maze generation algorithm in c with DFS - c

recently i read this topic about generating mazes in c . see here https://www.algosome.com/articles/maze-generation-depth-first.html
and i want to write it in c . here is my code and it's not working right .
#include <stdio.h>
#include <time.h>
#include <stdlib.h>
int check[5][5];
int v[5][5];
int border(int x , int y ){
if(x> -1 && x< 6 && y > -1 && y<6)
return 1;
else
return 0 ;
}
int wall[6][6][6][6];
void dfs ( int x , int y){
srand(time(NULL));
int s = 1/*rand() % 4 ;*/ ;
if(s=1 ){
if(border(x ,y-1)&& check[x][y-1]==0){
check[x][y]=1;
wall[x][y][x+1][y]=1;
dfs(x , y-1);
}
else
return ;
}
else if(s=2){
if(border(x+1 ,y)&&check[x+1][y]==0){
check[x][y]=1;
wall[x+1][y][x+1][y+1]=1;
dfs(x+1 , y);
}
else return ;
}
else if(s=3){
if(border(x ,y+1)&&check[x][y+1]==0){
check[x][y]=1;
wall[x][y+1][x+1][y+1]=1;
dfs(x , y+1);
}
else return ;
}
else if(s=0){
if(border(x-1 ,y)&&check[x-1][y]==0){
check[x][y]=1;
wall[x][y][x][y+1]=1;
dfs(x-1 , y);
}
else return ;
}
return ;
}
int main(){
dfs( 4, 4);
for(int i =0 ; i < 6 ; i++)
for (int j =0 ; j < 6 ; j++)
for ( int h =0 ; h <6 ; h++)
for (int k =0 ; k < 6 ; k ++)
printf("%d \n" , wall[i][j][h][k]);
return 0 ;
}
i invert my table to graph , and i want to show me the coordinates of my walls .
what's the problem ?

You have several errors – programming errors and logic errors – in your code:
When you distiguish between the directions the s=1 and so on should be s == 1. You want a comparison, not an assignment. (Your code is legal C, so there is no error.)
You call srand at the beginning of dfs, which you call recursively. This will make your single (commented) rand call always create the same random number. You should seed the pseudo random number generator only once at the beginning of main.
You can store the paths the way you do, but it is wasteful. There are only four possible paths from each cell, so you don't need an array that allows to create a path between (0,0) and (3,4), for example.
Your code would benefit from using constants or enumerated values instead of the hard-coded 5's and 6's. This will allow you to change the dimensions later easily.
But your principal error is in how you implement the algorithm. You pick one of the for directions at random, then test whether that direction leads to a valid unvisited cell. If so, you recurse. If not, you stop. This will create a single unbranched path through the cells. Note that if you start in a corner cell, you have already a 50% chance of stopping the recursion short.
But you want something else: You want a maze with many branches that leads to every cell in the maze. Therefore, when the first recursion returns, you must try to branch to other cells. The algorithm goes like this:
Make a list of all possible exits.
If there are possible exits:
Pick one exit, create a path to that exit and recurse.
Update the list of possible exits.
Note that you cannot re-use the old list of exits, because the recursion may have rendered some possible exits invalid by visiting the destination cells.
Below is code that creates a maze with the described algorithm. I've used two distinct arrays to describe horizontal and vertical paths:
#include <stdlib.h>
#include <stdio.h>
#include <time.h>
enum {
W = 36, // width of maze
H = 25 // height of maze
};
enum {
North,
East,
South,
West,
NDir
};
char visited[H][W];
char horz[H][W - 1]; // horizontal E-W paths in the maze
char vert[H - 1][W]; // veritcal N-S paths in the maze
/*
* Fill dir with directions to unvisited cells, return count
*/
int adjacent(int dir[], int x, int y)
{
int ndir = 0;
if (y > 0 && visited[y - 1][x] == 0) dir[ndir++] = North;
if (x < W - 1 && visited[y][x + 1] == 0) dir[ndir++] = East;
if (y < H - 1 && visited[y + 1][x] == 0) dir[ndir++] = South;
if (x > 0 && visited[y][x - 1] == 0) dir[ndir++] = West;
return ndir;
}
/*
* Traverse cells depth first and create paths as you go
*/
void dfs(int x, int y)
{
int dir[NDir];
int ndir;
visited[y][x] = 1;
ndir = adjacent(dir, x, y);
while (ndir) {
int pick = rand() % ndir;
switch (dir[pick]) {
case North: vert[y - 1][x] = 1; dfs(x, y - 1); break;
case East: horz[y][x] = 1; dfs(x + 1, y); break;
case South: vert[y][x] = 1; dfs(x, y + 1); break;
case West: horz[y][x - 1] = 1; dfs(x - 1, y); break;
}
ndir = adjacent(dir, x, y);
}
}
/*
* Print a map of the maze
*/
void map(void)
{
int i, j;
for (i = 0; i < W; i++) {
putchar('_');
putchar('_');
}
putchar('\n');
for (j = 0; j < H; j++) {
putchar('|');
for (i = 0; i < W; i++) {
putchar(j < H - 1 && vert[j][i] ? ' ' : '_');
putchar(i < W - 1 && horz[j][i] ? '_' : '|');
}
putchar('\n');
}
}
int main()
{
srand(time(NULL));
dfs(0, 0);
map();
return 0;
}
You can test it here. If you replace the while in dsf with a simple if, you get more or less what you implemented. Note that this creates only a single, usually short path.

