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\nABC, XYZ India Pakistan
\nLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
\nLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
\nLorem ipsum dolor sit amet. Quo perspiciatis sunt qui nemo velit aut eaque accusamus ut commodi porro quo alias praesentium At provident error
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\n\r\n The whole universe of A* search technique revolves around the equation:\r\n\r\n f(n) = g(n) + h(n)\r\n where; g(n) - it refers to the actual cost with respect to time taken from the start node to the nth node. and, h(n) - it refers to the estimated cost with respect to the time taken from nth node to the goal.
{\"function heuristic(a,b) {\"} {\"var d = abs(a.i-b.i) + abs(a.j-b.j);\"} {\" return d ; \"} {\" } \"} {\" var cols = 25; \"} {\"var rows = 25; \"} {\"var grid = new Array(cols); \"} {\" var OpenSet = []; \"} {\" var ClosedSet = []; \"} {\" var start; \"} {\" var end; \"} {\" var w,h; \"} {\" var path = []; \"} {\" function setup() \"} {\" { \"} {\" createCanvas(400, 400); \"} {\" console.log('A*'); \"} {\" for( var i=0; i
\r\n {\" for( var j=0; j
\r\n {\" grid[i][j]= new spot(); \"}
\r\n {\" } \"}
\r\n {\" } \"}
\r\n\r\n {\" for( var i=0; i
\r\n {\" for( var j=0; j
\r\n {\" grid[i][j].addNeighbours(grid); \"}
\r\n {\" } \"}
\r\n\r\n {\" start = grid[0][0]; \"}
\r\n {\" end = grid[cols - 1][rows - 1]; \"}
\r\n\r\n {\" OpenSet.push(start); \"}
\r\n\r\n {\" console.log(grid); \"}
\r\n {\" } \"}
\r\n\r\n\r\n {\" function draw(){ \"} {\" if(OpenSet.length > 0){ \"} {\" var winner = 0; \"} {\" for( var i=0; i< OpenSet.length; i++){ \"} {\" if( OpenSet[i].f < OpenSet[winner].f) { \"} {\" winner = i; \"} {\" } \"} {\" } \"} {\" var current = OpenSet[winner]; \"} {\" if( current === end){ \"} {\" noLoop(); \"} {\" console.log(DONE!); \"} {\" } \"} {\" removeFromArray(OpenSet, current); \"} {\" ClosedSet.push(current); \"} \r\n\r\n {\" var neighbours = current.neighbours; \"} {\" for(var i = 0; i < neighbours.length; i++) \"} {\" var neighbours = neighbours[i]; \"} {\" if(!ClosedSet.includes(neighbour)){ \"} {\" var tempG = current.g + 1; \"} {\" if(OpenSet.includes(neighbour)){ \"} {\" if(tempG < neighbour.g){ \"} {\" neighbour.g = tempG; \"} {\" } \"} {\" } \"} {\" else { \"} {\" neighbour.g = tempG; \"} {\" OpenSet.push(neighbour); \"} {\" } \"} {\" neighbour.h = heuristic(neighbour, end); \"} {\" neighbour.f = neighbour.g + neighbour.h; \"} {\" neighbour.previous = current; \"} {\" } \"} {\" }else { \"} {\" } \"} \n Greedy best-first search algorithm always selects the path which appears best at that moment. It is the combination of depth-first search and breadth-first search algorithms. It uses the heuristic function and search. Best-first search allows us to take the advantages of both algorithms. With the help of best-first search, at each step, we can choose the most promising node. In the best first search algorithm, we expand the node which is closest to the goal node and the closest cost is estimated by heuristic function, i.e.
\n\n f(n)= g(n). Where, h(n)= estimated cost from node n to the goal.
\n\n The greedy best first algorithm is implemented by the priority queue.
\n\n Advantages: Best first search can switch between BFS and DFS by gaining the advantages of both the algorithms. This algorithm is more efficient than BFS and DFS algorithms.
\n\n Disadvantages: It can behave as an unguided depth-first search in the worst case scenario. It can get stuck in a loop as DFS. This algorithm is not optimal.
\n
\n Best first search algorithm:
\n Step 1: Place the starting node into the OPEN list.
\n Step 2: If the OPEN list is empty, Stop and return failure.
\n Step 3: Remove the node n, from the OPEN list which has the lowest value of h(n), and places it in the CLOSED list.
\n Step 4: Expand the node n, and generate the successors of node n.
\n Step 5: Check each successor of node n, and find whether any node is a goal node or not. If any successor node is goal node, then return success and terminate the search, else proceed to Step 6.
