1595797200
N-Queen Problem | Local Search using Hill climbing with random neighbour
The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other.
For example, the following is a solution for 8 Queen problem.
Input:_ N = 4_
Output:
0 1 0 0
0 0 0 1
1 0 0 0
0 0 1 0
Explanation:
The Position of queens are:
1 – {1, 2}
2 – {2, 4}
3 – {3, 1}
4 – {4, 3}
As we can see that we have placed all 4 queens
in a way that no two queens are attacking each other.
So, the output is correct
Input:_ N = 8_
Output:
0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0
0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0
Approach: The idea is to use Hill Climbing Algorithm.
- While there are algorithms like Backtracking to solve N Queen problem, let’s take an AI approach in solving the problem.
- It’s obvious that AI does not guarantee a globally correct solution all the time but it has quite a good success rate of about 97% which is not bad.
- A description of the notions of all terminologies used in the problem will be given and are as follows:-
- Notion of a State – A state here in this context is any configuration of the N queens on the N X N board. Also, in order to reduce the search space let’s add an additional constraint that there can only be a single queen in a particular column. A state in the program is implemented using an array of length N, such that if state[i]=j then there is a queen at column index i and row index j.
- Notion of Neighbours – Neighbours of a state are other states with board configuration that differ from the current state’s board configuration with respect to the position of only a single queen. This queen that differs a state from its neighbour may be displaced anywhere in the same column.
- Optimisation function or Objective function – We know that local search is an optimization algorithm that searches the local space to optimize a function that takes the state as input and gives some value as an output. The value of the objective function of a state here in this context is the number of pairs of queens attacking each other. Our goal here is to find a state with the minimum objective value. This function has a maximum value of NC2 and a minimum value of 0.
Algorithm:
- Start with a random state(i.e, a random configuration of the board).
- Scan through all possible neighbours of the current state and jump to the neighbour with the highest objective value, if found any. If there does not exist, a neighbour, objective strictly higher than the current state but there exists one with equal then jump to any random neighbour(escaping shoulder and/or local optimum).
- Repeat step 2, until a state whose objective is strictly higher than all it’s neighbour’s objectives, is found and then go to step 4.
- The state thus found after the local search is either the local optimum or the global optimum. There is no way of escaping local optima but adding a random neighbour or a random restart each time a local optimum is encountered increases the chances of achieving global optimum(the solution to our problem).
- Output the state and return.
- It is easily visible that the global optimum in our case is 0 since it is the minimum number of pairs of queens that can attack each other. Also, the random restart has a higher chance of achieving global optimum but we still use random neighbour because our problem of N queens does not has a high number of local optima and random neighbour is faster than random restart.
- Conclusion:
- Random Neighbour escapes shoulders but only has a little chance of escaping local optima.
- Random Restart both escapes shoulders and had a high chance of escaping local optima.
Below is the implementation of the Hill-Climbing algorithm.
CPP
// C++ implementation of the
// above approach
#include <iostream>
#include <math.h>
#define N 8
**using** **namespace** std;
// A utility function that configures
// the 2D array "board" and
// array "state" randomly to provide
// a starting point for the algorithm.
**void** configureRandomly(``**int** board[][N],
**int**``* state)
{
// Seed for the random function
**srand**``(``**time**``(0));
// Iterating through the
// column indices
**for** (``**int** i = 0; i < N; i++) {
// Getting a random row index
state[i] = **rand**``() % N;
// Placing a queen on the
// obtained place in
// chessboard.
board[state[i]][i] = 1;
}
}
// A utility function that prints
// the 2D array "board".
**void** printBoard(``**int** board[][N])
{
**for** (``**int** i = 0; i < N; i++) {
cout << " "``;
**for** (``**int** j = 0; j < N; j++) {
cout << board[i][j] << " "``;
}
cout << "\n"``;
}
}
// A utility function that prints
// the array "state".
**void** printState(``**int**``* state)
{
**for** (``**int** i = 0; i < N; i++) {
cout << " " << state[i] << " "``;
}
cout << endl;
}
// A utility function that compares
// two arrays, state1 and state2 and
// returns true if equal
// and false otherwise.
**bool** compareStates(``**int**``* state1,
**int**``* state2)
{
**for** (``**int** i = 0; i < N; i++) {
**if** (state1[i] != state2[i]) {
**return** **false**``;
}
}
**return** **true**``;
}
// A utility function that fills
// the 2D array "board" with
// values "value"
**void** fill(``**int** board[][N], **int** value)
{
**for** (``**int** i = 0; i < N; i++) {
**for** (``**int** j = 0; j < N; j++) {
board[i][j] = value;
}
}
}
// This function calculates the
// objective value of the
// state(queens attacking each other)
// using the board by the
// following logic.
**int** calculateObjective(``**int** board[][N],
**int**``* state)
{
// For each queen in a column, we check
// for other queens falling in the line
// of our current queen and if found,
// any, then we increment the variable
// attacking count.
// Number of queens attacking each other,
// initially zero.
**int** attacking = 0;
// Variables to index a particular
// row and column on board.
**int** row, col;
**for** (``**int** i = 0; i < N; i++) {
// At each column 'i', the queen is
// placed at row 'state[i]', by the
// definition of our state.