Related

How to print V in c programming in 10X10 row and column in a optimized way?

I printed V using * in specific rows and columns. I had lots of if statements. I am sharing my code below.
Is there any optimised way to print the V pattern in 10X10 row column? (without many if conditions)?
#include <stdio.h>
int main() {
int row, column;
for (row = 1; row <= 10; row++) {
for (column = 1; column <= 10; column++) {
if (row == 1 && (column == 1 || column == 10)
|| row == 3 && (column == 2 || column == 9)
|| row == 5 && (column == 3 || column == 8)
|| row == 7 && (column == 4 || column == 7)
|| row == 10 && column == 5)
printf("*");
else
printf(" ");
}
printf("\n");
}
return 0;
}
A reasonable option when you need to output arbitrary amounts of spaces is to use printf string width specifier to left-pad with spaces:
printf("%*s*", spaces, "");
The above will output the empty string, padded up to a width of the integer value spaces, and then output a *. Note that the format string %*s means that you specify both a width and then a string as extra arguments. The * in that part has nothing to do with an actual *. We add that onto the end of the format string.
So, for the V shape, each line has two * characters on it, except the last line (if the width is odd). One way to do this intuitively is to track the position of the left and the right part of the V for each line, and then do the math for determining how much padding to add.
Example:
void v(int width)
{
int l = 0, r = width;
for (; l < r; l++, r--)
{
printf("%*s*%*s\n", l, "", r-l, "*");
}
if (l == r)
printf("%*s*\n", l, "");
}
If you really want more condensed code, you can elect to roll that last line into the loop. In this case, when l == r you want to only output a single asterisk. Otherwise you want two. So you could output the string &"*"[l==r] -- that will mean that when l==r is true, you'll skip over the asterisk and it will look like an empty string (because you land on the NUL terminator).
Note this is not great style. It sacrifices readability for compactness.
void v(int width)
{
for (int l = 0, r = width; l <= r; l++, r--)
{
printf("%*s*%*s\n", l, "", r-l, &"*"[l==r]);
}
}
So, this is "efficient" in terms of compact code and not many function calls. If you instead are concerned about the format parsing of printf then you can avoid it entirely. Below, we use the same left/right bounds and just walk through each row using loops. This essentially does what our printf is doing internally, except it's more obvious what's going on:
void v(int width)
{
int l = 0, r = width-1;
for (; l <= r; l++, r--)
{
int x = 0;
for (; x < l; x++) putchar(' ');
putchar('*');
if (x < r)
{
for (x++; x < r; x++) putchar(' ');
putchar('*');
}
putchar('\n');
}
}
Now for some fun...
As an exercise, here is the printf approach but with no loops (using recursion):
void vv(int width, int row) {
if(width >= 0) {
printf("%*s*%*s\n", row, "", width, &"*"[width==0]);
vv(width-2, row+1);
}
}
void v(int width) {
vv(width, 0);
}
And here is that idea turned into an intentionally horrendous mess that looks cool. ;)
#include <stdio.h>
#define VV int
#define vV "*\0%*s%*s\n"
VV Vv( VV v ,VV
vv){if(v -->0){
printf (vV+2,
vv++ ,vV,v
,vV+ !v);
Vv(-- v,vv