\n Step 6: For each successor node, algorithm checks for evaluation function f(n), and then check if the node has been in either OPEN or CLOSED list. If the node has not been in both list, then add it to the OPEN list.
\n Step 7: Return to Step 2.\n
\n \n {\"function getNeighbours(node, grid) {\"}
\n {\"let neighbours = [];\"}
\n {\"let { row, col } = node;\"}
\n {\"if (row !== 0) neighbours.push(grid[row - 1][col]);\"}
\n {\"if (col !== grid[0].length - 1) neighbours.push(grid[row][col + 1]);\"}
\n {\"if (row !== grid.length - 1) neighbours.push(grid[row + 1][col]);\"}
\n {\"if (col !== 0) neighbours.push(grid[row][col - 1]);\"}
\n {\"return neighbours.filter(\"}
\n {\"(neighbour) => !neighbour.isWall && !neighbour.isVisited\"}
\n {\" );\"}
\n {\"}\"}
\n {\"\"}
\n {\"function manhattenDistance(node, finishNode) {\"}
\n {\"let x = Math.abs(node.row - finishNode.row);\"}
\n {\"let y = Math.abs(node.col - finishNode.col);\"}
\n {\"return x + y;\"}
\n {\"}\"}
\n {\"\"}
\n {\"function neighbourNotInUnvisitedNodes(neighbour, unvisitedNodes) {\"}
\n {\"for (let node of unvisitedNodes) {\"}
\n {\"if (node.row === neighbour.row && node.col === neighbour.col) {\"}
\n {\"return false;\"}
\n {\"}\"}
\n {\"}\"}
\n {\"return true;\"}
\n {\"}\"}
\n \n
\n Bidirectional search is a graph search where unlike Breadth First search and Depth First Search, the search begins simultaneously from Source vertex and Goal vertex and ends when the two searches meet somewhere in between in the graph. This is thus especially used for getting results in a fraction of the time taken by both DFS and FS searches. The search from the initial node is forward search while that from the goal node is backwards. It is also based on heuristic search meaning finding the shortest path to goal optimally.
\n\n Advantages:
\n\n 1.One of the main advantages of bidirectional searches is the speed at which we get the desired results.
\n 2.It drastically reduces the time taken by the search by having simultaneous searches.
\n 3.It also saves resources for users as it requires less memory capacity to store all the searches.
\n\n Disadvantages:
\n\n 1.The fundamental issue with bidirectional search is that the user should be aware of the goal state to use bidirectional search and thereby to decrease its use cases drastically.
\n 2.The implementation is another challenge as additional code and instructions are needed to implement this algorithm, and also care has to be taken as each node and step to implement such searches.
\n 3.The algorithm must be robust enough to understand the intersection when the search should come to an end or else there’s a possibility of an infinite loop.
\n 4.It is also not possible to search backwards through all states.
\n
\n Bidirectional Search Algorithm Steps:
\n \n Step 1: Say, A is the initial node and O is the goal node, and H is the intersection node.
\n\n Step 2: We will start searching simultaneously from start to goal node and backward from goal to start node.
\n\n Step 3: Whenever the forward search and backward search intersect at one node, then the searching stops.
\n
\n \n {\"export function bidirectionalSearch(grid, startRow, startCol, finRow, finCol, checkboxVal) {\"}
\n {\"const visitedNodesInOrder = [];\"}
\n {\"let q1 = [], q2 = [];\"}
\n {\"let dirx = [-1, 1, 0, 0];\"}
\n {\"let diry = [0, 0, -1, 1];\"}
\n {\"q1.push([startRow, startCol]);\"}
\n {\" q2.push([finRow, finCol]);\"}
\n {\"let table = [];\"}
\n {\"\"}
\n {\" for (let i = 0; i < grid.length; ++i) {\"}
\n {\"let tmp = [];\"}
\n {\"\"}
\n {\"for (let j = 0; j < grid[0].length; ++j)\"}
\n {\"tmp.push(false);\"}
\n {\"\"}
\n {\"table.push(tmp);\"}
\n {\"}\"}
\n {\"\"}
\n {\"if (checkboxVal) {\"}
\n {\"dirx = [-1, -1, -1, 0, 0, 1, 1, 1];\"}
\n {\"diry = [-1, 0, 1, -1, 1, -1, 0, 1];\"}
\n {\"}\"}
\n {\"\"}
\n {\"while (q1.length || q2.length) {\"}
\n {\"const [row1, col1] = (!q1.length) ? [-1, -1]:q1.shift();\"}
\n {\"const [row2, col2] = (!q2.length) ? [-1, -1]:q2.shift();\"}
\n {\"if (isValid(grid, row1, col1)) grid[row1][col1].isVisited = true;\"}
\n {\"if (isValid(grid, row2, col2)) table[row2][col2] = true;\"}