// To the left of same row
// (row remains constant
// and col decreases)
row = state[i], col = i - 1;
**while** (col >= 0
&& board[row][col] != 1) {
col--;
}
**if** (col >= 0
&& board[row][col] == 1) {
attacking++;
}
// To the right of same row
// (row remains constant
// and col increases)
row = state[i], col = i + 1;
**while** (col < N
&& board[row][col] != 1) {
col++;
}
**if** (col < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the left up
// (row and col simoultaneously
// decrease)
row = state[i] - 1, col = i - 1;
**while** (col >= 0 && row >= 0
&& board[row][col] != 1) {
col--;
row--;
}
**if** (col >= 0 && row >= 0
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the right down
// (row and col simoultaneously
// increase)
row = state[i] + 1, col = i + 1;
**while** (col < N && row < N
&& board[row][col] != 1) {
col++;
row++;
}
**if** (col < N && row < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the left down
// (col decreases and row
// increases)
row = state[i] + 1, col = i - 1;
**while** (col >= 0 && row < N
&& board[row][col] != 1) {
col--;
row++;
}
**if** (col >= 0 && row < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the right up
// (col increases and row
// decreases)
row = state[i] - 1, col = i + 1;
**while** (col < N && row >= 0
&& board[row][col] != 1) {
col++;
row--;
}
**if** (col < N && row >= 0
&& board[row][col] == 1) {
attacking++;
}
}
// Return pairs.
**return** (``**int**``)(attacking / 2);
}
// A utility function that
// generates a board configuration
// given the state.
**void** generateBoard(``**int** board[][N],
**int**``* state)
{
fill(board, 0);
**for** (``**int** i = 0; i < N; i++) {
board[state[i]][i] = 1;
}
}
// A utility function that copies
// contents of state2 to state1\.
**void** copyState(``**int**``* state1, **int**``* state2)
{
**for** (``**int** i = 0; i < N; i++) {
state1[i] = state2[i];
}
}
// This function gets the neighbour
// of the current state having
// the least objective value
// amongst all neighbours as
// well as the current state.
**void** getNeighbour(``**int** board[][N],
**int**``* state)
{
// Declaring and initializing the
// optimal board and state with
// the current board and the state
// as the starting point.
**int** opBoard[N][N];
**int** opState[N];
copyState(opState,
state);
generateBoard(opBoard,
opState);
// Initializing the optimal
// objective value
**int** opObjective
= calculateObjective(opBoard,
opState);
// Declaring and initializing
// the temporary board and
// state for the purpose
// of computation.
**int** NeighbourBoard[N][N];
**int** NeighbourState[N];
copyState(NeighbourState,
state);
generateBoard(NeighbourBoard,
NeighbourState);
// Iterating through all
// possible neighbours
// of the board.
**for** (``**int** i = 0; i < N; i++) {
**for** (``**int** j = 0; j < N; j++) {
// Condition for skipping the
// current state
**if** (j != state[i]) {
// Initializing temporary
// neighbour with the
// current neighbour.
NeighbourState[i] = j;
NeighbourBoard[NeighbourState[i]][i]
= 1;
NeighbourBoard[state[i]][i]
= 0;
// Calculating the objective
// value of the neighbour.
**int** temp
= calculateObjective(
NeighbourBoard,
NeighbourState);
// Comparing temporary and optimal
// neighbour objectives and if
// temporary is less than optimal
// then updating accordingly.
**if** (temp <= opObjective) {
opObjective = temp;
copyState(opState,
NeighbourState);
generateBoard(opBoard,
opState);
}
// Going back to the original
// configuration for the next
// iteration.
NeighbourBoard[NeighbourState[i]][i]
= 0;
NeighbourState[i] = state[i];
NeighbourBoard[state[i]][i] = 1;
}
}
}
// Copying the optimal board and
// state thus found to the current
// board and, state since c++ doesn't
// allow returning multiple values.
copyState(state, opState);
fill(board, 0);
generateBoard(board, state);
}
**void** hillClimbing(``**int** board[][N],
**int**``* state)
{
// Declaring and initializing the
// neighbour board and state with
// the current board and the state
// as the starting point.
**int** neighbourBoard[N][N] = {};
**int** neighbourState[N];
copyState(neighbourState, state);
generateBoard(neighbourBoard,
neighbourState);
**do** {
// Copying the neighbour board and
// state to the current board and
// state, since a neighbour
// becomes current after the jump.
copyState(state, neighbourState);
generateBoard(board, state);
// Getting the optimal neighbour
getNeighbour(neighbourBoard,
neighbourState);
**if** (compareStates(state,
neighbourState)) {
// If neighbour and current are
// equal then no optimal neighbour
// exists and therefore output the
// result and break the loop.
printBoard(board);
**break**``;
}
**else** **if** (calculateObjective(board,
state)
== calculateObjective(
neighbourBoard,
neighbourState)) {
// If neighbour and current are
// not equal but their objectives
// are equal then we are either
// approaching a shoulder or a
// local optimum, in any case,
// jump to a random neighbour
// to escape it.
// Random neighbour
neighbourState[``**rand**``() % N]
= **rand**``() % N;
generateBoard(neighbourBoard,
neighbourState);
}
} **while** (``**true**``);
}
// Driver code
**int** main()
{
**int** state[N] = {};
**int** board[N][N] = {};
// Getting a starting point by
// randomly configuring the board
configureRandomly(board, state);
// Do hill climbing on the
// board obtained
hillClimbing(board, state);
**return** 0;
}
Output:
0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0
Complexity Analysis
- The time complexity for this algorithm can be divided into three parts:
- Calculating Objective – The calculation of objective involves iterating through all queens on board and checking the no. of attacking queens, which is done by our calculateObjective function in O(N2) time.
