeRandom(buildings);
}
public Skyline(int[][] buildings, int dimensions) {
this.maxLength = maxLength;
this.maxHeight = maxHeight;
this.buildings = buildings;
}
public void makeRandom(int buildings) {
this.buildings = new int[buildings][3];
Random rand = new Random();
for(int i = 0; i < buildings; i++) {
int start = rand.nextInt(maxLength-3);
int end = rand.nextInt(maxLength - start - 1) + start + 1;
int height = rand.nextInt(maxHeight-1) + 1;
this.buildings[i][0] = start;
this.buildings[i][1] = height;
this.buildings[i][2] = end;
}
boolean swapped = true;
while(swapped) {
swapped = false;
for(int i = 0; i < this.buildings.length-1; i++) {
if(this.buildings[i][0] > this.buildings[i+1][0]) {
swapped = true;
int[] temp = this.buildings[i];
this.buildings[i] = this.buildings[i+1];
this.buildings[i+1] = temp;
}
}
}
// this.buildings[0][0] = 2;
// this.buildings[0][1] = 3;
// this.buildings[0][2] = 8;
}
public void printBuildings() {
print(this.buildings, false);
}
public void printSkyline() {
print(this.buildings, true);
}
public void print(int[][] buildings, boolean outline) {
char[][] str = new char[this.maxLength][this.maxHeight];
for(int i = 0; i < this.maxLength; i++) {
for(int j = 0; j < this.maxHeight; j++) {
str[i][j] = '.';
}
}
for(int i = 0; i < buildings.length; i++) {
int start = buildings[i][0];
int height = buildings[i][1];
int end = buildings[i][2];
//print the starting vertical
for(int j = 0; j < height; j++) {
if(outline) str[start][j] = str[start][j] == '|' ? '.' : '|';
else str[start][j] = '|';
}
//print the ending vertical
for(int j = 0; j < height; j++) {
if(outline) str[end][j] = str[end][j] == '|' ? '.' : '|';
else str[end][j] = '|';
}
//print the horizontal
if(height > 0) {
for(int j = start; j <= end; j++) {
str[j][height] = str[j][height] == '|' ? '|' : '-';
}
}
}
for(int i = maxHeight-1; i >= 0; i--) {
for(int j = 0; j < maxLength; j++) {
System.out.print(str[j][i]);
}
System.out.println();
}
System.out.println();
}
public void solveSkyline() {
for(int i = 0; i < buildings.length; i++) {
boolean reduced = true;
while(reduced) {
reduced = false;
for(int j = i+1; j < buildings.length; j++) {
if(buildings[j][0] < buildings[i][2] && buildings[j][1] > buildings[i][1] && buildings[j][2] >= buildings[i][2]) { //if intersecting building is taller, and longer
buildings[i][2] = buildings[j][0];
reduced = true;
break;
} else if(buildings[j][0] < buildings[i][2] && buildings[j][1] <= buildings[i][1] && buildings[j][2] >= buildings[i][2]) { //intersecting building is shorter, but longer
buildings[j][0] = buildings[i][2];
reduced = true;
break;
} else if(buildings[j][0] < buildings[i][2] && buildings[j][1] > 0 && buildings[j][1] < buildings[i][1] && buildings[j][2] <= buildings[i][2]) { //building is invisible, so ignore it
buildings[j][1] = 0;
reduced = true;
break;
} else if(buildings[j][0] < buildings[i][2] && buildings[j][2] <= buildings[i][2] && buildings[j][1] > buildings[i][1]) {
int[] newBuilding = new int[]{buildings[j][2], buildings[i][1], buildings[i][2]};
int[][] newBuildings = new int[buildings.length+1][3];
boolean inserted = false;
buildings[i][2] = buildings[j][0];
for(int k = 0; k < buildings.length; k++) {
if(inserted == false) {
if(newBuilding[0] < buildings[k][0]) {
newBuildings[k] = newBuilding;
newBuildings[k+1] = buildings[k];
inserted = true;
} else {
newBuildings[k] = buildings[k];
}
}
if(inserted == false && k == buildings.length - 1) {
newBuildings[k+1] = newBuilding;
} else {
newBuildings[k+1] = buildings[k];
}
}
buildings = newBuildings;
reduced = true;
break;
}
}
}
}
}
public static void main(String args[]) {
Skyline s = new Skyline(5, 100, 10);
s.printBuildings();
s.solveSkyline();
s.printBuildings();
s.printSkyline();
}
}
My solution to the problem as described here https://leetcode.com/problems/the-skyline-problem/ it iterates the list of buildings twice, however this could be combined into a single iteration. However, there are more optimal approaches if you consider the pure algorithm solution explained here http://www.algorithmist.com/index.php/UVa_105
class Solution {
public:
vector<pair<int, int>> getSkyline(vector<vector<int>>& buildings) {
// The final result.