);}} VV V
(VV v){
Vv(v,
1);
}
int main() {
for (int v = 1; v < 12; v++) {
printf("size %d\n", v);
V(v);
}
}
I don't think this is optimized but will be simpler and scalable with SIZE.
#include <stdio.h>
#define SIZE 10
#define MID ((SIZE-1)/2) // midst position of SIZE
#define ABS(x) ((x)<0?-(x):(x)) // absolute value of x
int main()
{
int i, j;
for (i = 0; i < SIZE; i++) {
for (j = 0; j < SIZE; j++) {
if (i % 2 == 0 && ABS(j - MID) == MID - i / 2) putchar('*');
else putchar(' ');
}
putchar('\n');
}
return 0;
}
[Explanation]
Assuming SIZE equals to 10, the value MID is calculated to be 4.
Then the v shaped asterisks will be placed symmetrically wrt the 4th column.
Let's put numbers in columns (j) and rows (i) as follows:
012345678
* * 0 ABS(0 - 4) == 4 - 0, ABS(8 - 4) == 4 - 0
1 skipped as i & 2 != 0
* * 2 ABS(1 - 4) == 4 - 1, ABS(7 - 4) == 4 - 1
3 skipped
* * 4 ABS(2 - 4) == 4 - 2, ABS(6 - 4) == 4 - 2
5 skipped
* * 6 ABS(3 - 4) == 4 - 3, ABS(5 - 4) == 4 - 3
7 skipped
* 8 ABS(4 - 4) == 4 - 4
The equations above are the conditions to put the asterisks.
For instance, in the 0th row, we want to put it on 0th column and 8th.
The condition j - 4 == +/- 4 or ABS(j - 4) == 4 will represent the conditions due to the symmetricity.
If we generarize the condition across rows, we can describe it as
i % 2 == 0 && ABS(j - MID) == MID - i / 2.
This code considers the relation between the row and the position of the *, if you are in the first row, then we want the column 0 and colum 9 to print *, then second row, we want column 1 and column 8 and so on. Thus, I used an iterator for the rows and iterator for columns to know in a concrete row which column I'm printing.
#include <stdio.h>
int main()
{
int matrix_size = 10; //Assuming is squared matrix 10x10
int counter = 0;
int i,j;
for(i=0;i<(int)(matrix_size/2);i++) {
for(j=0;j<matrix_size;j++) {
if(j==i || j==(matrix_size-1-i)) {
printf("*");
}else{
printf(" ");
}
}
printf("\n");
}
return 0;
}
EDIT: compared to tshiono solution, I write the V in just 5 rows and he prints it in 10 rows but assuming an space line between each line. Boths solutions are ok depending on what u want.
For the V shape to be symmetric, the number of rows and columns should be odd. Here is a simpler method:
#include <stdio.h>
#include <stdlib.h>
int main() {
for (int n = 11, row = 0; row < n; row++) {
for (int column = 0; column < n; column++)
putchar(" *"[2 * abs(column - n / 2) == n - 1 - row]);
printf("\n");
}
return 0;
}
Output:
* *
* *
* *
* *
* *
*
For a thicker V shape:
#include <stdio.h>
#include <stdlib.h>
int main() {
for (int n = 11, row = 0; row < n; row++) {
for (int column = 0; column < n; column++)
putchar(" *"[abs(2 * abs(column - n / 2) - (n - 1 - row)) <= 1]);
printf("\n");
}
return 0;
}
Output:
* *
** **
* *
** **
* *
** **
* *
** **
* *
***
*
Other answers take into account the specific shape of V and optimize around that.
I suggest an optimized solution for any shape.
This involves a lookup table containing all the locations of * characters composing the shape.
struct { int row,col; } shape[] = {
{1,1}, {1,10}, {3,2}, {3,9}, {5,3}, {5,8}, {7,4}, {7,7}, {10,5},
{-1,-1}
};
The last location ({-1,-1}) has the same purpose as terminating '\0' for strings.