- Neighbour Selection and Number of neighbours – The description of neighbours in our problem gives a total of N(N-1) neighbours for the current state. The selection procedure is best fit and therefore requires iterating through all neighbours, which is again O(N2).
- Search Space – The description of neighbours in our problem gives a total of N(N-1) neighbours for the current state. The selection procedure is best fit and therefore requires iterating through all neighbours, which is again O(N2).
- Therefore, the worst-case time complexity of our algorithm is O(NN). But, this worst-case occurs rarely in practice and thus we can safely consider it to be as good as any other algorithm there is for the N Queen problem. Hence, the effective time complexity is O(N2).
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
#arrays #backtracking #mathematical #chessboard-problems #cpp #python
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Pdf2gerb: Perl Script Converts PDF Files to Gerber format
pdf2gerb
Perl script converts PDF files to Gerber format
Pdf2Gerb generates Gerber 274X photoplotting and Excellon drill files from PDFs of a PCB. Up to three PDFs are used: the top copper layer, the bottom copper layer (for 2-sided PCBs), and an optional silk screen layer. The PDFs can be created directly from any PDF drawing software, or a PDF print driver can be used to capture the Print output if the drawing software does not directly support output to PDF.
The general workflow is as follows:
- Design the PCB using your favorite CAD or drawing software.
- Print the top and bottom copper and top silk screen layers to a PDF file.
- Run Pdf2Gerb on the PDFs to create Gerber and Excellon files.
- Use a Gerber viewer to double-check the output against the original PCB design.
- Make adjustments as needed.
- Submit the files to a PCB manufacturer.
Please note that Pdf2Gerb does NOT perform DRC (Design Rule Checks), as these will vary according to individual PCB manufacturer conventions and capabilities. Also note that Pdf2Gerb is not perfect, so the output files must always be checked before submitting them. As of version 1.6, Pdf2Gerb supports most PCB elements, such as round and square pads, round holes, traces, SMD pads, ground planes, no-fill areas, and panelization. However, because it interprets the graphical output of a Print function, there are limitations in what it can recognize (or there may be bugs).
See docs/Pdf2Gerb.pdf for install/setup, config, usage, and other info.
pdf2gerb_cfg.pm
#Pdf2Gerb config settings:
#Put this file in same folder/directory as pdf2gerb.pl itself (global settings),
#or copy to another folder/directory with PDFs if you want PCB-specific settings.
#There is only one user of this file, so we don't need a custom package or namespace.
#NOTE: all constants defined in here will be added to main namespace.
#package pdf2gerb_cfg;
use strict; #trap undef vars (easier debug)
use warnings; #other useful info (easier debug)
##############################################################################################
#configurable settings:
#change values here instead of in main pfg2gerb.pl file
use constant WANT_COLORS => ($^O !~ m/Win/); #ANSI colors no worky on Windows? this must be set < first DebugPrint() call
#just a little warning; set realistic expectations:
#DebugPrint("${\(CYAN)}Pdf2Gerb.pl ${\(VERSION)}, $^O O/S\n${\(YELLOW)}${\(BOLD)}${\(ITALIC)}This is EXPERIMENTAL software. \nGerber files MAY CONTAIN ERRORS. Please CHECK them before fabrication!${\(RESET)}", 0); #if WANT_DEBUG
use constant METRIC => FALSE; #set to TRUE for metric units (only affect final numbers in output files, not internal arithmetic)
use constant APERTURE_LIMIT => 0; #34; #max #apertures to use; generate warnings if too many apertures are used (0 to not check)
use constant DRILL_FMT => '2.4'; #'2.3'; #'2.4' is the default for PCB fab; change to '2.3' for CNC
use constant WANT_DEBUG => 0; #10; #level of debug wanted; higher == more, lower == less, 0 == none
use constant GERBER_DEBUG => 0; #level of debug to include in Gerber file; DON'T USE FOR FABRICATION
use constant WANT_STREAMS => FALSE; #TRUE; #save decompressed streams to files (for debug)
use constant WANT_ALLINPUT => FALSE; #TRUE; #save entire input stream (for debug ONLY)
#DebugPrint(sprintf("${\(CYAN)}DEBUG: stdout %d, gerber %d, want streams? %d, all input? %d, O/S: $^O, Perl: $]${\(RESET)}\n", WANT_DEBUG, GERBER_DEBUG, WANT_STREAMS, WANT_ALLINPUT), 1);
#DebugPrint(sprintf("max int = %d, min int = %d\n", MAXINT, MININT), 1);
#define standard trace and pad sizes to reduce scaling or PDF rendering errors:
#This avoids weird aperture settings and replaces them with more standardized values.
#(I'm not sure how photoplotters handle strange sizes).
#Fewer choices here gives more accurate mapping in the final Gerber files.