\n {\"let newLvl = [];\"}
\n {\"\"}
\n {\"for (let i = 0; i < dirx.length; ++i) {\"}
\n {\"const newRow1 = row1 + dirx[i];\"}
\n {\"const newRow2 = row2 + dirx[i];\"}
\n {\"const newCol1 = col1 + diry[i];\"}
\n {\"const newCol2 = col2 + diry[i];\"}
\n {\"\"}
\n {\"if (isValid(grid, row1, col1) && isValid(grid, newRow1, newCol1)) {\"}
\n {\"if (!grid[newRow1][newCol1].isVisited && !grid[newRow1][newCol1].isWall) {\"}
\n {\"if (table[newRow1][newCol1]) {\"}
\n {\"if (newLvl.length) visitedNodesInOrder.push(newLvl);\"}
\n {\"return [visitedNodesInOrder, grid[row1][col1], grid[newRow1][newCol1]];\"}
\n {\"}\"}
\n {\"grid[newRow1][newCol1].isVisited = true;\"}
\n {\"grid[newRow1][newCol1].previousNode = grid[row1][col1];\"}
\n {\"q1.push([newRow1, newCol1]);\"}
\n {\"newLvl.push([newRow1, newCol1]);\"}
\n {\"}\"}
\n {\"}\"}
\n {\"if (isValid(grid, row2, col2) && isValid(grid, newRow2, newCol2)) {\"}
\n {\"if (!table[newRow2][newCol2] && !grid[newRow2][newCol2].isWall) {\"}
\n {\"if (grid[newRow2][newCol2].isVisited) {\"}
\n {\"if (newLvl.length) visitedNodesInOrder.push(newLvl);\"}
\n {\"return [visitedNodesInOrder, grid[newRow2][newCol2], grid[row2][col2]];\"}
\n {\"}\"}
\n {\"table[newRow2][newCol2] = true;\"}
\n {\"grid[newRow2][newCol2].previousNode = grid[row2][col2];\"}
\n {\"q2.push([newRow2, newCol2]);\"}
\n {\"newLvl.push([newRow2, newCol2]);\"}
\n {\"}\"}
\n {\"}\"}
\n {\"}\"}
\n {\"visitedNodesInOrder.push(newLvl);\"}
\n {\"}\"}
\n {\"return [visitedNodesInOrder, grid[startRow][startCol], grid[finRow][finCol]];\"}
\n {\"}\"}
\n {\"function isValid(grid, row, col) {\"}
\n {\"return (row < 0 || row >= grid.length || col < 0 || col >= grid[0].length) ? false:true;\"}
\n {\"}\"}
\n \n\n
\n Depth first search algorithm begins the searching from the root node and goes down till the leaf of a branch at a time looking for a particular key. If the key is not found, the searching retraces its steps back to the point from where the other branch was left unexplored and the same procedure is repeated for that branch.\n
Since DFS is of RECURSIVE nature, this can be implemented using STACKS.\n
APPLICATION
\n 1. Solving maze-like puzzles with only one solution: DFS can be used to find all solutions to a maze problem by only considering nodes on the current path in the visited set.
\n 2. Path Finding: DFS is used for finding path between two given nodes - source and destination and cycle detection in graphs\n
\n Depth first search algorithm:
\n Step 1:Push the source node to the stack.
\n Step 2:Maintain a data structure to mark if a node is visited or not.
\n Step 3:Mark source node S as visited: visited[S] = True
\n Step 4: While stack is not empty repeat steps 5 - 8 below
\n Step 5: Check each successor of node n, and find whether any node is a goal node or not. If any successor node is goal node, then return success and terminate the search, else proceed to Step 6.
\n Step 6: For each successor node, algorithm checks for evaluation function f(n), and then check if the node has been in either OPEN or CLOSED list. If the node has not been in both list, then add it to the OPEN list.
\n Step 7: Return to Step 2.\n
\n \n {\"Graph.prototype.dfsRecursive = function (start) {\"}
\n {\"const result = [];\"}
\n {\"const visited = {};\"}
\n {\"const adjacencyList = this.adjacencyList;\"}
\n {\"(function dfs(vertex) {\"}
\n {\"if (!vertex) return null;\"}
\n {\"visited[vertex] = true;\"}
\n {\"result.push(vertex);\"}
\n {\"adjacencyList[vertex].forEach((neighbor) => {\"}
\n {\" if (!visited[neighbor]) {\"}
\n {\"return dfs(neighbor);\"}
\n {\"}\"}
\n {\" });\"}
\n {\" })(start);\"}
\n {\"return result;\"}
\n {\"};\"}
\n
\n Step 1. Initialization Phase: All the vectors of the population of food source, , are initialized (i = 1…SN, where SN is population size) by scout bees and control parameters being set. Each vector holds n variables, which is optimized, to minimize the objective function. The following equation is used for initialization phase:\n where li and ui respectively are the lower and upper bound parameters of xi.