How to find all possible 5 dots alignments in Join Five game

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;
}

Grids and pointers in c

I made this program in C where an object R is placed on a grid and it's supposed to move taking inputs from they keyboard. For example, thi is what happens if you press N.
0 1 2
0 - - - R - - - - -
1 R - - PRESS N -> GO UP -> - - - PRESS N AGAIN -> - - -
2 - - - - - - R - -
So R makes it go up. The object has to move around, so when it is at [A0][B0], for example, it needs to go all the way down [A2][B0]. See above.
It will move up, down, left and right.
Right now i'm creating the function to make it move up, but i'm having a lot of troubles: sometimes it randomly freezes to 2:0 and 0:0 without goind up, and when it's at A = 2, instead of going up of 1, it goes to 0, although i set it to do 2-1 (to go up it has to subtract 1).
I don't understand what's causing those troubles, any advice?
#include <stdio.h>
#include <time.h>
#include <stdlib.h>
#define X 3
#define Y 3
struct coords{
int a;
int b;
};
typedef struct coords cord;
// Print the array
char printArray(char row[][Y], size_t one, size_t two, struct coords cord)
{
row[cord.a][cord.b] = 'X';
// output column heads
printf("%s", " [0] [1] [2]");
// output the row in tabular format
for (size_t i = 0; i < one; ++i) {
printf("\nrow[%lu] ", i);
for (size_t j = 0; j < two; ++j) {
printf("%-5c", row[i][j]);
}
}
}
int moveUp(struct coords * cord);
int main(void)
{
struct coords cord;
char row[X][Y] =
{ { '-', '-', '-'},
{ '-', '-', '-'},
{ '-', '-', '-'} };
srand(time(NULL));
cord.a = (rand() % 3);
cord.b = (rand() % 3);
printf("\nValori rand: A %d, B %d\n", cord.a, cord.b);
// output the row
//printf("\nrobot:%c\n", robot);
puts("The array is:");
printf("\n");
printArray(row, X, Y, cord);
row[cord.a][cord.b] = '-';
//printArray(row, X, Y, &m, &n);
char h;
while(h != '3'){
switch (h) {
case 'N':
moveUp(&cord);
printArray(row, X, Y, cord);
row[cord.a][cord.b] = '-';
break;
}
scanf("%s", &h);
}
printf("\n");
}
int moveUp(struct coords * cord)
{
cord->a - 1;
if (cord->a == 2){
cord->a - 1;
} else if (cord->a == 1){
cord->a - 1;
} else if (cord->a == 0){
cord->a + 2;
}
/*
if (cord->a == 0) {
cord-> a = 2;
} else {
cord->a - 1;
}
*/
printf("\n A = %d, B = %d\n", cord->a, cord->b);
}
In the below code, you are checking the value of h before having read anything into it. If the uninitialized value of h happens to be 3, then execution will not enter the while loop.
char h;
while(h != '3')
So read in a value into h and then do the check in the while loop.
In the moveUp function, you can use the ternary conditional operator to assign the next position or the object R.
cord->a = (cord->a)? (cord->a - 1): 2;