#units are in inches
use constant TOOL_SIZES => #add more as desired
(
#round or square pads (> 0) and drills (< 0):
.010, -.001, #tiny pads for SMD; dummy drill size (too small for practical use, but needed so StandardTool will use this entry)
.031, -.014, #used for vias
.041, -.020, #smallest non-filled plated hole
.051, -.025,
.056, -.029, #useful for IC pins
.070, -.033,
.075, -.040, #heavier leads
# .090, -.043, #NOTE: 600 dpi is not high enough resolution to reliably distinguish between .043" and .046", so choose 1 of the 2 here
.100, -.046,
.115, -.052,
.130, -.061,
.140, -.067,
.150, -.079,
.175, -.088,
.190, -.093,
.200, -.100,
.220, -.110,
.160, -.125, #useful for mounting holes
#some additional pad sizes without holes (repeat a previous hole size if you just want the pad size):
.090, -.040, #want a .090 pad option, but use dummy hole size
.065, -.040, #.065 x .065 rect pad
.035, -.040, #.035 x .065 rect pad
#traces:
.001, #too thin for real traces; use only for board outlines
.006, #minimum real trace width; mainly used for text
.008, #mainly used for mid-sized text, not traces
.010, #minimum recommended trace width for low-current signals
.012,
.015, #moderate low-voltage current
.020, #heavier trace for power, ground (even if a lighter one is adequate)
.025,
.030, #heavy-current traces; be careful with these ones!
.040,
.050,
.060,
.080,
.100,
.120,
);
#Areas larger than the values below will be filled with parallel lines:
#This cuts down on the number of aperture sizes used.
#Set to 0 to always use an aperture or drill, regardless of size.
use constant { MAX_APERTURE => max((TOOL_SIZES)) + .004, MAX_DRILL => -min((TOOL_SIZES)) + .004 }; #max aperture and drill sizes (plus a little tolerance)
#DebugPrint(sprintf("using %d standard tool sizes: %s, max aper %.3f, max drill %.3f\n", scalar((TOOL_SIZES)), join(", ", (TOOL_SIZES)), MAX_APERTURE, MAX_DRILL), 1);
#NOTE: Compare the PDF to the original CAD file to check the accuracy of the PDF rendering and parsing!
#for example, the CAD software I used generated the following circles for holes:
#CAD hole size: parsed PDF diameter: error:
# .014 .016 +.002
# .020 .02267 +.00267
# .025 .026 +.001
# .029 .03167 +.00267
# .033 .036 +.003
# .040 .04267 +.00267
#This was usually ~ .002" - .003" too big compared to the hole as displayed in the CAD software.
#To compensate for PDF rendering errors (either during CAD Print function or PDF parsing logic), adjust the values below as needed.
#units are pixels; for example, a value of 2.4 at 600 dpi = .0004 inch, 2 at 600 dpi = .0033"
use constant
{
HOLE_ADJUST => -0.004 * 600, #-2.6, #holes seemed to be slightly oversized (by .002" - .004"), so shrink them a little
RNDPAD_ADJUST => -0.003 * 600, #-2, #-2.4, #round pads seemed to be slightly oversized, so shrink them a little
SQRPAD_ADJUST => +0.001 * 600, #+.5, #square pads are sometimes too small by .00067, so bump them up a little
RECTPAD_ADJUST => 0, #(pixels) rectangular pads seem to be okay? (not tested much)
TRACE_ADJUST => 0, #(pixels) traces seemed to be okay?
REDUCE_TOLERANCE => .001, #(inches) allow this much variation when reducing circles and rects
};
#Also, my CAD's Print function or the PDF print driver I used was a little off for circles, so define some additional adjustment values here:
#Values are added to X/Y coordinates; units are pixels; for example, a value of 1 at 600 dpi would be ~= .002 inch
use constant
{
CIRCLE_ADJUST_MINX => 0,
CIRCLE_ADJUST_MINY => -0.001 * 600, #-1, #circles were a little too high, so nudge them a little lower
CIRCLE_ADJUST_MAXX => +0.001 * 600, #+1, #circles were a little too far to the left, so nudge them a little to the right
CIRCLE_ADJUST_MAXY => 0,
SUBST_CIRCLE_CLIPRECT => FALSE, #generate circle and substitute for clip rects (to compensate for the way some CAD software draws circles)
WANT_CLIPRECT => TRUE, #FALSE, #AI doesn't need clip rect at all? should be on normally?
RECT_COMPLETION => FALSE, #TRUE, #fill in 4th side of rect when 3 sides found
};
#allow .012 clearance around pads for solder mask:
#This value effectively adjusts pad sizes in the TOOL_SIZES list above (only for solder mask layers).
use constant SOLDER_MARGIN => +.012; #units are inches
#line join/cap styles:
use constant
{
CAP_NONE => 0, #butt (none); line is exact length
CAP_ROUND => 1, #round cap/join; line overhangs by a semi-circle at either end
CAP_SQUARE => 2, #square cap/join; line overhangs by a half square on either end
CAP_OVERRIDE => FALSE, #cap style overrides drawing logic
};
#number of elements in each shape type:
use constant
{
RECT_SHAPELEN => 6, #x0, y0, x1, y1, count, "rect" (start, end corners)
LINE_SHAPELEN => 6, #x0, y0, x1, y1, count, "line" (line seg)
CURVE_SHAPELEN => 10, #xstart, ystart, x0, y0, x1, y1, xend, yend, count, "curve" (bezier 2 points)
CIRCLE_SHAPELEN => 5, #x, y, 5, count, "circle" (center + radius)
};
#const my %SHAPELEN =
#Readonly my %SHAPELEN =>
our %SHAPELEN =
(
rect => RECT_SHAPELEN,
line => LINE_SHAPELEN,
curve => CURVE_SHAPELEN,
circle => CIRCLE_SHAPELEN,
);
#panelization:
#This will repeat the entire body the number of times indicated along the X or Y axes (files grow accordingly).