\n Step 2.Employed Bees Phase: In this phase, the search for a new food source, , increases in order to have more nectar around the neighbourhood of the food source, . Once a neighbouring food source is found, its profitability or fitness is evaluated. The new neighbouring food source is defined by using following formula:\n where xj is a random selected food source and Øi is a random number of [-a, a]. Once the new food source, vi, is produced its profitability is measured and a greedy selection is applied between and . The exploration happens if the difference between xi − xj is large and the exploitation behaviour is when the difference is small. The fitness value of the solution, fiti(), is determined using following equation:\n where is the objective function value of solution.
\n Step 3. Onlooker Phase: Onlooker bees that are waiting in the hive choose their food sources depending on probability values measured using the fitness value and the information shared by employed bees.
\n Step 4. Scout Bees Phase: The scout bees are those unemployed bees that choose their food sources randomly. Employed bees whose fitness values cannot be improved through predetermined number of iterations, called as limit or abandonment criteria, become the scout bees and all their food sources get abandoned.
\n Step 5. The best fitness value and the position associated to that value are memorized.
\n Step 6. Termination Checking Phase: If the termination condition is met, the programme terminates, otherwise the programme returns to Step 2 and repeats until the termination condition is met.
\n \n
\n\n \n
\nCongratulations!!! You did it.
\n You went wrong somewhere!!!\n
\n Click on Undo to try again.\n
\n Assume given set of some elements, say w[1] … w[n]. Tree diagrams can be used to design backtracking algorithms. The following tree diagram depicts approach of generating variable sized tuple.
\n\n A node represents function call and a branch represents candidate element. The root node contains n children. In other words, root considers every element of the set as different branch. The next level sub-trees correspond to the subsets that includes the parent node. The branches at each level represent tuple element to be considered. For example, if we are at level 1, tuple_vector[1] can take any value of n branches generated. If we are at level 2 of left most node, tuple_vector[2] can take any value of (n-1) branches generated, and so on…
\n\n For example the left most child of root generates all those subsets that include w[1]. Similarly the second child of root generates all those subsets that includes w[2] and excludes w[1].
\n\n As we go down along depth of tree we perform required operation on elements so far, and if the current sub-solution is satisfying explicit constraints, we will continue to generate child nodes further. Whenever the constraints are not met, we stop further generation of sub-trees of that node, and backtrack to previous node to explore the nodes not yet explored. In many scenarios, it saves considerable amount of processing time.\n
\n\n The tree should trigger a clue to implement the backtracking algorithm. It prints all those subsets whose solution meeting required condition. We need to explore the nodes along the breadth and depth of the tree. Generating nodes along breadth is controlled by loop and nodes along the depth are generated using recursion (post order traversal).
\n
{\"// pseudo code\"} {\"bool BacktrackingSolve(configuration Conf)\"} {\"{\"} {\"// Base case\"}{\"if (no more choices):\"}{\"if (whether Conf is goal state)\"} {\"return true\"} {\"else\"} {\"return false\"}{\"// recursively making a choice c\"} {\"for (all available choices) {\"} {\"// make a choice\"} {\"Make one choice c and update the Conf\"} {\"status = BacktrackingSolve(updated conf)\"} {\"if (status is true)\"} {\"Execute some logics\"} {\"else\"} {\"Unmake the choice c and revert to old Conf\"} {\"}\"}{\"return false\"} {\"}\"} \n {\"//function type variable solveSudoku is created\"}