C - getting prime numbers using this algorithm

I am fighting some simple question.
I want to get prime numbers
I will use this algorithm
and... I finished code writing like this.
int k = 0, x = 1, n, prim, lim = 1;
int p[100000];
int xCount=0, limCount=0, kCount=0;
p[0] = 2;
scanf("%d", &n);
start = clock();
do
{
x += 2; xCount++;
if (sqrt(p[lim]) <= x)
{
lim++; limCount++;
}
k = 2; prim = true;
while (prim && k<lim)
{
if (x % p[k] == 0)
prim = false;
k++; kCount++;
}
if (prim == true)
{
p[lim] = x;
printf("prime number : %d\n", p[lim]);
}
} while (k<n);
I want to check how much repeat this code (x+=2; lim++; k++;)
so I used xCount, limCount, kCount variables.
when input(n) is 10, the results are x : 14, lim : 9, k : 43. wrong answer.
answer is (14,3,13).
Did I write code not well?
tell me correct point plz...
If you want to adapt an algorithm to your needs, it's always a good idea to implement it verbatim first, especially if you have pseudocode that is detailed enough to allow for such a verbatim translation into C-code (even more so with Fortran but I digress)
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
int main (void){
// type index 1..n
int index;
// var
// x: integer
int x;
//i, k, lim: integer
int i, k, lim;
// prim: boolean
bool prim;
// p: array[index] of integer {p[i] = i'th prime number}
/*
We cannot do that directly, we need to know the value of "index" first
*/
int res;
res = scanf("%d", &index);
if(res != 1 || index < 1){
fprintf(stderr,"Only integral values >= 1, please. Thank you.\n");
return EXIT_FAILURE;
}
/*
The array from the pseudocode is a one-based array, take care
*/
int p[index + 1];
// initialize the whole array with distinguishable values in case of debugging
for(i = 0;i<index;i++){
p[i] = -i;
}
/*
Your variables
*/
int lim_count = 0, k_count = 0;
// begin
// p[1] = 2
p[1] = 2;
// write(2)
puts("2");
// x = 1
x = 1;
// lim = 1
lim = 1;
// for i:=2 to n do
for(i = 2;i < index; i++){
// repeat (until prim)
do {
// x = x + 2
x += 2;
// if(sqr(p[lim]) <= x) then
if(p[lim] * p[lim] <= x){
// lim = lim +1
lim++;
lim_count++;
}
// k = 2
k = 2;
// prim = true
prim = true;
// while (prim and (k < lim)) do
while (prim && (k < lim)){
// prim = "x is not divisible by p[k]"
if((x % p[k]) == 0){
prim = false;
}
// k = k + 1
k++;
k_count++;
}
// (repeat) until prim
} while(!prim);
// p[i] := x
p[i] = x;
// write(x)
printf("%d\n",x);
}
// end
printf("x = %d, lim_count = %d, k_count = %d \n",x,lim_count,k_count);
for(i = 0;i<index;i++){
printf("%d, ",p[i]);
}
putchar('\n');
return EXIT_SUCCESS;
}
It will print an index - 1 number of primes starting at 2.
You can easily change it now--for example: print only the primes up to index instead of index - 1 primes.
In your case the numbers for all six primes up to 13 gives
x = 13, lim_count = 2, k_count = 3
which is distinctly different from the result you want.
Your translation looks very sloppy.
for i:= 2 to n do begin
must translate to:
for (i=2; i<=n; i++)
repeat
....
until prim
must translate to:
do {
...
} while (!prim);
The while prim... loop is inside the repeat...until prim loop.
I leave it to you to apply this to your code and to check that all constructs have been properly translated. it doesn't look too difficult to do that correctly.
Note: it looks like the algorithm uses 1-based arrays whereas C uses 0-based arrays.

Optimization of Brute-Force algorithm or Alternative?

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.

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