#Display elements that overhang PCB boundary can be squashed or left as-is (typically text or other silk screen markings).
#Set "overhangs" TRUE to allow overhangs, FALSE to truncate them.
#xpad and ypad allow margins to be added around outer edge of panelized PCB.
use constant PANELIZE => {'x' => 1, 'y' => 1, 'xpad' => 0, 'ypad' => 0, 'overhangs' => TRUE}; #number of times to repeat in X and Y directions
# Set this to 1 if you need TurboCAD support.
#$turboCAD = FALSE; #is this still needed as an option?
#CIRCAD pad generation uses an appropriate aperture, then moves it (stroke) "a little" - we use this to find pads and distinguish them from PCB holes.
use constant PAD_STROKE => 0.3; #0.0005 * 600; #units are pixels
#convert very short traces to pads or holes:
use constant TRACE_MINLEN => .001; #units are inches
#use constant ALWAYS_XY => TRUE; #FALSE; #force XY even if X or Y doesn't change; NOTE: needs to be TRUE for all pads to show in FlatCAM and ViewPlot
use constant REMOVE_POLARITY => FALSE; #TRUE; #set to remove subtractive (negative) polarity; NOTE: must be FALSE for ground planes
#PDF uses "points", each point = 1/72 inch
#combined with a PDF scale factor of .12, this gives 600 dpi resolution (1/72 * .12 = 600 dpi)
use constant INCHES_PER_POINT => 1/72; #0.0138888889; #multiply point-size by this to get inches
# The precision used when computing a bezier curve. Higher numbers are more precise but slower (and generate larger files).
#$bezierPrecision = 100;
use constant BEZIER_PRECISION => 36; #100; #use const; reduced for faster rendering (mainly used for silk screen and thermal pads)
# Ground planes and silk screen or larger copper rectangles or circles are filled line-by-line using this resolution.
use constant FILL_WIDTH => .01; #fill at most 0.01 inch at a time
# The max number of characters to read into memory
use constant MAX_BYTES => 10 * M; #bumped up to 10 MB, use const
use constant DUP_DRILL1 => TRUE; #FALSE; #kludge: ViewPlot doesn't load drill files that are too small so duplicate first tool
my $runtime = time(); #Time::HiRes::gettimeofday(); #measure my execution time
print STDERR "Loaded config settings from '${\(__FILE__)}'.\n";
1; #last value must be truthful to indicate successful load
#############################################################################################
#junk/experiment:
#use Package::Constants;
#use Exporter qw(import); #https://perldoc.perl.org/Exporter.html
#my $caller = "pdf2gerb::";
#sub cfg
#{
# my $proto = shift;
# my $class = ref($proto) || $proto;
# my $settings =
# {
# $WANT_DEBUG => 990, #10; #level of debug wanted; higher == more, lower == less, 0 == none
# };
# bless($settings, $class);
# return $settings;
#}
#use constant HELLO => "hi there2"; #"main::HELLO" => "hi there";
#use constant GOODBYE => 14; #"main::GOODBYE" => 12;
#print STDERR "read cfg file\n";
#our @EXPORT_OK = Package::Constants->list(__PACKAGE__); #https://www.perlmonks.org/?node_id=1072691; NOTE: "_OK" skips short/common names
#print STDERR scalar(@EXPORT_OK) . " consts exported:\n";
#foreach(@EXPORT_OK) { print STDERR "$_\n"; }
#my $val = main::thing("xyz");
#print STDERR "caller gave me $val\n";
#foreach my $arg (@ARGV) { print STDERR "arg $arg\n"; }Download Details:
Author: swannman
Source Code: https://github.com/swannman/pdf2gerb
License: GPL-3.0 license
1595797200
N-Queen Problem | Local Search using Hill climbing with random neighbour
The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other.
For example, the following is a solution for 8 Queen problem.
Input:_ N = 4_
Output:
0 1 0 0
0 0 0 1
1 0 0 0
0 0 1 0
Explanation:
The Position of queens are:
1 – {1, 2}
2 – {2, 4}
3 – {3, 1}
4 – {4, 3}
As we can see that we have placed all 4 queens
in a way that no two queens are attacking each other.
So, the output is correct
Input:_ N = 8_
Output:
0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0
0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0
Approach: The idea is to use Hill Climbing Algorithm.
- While there are algorithms like Backtracking to solve N Queen problem, let’s take an AI approach in solving the problem.
- It’s obvious that AI does not guarantee a globally correct solution all the time but it has quite a good success rate of about 97% which is not bad.
- A description of the notions of all terminologies used in the problem will be given and are as follows:-
- Notion of a State – A state here in this context is any configuration of the N queens on the N X N board. Also, in order to reduce the search space let’s add an additional constraint that there can only be a single queen in a particular column. A state in the program is implemented using an array of length N, such that if state[i]=j then there is a queen at column index i and row index j.
- Notion of Neighbours – Neighbours of a state are other states with board configuration that differ from the current state’s board configuration with respect to the position of only a single queen. This queen that differs a state from its neighbour may be displaced anywhere in the same column.
- Optimisation function or Objective function – We know that local search is an optimization algorithm that searches the local space to optimize a function that takes the state as input and gives some value as an output. The value of the objective function of a state here in this context is the number of pairs of queens attacking each other. Our goal here is to find a state with the minimum objective value. This function has a maximum value of NC2 and a minimum value of 0.