\n {\"var solveSudoku = function(board) {\"}
\n {\"//sudokusolver is recursively called till we obtain the solution\"}
\n {\"function sudokusolver(board,i,j) {\"}
\n {\"if(i===9)\"}
\n {\"return true;\"}
\n {\"//move to next line\"}
\n {\"if(j===9)\"}
\n {\"return sudokusolver(board,i+1,0);\"}
\n {\"if(board[i][j]==='.') {\"}
\n {\"let char = '1';\"}
\n {\"while(char <= 9){\"}
\n {\"if(isValidSudoku(i, j, char)) {\"}
\n {\"board[i][j] = char;\"}
\n {\"if(sudokusolver(board,i,j+1))\"}
\n {\"return true;\"}
\n {\"else\"}
\n {\"board[i][j] = '.';\"}
\n {\"}\"}
\n {\"char = (parseInt(char) + 1).toString();\"}
\n {\"}\"}
\n {\"return false;\"}
\n {\"}\"}
\n {\"else\"}
\n {\"return sudokusolver(board,i,j+1);\"}
\n {\"}\"}
\n
\n {\"//check if the current char at index [row,col] is valid or not\"}
\n {\"function isValidSudoku(row, col, char) {\"}
\n {\"//check if char in present in row\"}
\n {\"for(let i=0;i<9;i++)\"}
\n {\"if(board[row][i]===char)\"}
\n {\"return false;\"}
\n {\"//check of char is present in column\"}
\n {\"for(let i=0;i<9;i++)\"}
\n {\"if(board[i][col]===char)\"}
\n {\"return false;\"}
\n {\"//check if char is present in box\"}
\n {\"let x=Math.floor(row/3)*3;\"}
\n {\"let y=Math.floor(col/3)*3;\"}
\n {\"for(let i=0;i<3;i++)\"}
\n {\"for(let j=0;j<3;j++)\"}
\n {\"if(board[x + i][y + j]===char)\"}
\n {\"return false;\"}
\n {\"return true;\"}
\n {\"}\"}
\n {\"sudokusolver(board,0,0);\"}
\n {\"};\"}
\n
\n The whole universe of A* search technique revolves around the equation:\n\n f(n) = g(n) + h(n)\n where; g(n) - it refers to the actual cost with respect to time taken from the start node to the nth node. and, h(n) - it refers to the estimated cost with respect to the time taken from nth node to the goal.
{\"function heuristic(a,b) {\"} {\"var d = abs(a.i-b.i) + abs(a.j-b.j);\"} {\" return d ; \"} {\" } \"} {\" var cols = 25; \"} {\"var rows = 25; \"} {\"var grid = new Array(cols); \"} {\" var OpenSet = []; \"} {\" var ClosedSet = []; \"} {\" var start; \"} {\" var end; \"} {\" var w,h; \"} {\" var path = []; \"} {\" function setup() \"} {\" { \"} {\" createCanvas(400, 400); \"} {\" console.log('A*'); \"} {\" for( var i=0; i
\n {\" for( var j=0; j
\n {\" grid[i][j]= new spot(); \"}
\n {\" } \"}
\n {\" } \"}
\n\n {\" for( var i=0; i
\n {\" for( var j=0; j
\n {\" grid[i][j].addNeighbours(grid); \"}
\n {\" } \"}
\n\n {\" start = grid[0][0]; \"}
\n {\" end = grid[cols - 1][rows - 1]; \"}
\n\n {\" OpenSet.push(start); \"}
\n\n {\" console.log(grid); \"}
\n {\" } \"}
\n\n\n {\" function draw(){ \"} {\" if(OpenSet.length > 0){ \"} {\" var winner = 0; \"} {\" for( var i=0; i< OpenSet.length; i++){ \"} {\" if( OpenSet[i].f < OpenSet[winner].f) { \"} {\" winner = i; \"} {\" } \"} {\" } \"} {\" var current = OpenSet[winner]; \"} {\" if( current === end){ \"} {\" noLoop(); \"} {\" console.log(DONE!); \"} {\" } \"} {\" removeFromArray(OpenSet, current); \"} {\" ClosedSet.push(current); \"} \n\n {\" var neighbours = current.neighbours; \"} {\" for(var i = 0; i < neighbours.length; i++) \"} {\" var neighbours = neighbours[i]; \"} {\" if(!ClosedSet.includes(neighbour)){ \"} {\" var tempG = current.g + 1; \"} {\" if(OpenSet.includes(neighbour)){ \"} {\" if(tempG < neighbour.g){ \"} {\" neighbour.g = tempG; \"} {\" } \"} {\" } \"} {\" else { \"} {\" neighbour.g = tempG; \"} {\" OpenSet.push(neighbour); \"} {\" } \"} {\" neighbour.h = heuristic(neighbour, end); \"} {\" neighbour.f = neighbour.g + neighbour.h; \"} {\" neighbour.previous = current; \"} {\" } \"} {\" }else { \"} {\" } \"} \n Lorem ipsum dolor sit amet consectetur, adipisicing elit.\n Accusamus at nulla rem. Ullam, at voluptas reprehenderit odit\n molestiae autem nam.\n
\nCongratulations!!! You did it.
\n You went wrong somewhere!!!\n
\n Press on Undo to try again.\n
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