vector<pair<int, int>> result;
// To hold information about the buildings
std::set<BuildingInformation> buildingInformation;
// Go through each building, and store information about the start and end heights.
for ( vector<vector<int>>::iterator buildingIt = buildings.begin( ); buildingIt != buildings.end( ); ++buildingIt ) {
BuildingInformation buildingStart;
buildingStart.x = (*buildingIt)[0];
buildingStart.h = (*buildingIt)[2];
buildingStart.StartOrEnd = Start;
buildingInformation.insert(buildingStart);
buildingStart.x = (*buildingIt)[1];
buildingStart.StartOrEnd = End;
buildingInformation.insert(buildingStart);
}
// Keep track of the current height.
int currentHeight = 0;
// A map of active building heights against number of buildings (to handle multiple buildings overlapping with same height).
// As it is a map, it'll be sorted by key, which is the height.
std::map<int, int> heights;
// Go through each building information that we generated earlier.
for ( std::set<BuildingInformation>::iterator it = buildingInformation.begin( ); it != buildingInformation.end( ); ++it ) {
if ( it->StartOrEnd == Start ) {
// This is a start point, do we have this height already in our map?
if ( heights.find( it->h ) != heights.end( ) ) {
// Yes, increment count of active buildings with this height/
heights[ it->h ] += 1;
} else {
// Nope, add this building to our map.
heights[ it->h ] = 1;
}
// Check if building height is taller than current height.
if ( it->h > currentHeight ) {
// Update current height and add marker to results.
currentHeight = it->h;
result.push_back( pair<int, int>( it->x, currentHeight ) );
}
} else {
// This is an end point, get iterator into our heights map.
std::map<int, int>::iterator heightIt = heights.find( it->h );
// Reduce by one.
heightIt->second -= 1;
// If this was the last building of the current height in the map...
if ( heightIt->second == 0 ) {
// Remove from heights map.
heights.erase( heightIt );
// If our height was the current height...
if ( it->h == currentHeight ) {
// If we have no more active buildings...
if ( heights.size( ) == 0 ) {
// Current height is zero.
currentHeight = 0;
} else {
// Otherwise, get iterator to one past last.
heightIt = heights.end( );
// Go back to get last valid iterator.
--heightIt;
// Store current height.
currentHeight = heightIt->first;
}
// Add marker to results.
result.push_back( pair<int, int>( it->x, currentHeight ) );
}
}
}
}
return result;
}
private:
// Is this a building start or end?
enum BuildingStartOrEnd
{
Start = 0,
End
};
// Information about building, there are two of these for each building, one for start, one for end.
struct BuildingInformation
{
int x;
int h;
BuildingStartOrEnd StartOrEnd;
// The ordering algorithm for the key, the rules we want to implement is keys are put in X order, and
// in the case of a tie (x values the same), we want Start pieces to come before End pieces (this is
// to handle cases where an old building ends and a new building begins on same X index, in which case
// we want to process the new start before processing the old end), however if we have two Start pieces
// at the same index, we wish to favour taller pieces (in this scenario we want to add a marker for the
// tallest building), finally if we have two End pieces at the same index, we wish to prefer lower
// pieces, as when multiple buildings end, we only want to add one result for the ultimate lowest point.
bool operator < ( const BuildingInformation & rhs ) const
{
if ( x == rhs.x )
{
if ( StartOrEnd == rhs.StartOrEnd ) {
if ( StartOrEnd == Start )
return h > rhs.h;
else
return h < rhs.h;
} else {
return StartOrEnd < rhs.StartOrEnd;
}
}
return x < rhs.x;
}
};
};