Algorithm:
- Start with a random state(i.e, a random configuration of the board).
- Scan through all possible neighbours of the current state and jump to the neighbour with the highest objective value, if found any. If there does not exist, a neighbour, objective strictly higher than the current state but there exists one with equal then jump to any random neighbour(escaping shoulder and/or local optimum).
- Repeat step 2, until a state whose objective is strictly higher than all it’s neighbour’s objectives, is found and then go to step 4.
- The state thus found after the local search is either the local optimum or the global optimum. There is no way of escaping local optima but adding a random neighbour or a random restart each time a local optimum is encountered increases the chances of achieving global optimum(the solution to our problem).
- Output the state and return.
- It is easily visible that the global optimum in our case is 0 since it is the minimum number of pairs of queens that can attack each other. Also, the random restart has a higher chance of achieving global optimum but we still use random neighbour because our problem of N queens does not has a high number of local optima and random neighbour is faster than random restart.
- Conclusion:
- Random Neighbour escapes shoulders but only has a little chance of escaping local optima.
- Random Restart both escapes shoulders and had a high chance of escaping local optima.
Below is the implementation of the Hill-Climbing algorithm.
CPP
// C++ implementation of the
// above approach
#include <iostream>
#include <math.h>
#define N 8
**using** **namespace** std;
// A utility function that configures
// the 2D array "board" and
// array "state" randomly to provide
// a starting point for the algorithm.
**void** configureRandomly(``**int** board[][N],
**int**``* state)
{
// Seed for the random function
**srand**``(``**time**``(0));
// Iterating through the
// column indices
**for** (``**int** i = 0; i < N; i++) {
// Getting a random row index
state[i] = **rand**``() % N;
// Placing a queen on the
// obtained place in
// chessboard.
board[state[i]][i] = 1;
}
}
// A utility function that prints
// the 2D array "board".
**void** printBoard(``**int** board[][N])
{
**for** (``**int** i = 0; i < N; i++) {
cout << " "``;
**for** (``**int** j = 0; j < N; j++) {
cout << board[i][j] << " "``;
}
cout << "\n"``;
}
}
// A utility function that prints
// the array "state".
**void** printState(``**int**``* state)
{
**for** (``**int** i = 0; i < N; i++) {
cout << " " << state[i] << " "``;
}
cout << endl;
}
// A utility function that compares
// two arrays, state1 and state2 and
// returns true if equal
// and false otherwise.
**bool** compareStates(``**int**``* state1,
**int**``* state2)
{
**for** (``**int** i = 0; i < N; i++) {
**if** (state1[i] != state2[i]) {
**return** **false**``;
}
}
**return** **true**``;
}
// A utility function that fills
// the 2D array "board" with
// values "value"
**void** fill(``**int** board[][N], **int** value)
{
**for** (``**int** i = 0; i < N; i++) {
**for** (``**int** j = 0; j < N; j++) {
board[i][j] = value;
}
}
}
// This function calculates the
// objective value of the
// state(queens attacking each other)
// using the board by the
// following logic.
**int** calculateObjective(``**int** board[][N],
**int**``* state)
{
// For each queen in a column, we check
// for other queens falling in the line
// of our current queen and if found,
// any, then we increment the variable
// attacking count.
// Number of queens attacking each other,
// initially zero.
**int** attacking = 0;
// Variables to index a particular
// row and column on board.
**int** row, col;
**for** (``**int** i = 0; i < N; i++) {
// At each column 'i', the queen is
// placed at row 'state[i]', by the
// definition of our state.
// To the left of same row
// (row remains constant
// and col decreases)
row = state[i], col = i - 1;
**while** (col >= 0
&& board[row][col] != 1) {
col--;
}
**if** (col >= 0
&& board[row][col] == 1) {
attacking++;
}
// To the right of same row
// (row remains constant
// and col increases)
row = state[i], col = i + 1;
**while** (col < N
&& board[row][col] != 1) {
col++;
}
**if** (col < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the left up
// (row and col simoultaneously
// decrease)
row = state[i] - 1, col = i - 1;
**while** (col >= 0 && row >= 0
&& board[row][col] != 1) {
col--;
row--;
}
**if** (col >= 0 && row >= 0
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the right down
// (row and col simoultaneously
// increase)
row = state[i] + 1, col = i + 1;
**while** (col < N && row < N
&& board[row][col] != 1) {
col++;
row++;
}
**if** (col < N && row < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the left down
// (col decreases and row
// increases)
row = state[i] + 1, col = i - 1;
**while** (col >= 0 && row < N
&& board[row][col] != 1) {
col--;
row++;
}
**if** (col >= 0 && row < N
&& board[row][col] == 1) {
attacking++;
}
// Diagonally to the right up
// (col increases and row
// decreases)
row = state[i] - 1, col = i + 1;
**while** (col < N && row >= 0
&& board[row][col] != 1) {
col++;
row--;
}
**if** (col < N && row >= 0
&& board[row][col] == 1) {
attacking++;
}
}
// Return pairs.
**return** (``**int**``)(attacking / 2);
}
// A utility function that
// generates a board configuration
// given the state.
**void** generateBoard(``**int** board[][N],
**int**``* state)
{
fill(board, 0);
**for** (``**int** i = 0; i < N; i++) {
board[state[i]][i] = 1;
}
}
// A utility function that copies
// contents of state2 to state1\.
**void** copyState(``**int**``* state1, **int**``* state2)
{
**for** (``**int** i = 0; i < N; i++) {
state1[i] = state2[i];
}
}
// This function gets the neighbour
// of the current state having
// the least objective value
// amongst all neighbours as
// well as the current state.
**void** getNeighbour(``**int** board[][N],
**int**``* state)
{
// Declaring and initializing the
// optimal board and state with
// the current board and the state
// as the starting point.
**int** opBoard[N][N];
**int** opState[N];
copyState(opState,
state);
generateBoard(opBoard,
opState);
// Initializing the optimal
// objective value
**int** opObjective
= calculateObjective(opBoard,
opState);
// Declaring and initializing
// the temporary board and
// state for the purpose
// of computation.
**int** NeighbourBoard[N][N];
**int** NeighbourState[N];
copyState(NeighbourState,
state);
generateBoard(NeighbourBoard,
NeighbourState);
// Iterating through all
// possible neighbours
// of the board.
**for** (``**int** i = 0; i < N; i++) {
**for** (``**int** j = 0; j < N; j++) {
// Condition for skipping the
// current state
**if** (j != state[i]) {
// Initializing temporary
// neighbour with the
// current neighbour.
NeighbourState[i] = j;
NeighbourBoard[NeighbourState[i]][i]
= 1;
NeighbourBoard[state[i]][i]
= 0;
// Calculating the objective
// value of the neighbour.
**int** temp
= calculateObjective(
NeighbourBoard,
NeighbourState);
// Comparing temporary and optimal
// neighbour objectives and if
// temporary is less than optimal
// then updating accordingly.
**if** (temp <= opObjective) {
opObjective = temp;
copyState(opState,
NeighbourState);
generateBoard(opBoard,
opState);
}
// Going back to the original
// configuration for the next
// iteration.
NeighbourBoard[NeighbourState[i]][i]
= 0;
NeighbourState[i] = state[i];
NeighbourBoard[state[i]][i] = 1;
}
}
}
// Copying the optimal board and
// state thus found to the current
// board and, state since c++ doesn't
// allow returning multiple values.
copyState(state, opState);
fill(board, 0);
generateBoard(board, state);
}
**void** hillClimbing(``**int** board[][N],
**int**``* state)
{
// Declaring and initializing the
// neighbour board and state with
// the current board and the state
// as the starting point.
**int** neighbourBoard[N][N] = {};
**int** neighbourState[N];
copyState(neighbourState, state);
generateBoard(neighbourBoard,
neighbourState);
**do** {
// Copying the neighbour board and
// state to the current board and
// state, since a neighbour
// becomes current after the jump.
copyState(state, neighbourState);
generateBoard(board, state);
// Getting the optimal neighbour
getNeighbour(neighbourBoard,
neighbourState);
**if** (compareStates(state,
neighbourState)) {
// If neighbour and current are
// equal then no optimal neighbour
// exists and therefore output the
// result and break the loop.
printBoard(board);
**break**``;
}
**else** **if** (calculateObjective(board,
state)
== calculateObjective(
neighbourBoard,
neighbourState)) {
// If neighbour and current are
// not equal but their objectives
// are equal then we are either
// approaching a shoulder or a
// local optimum, in any case,
// jump to a random neighbour
// to escape it.
// Random neighbour
neighbourState[``**rand**``() % N]
= **rand**``() % N;
generateBoard(neighbourBoard,
neighbourState);
}
} **while** (``**true**``);
}
// Driver code
**int** main()
{
**int** state[N] = {};
**int** board[N][N] = {};
// Getting a starting point by
// randomly configuring the board
configureRandomly(board, state);
// Do hill climbing on the
// board obtained
hillClimbing(board, state);
**return** 0;
}
Output:
0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0
Complexity Analysis
- The time complexity for this algorithm can be divided into three parts:
- Calculating Objective – The calculation of objective involves iterating through all queens on board and checking the no. of attacking queens, which is done by our calculateObjective function in O(N2) time.
- Neighbour Selection and Number of neighbours – The description of neighbours in our problem gives a total of N(N-1) neighbours for the current state. The selection procedure is best fit and therefore requires iterating through all neighbours, which is again O(N2).
- Search Space – The description of neighbours in our problem gives a total of N(N-1) neighbours for the current state. The selection procedure is best fit and therefore requires iterating through all neighbours, which is again O(N2).
- Therefore, the worst-case time complexity of our algorithm is O(NN). But, this worst-case occurs rarely in practice and thus we can safely consider it to be as good as any other algorithm there is for the N Queen problem. Hence, the effective time complexity is O(N2).
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
#arrays #backtracking #mathematical #chessboard-problems #cpp #python
1611112146
Codeigniter 4 Autocomplete Textbox From Database using Typeahead JS - Tuts Make
Autocomplete textbox search from database in codeigniter 4 using jQuery Typeahead js. In this tutorial, you will learn how to implement an autocomplete search or textbox search with database using jquery typehead js example.
This tutorial will show you step by step how to implement autocomplete search from database in codeigniter 4 app using typeahead js.
Autocomplete Textbox Search using jQuery typeahead Js From Database in Codeigniter
- Download Codeigniter Latest
- Basic Configurations
- Create Table in Database
- Setup Database Credentials
- Create Controller
- Create View
- Create Route
- Start Development Server
https://www.tutsmake.com/codeigniter-4-autocomplete-textbox-from-database-using-typeahead-js/
#codeigniter 4 ajax autocomplete search #codeigniter 4 ajax autocomplete search from database #autocomplete textbox in jquery example using database in codeigniter #search data from database in codeigniter 4 using ajax #how to search and display data from database in codeigniter 4 using ajax #autocomplete in codeigniter 4 using typeahead js
1620729846
Why Use WordPress? What Can You Do With WordPress?
Can you use WordPress for anything other than blogging? To your surprise, yes. WordPress is more than just a blogging tool, and it has helped thousands of websites and web applications to thrive. The use of WordPress powers around 40% of online projects, and today in our blog, we would visit some amazing uses of WordPress other than blogging.
What Is The Use Of WordPress?
WordPress is the most popular website platform in the world. It is the first choice of businesses that want to set a feature-rich and dynamic Content Management System. So, if you ask what WordPress is used for, the answer is – everything. It is a super-flexible, feature-rich and secure platform that offers everything to build unique websites and applications. Let’s start knowing them:
1. Multiple Websites Under A Single Installation
WordPress Multisite allows you to develop multiple sites from a single WordPress installation. You can download WordPress and start building websites you want to launch under a single server. Literally speaking, you can handle hundreds of sites from one single dashboard, which now needs applause.
It is a highly efficient platform that allows you to easily run several websites under the same login credentials. One of the best things about WordPress is the themes it has to offer. You can simply download them and plugin for various sites and save space on sites without losing their speed.
2. WordPress Social Network
WordPress can be used for high-end projects such as Social Media Network. If you don’t have the money and patience to hire a coder and invest months in building a feature-rich social media site, go for WordPress. It is one of the most amazing uses of WordPress. Its stunning CMS is unbeatable. And you can build sites as good as Facebook or Reddit etc. It can just make the process a lot easier.
To set up a social media network, you would have to download a WordPress Plugin called BuddyPress. It would allow you to connect a community page with ease and would provide all the necessary features of a community or social media. It has direct messaging, activity stream, user groups, extended profiles, and so much more. You just have to download and configure it.
If BuddyPress doesn’t meet all your needs, don’t give up on your dreams. You can try out WP Symposium or PeepSo. There are also several themes you can use to build a social network.
3. Create A Forum For Your Brand’s Community
Communities are very important for your business. They help you stay in constant connection with your users and consumers. And allow you to turn them into a loyal customer base. Meanwhile, there are many good technologies that can be used for building a community page – the good old WordPress is still the best.
It is the best community development technology. If you want to build your online community, you need to consider all the amazing features you get with WordPress. Plugins such as BB Press is an open-source, template-driven PHP/ MySQL forum software. It is very simple and doesn’t hamper the experience of the website.
Other tools such as wpFoRo and Asgaros Forum are equally good for creating a community blog. They are lightweight tools that are easy to manage and integrate with your WordPress site easily. However, there is only one tiny problem; you need to have some technical knowledge to build a WordPress Community blog page.
4. Shortcodes
Since we gave you a problem in the previous section, we would also give you a perfect solution for it. You might not know to code, but you have shortcodes. Shortcodes help you execute functions without having to code. It is an easy way to build an amazing website, add new features, customize plugins easily. They are short lines of code, and rather than memorizing multiple lines; you can have zero technical knowledge and start building a feature-rich website or application.
There are also plugins like Shortcoder, Shortcodes Ultimate, and the Basics available on WordPress that can be used, and you would not even have to remember the shortcodes.
5. Build Online Stores
If you still think about why to use WordPress, use it to build an online store. You can start selling your goods online and start selling. It is an affordable technology that helps you build a feature-rich eCommerce store with WordPress.
WooCommerce is an extension of WordPress and is one of the most used eCommerce solutions. WooCommerce holds a 28% share of the global market and is one of the best ways to set up an online store. It allows you to build user-friendly and professional online stores and has thousands of free and paid extensions. Moreover as an open-source platform, and you don’t have to pay for the license.
Apart from WooCommerce, there are Easy Digital Downloads, iThemes Exchange, Shopify eCommerce plugin, and so much more available.
6. Security Features
WordPress takes security very seriously. It offers tons of external solutions that help you in safeguarding your WordPress site. While there is no way to ensure 100% security, it provides regular updates with security patches and provides several plugins to help with backups, two-factor authorization, and more.
By choosing hosting providers like WP Engine, you can improve the security of the website. It helps in threat detection, manage patching and updates, and internal security audits for the customers, and so much more.
#use of wordpress #use wordpress for business website #use wordpress for website #what is use of wordpress #why use wordpress #why use wordpress to build a website
1597475640
Laravel 7 Full Text Search MySQL
Here, I will show you how to create full text search in laravel app. You just follow the below easy steps and create full text search with mysql db in laravel.
Laravel 7 Full Text Search Mysql
Let’s start laravel full-text search implementation in laravel 7, 6 versions:
- Step 1: Install Laravel New App
- Step 2: Configuration DB .evn file
- Step 3: Run Migration
- Step 4: Install Full Text Search Package
- Step 5: Add Fake Records in DB
- Step 6: Add Routes,
- Step 7: Create Controller
- Step 8: Create Blade View
- Step 9: Start Development Server
https://www.tutsmake.com/laravel-full-text-search-tutorial/
#laravel full text search mysql #laravel full text search query #mysql full text search in laravel #full text search in laravel 6 #full text search in laravel 7 #using full text search in laravel