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Find korteste afstand fra en vagt i en bank

Givet en matrix, der er fyldt med 'O' 'G' og 'W', hvor 'O' repræsenterer åben plads 'G' repræsenterer vagter og 'W' repræsenterer vægge i en bank. Udskift alle O'erne i matrixen med deres korteste afstand fra en vagt uden at være i stand til at gå gennem nogen vægge. Udskift også afskærmningerne med 0 og væggene med -1 i outputmatrix.

Forventet Tidskompleksitet er O(MN) for en M x N matrix.
Forventet Hjælpeplads er O(MN) for en M x N matrix.



Eksempler:

O ==> Open Space G ==> Guard W ==> Wall   Input:    O O O O G O W W O O O O O W O G W W W O O O O O G   Output:    3 3 2 1 0 2 -1 -1 2 1 1 2 3 -1 2 0 -1 -1 -1 1 1 2 2 1 0

Ideen er at lave BFS. Vi sætter først alle celler, der indeholder vagterne i kø, og sløjfer, indtil køen ikke er tom. For hver iteration af løkken sætter vi den forreste celle ud af køen og for hver af dens fire tilstødende celler, hvis cellen er et åbent område, og dens afstand fra vagten ikke beregnes, men vi opdaterer dens afstand og sætter den i kø. Til sidst efter BFS-proceduren er overstået, udskriver vi afstandsmatrixen. 

maskinsprog

Nedenfor er implementering af ovenstående idé -  



C++
// C++ program to replace all of the O's in the matrix // with their shortest distance from a guard #include    using namespace std; // store dimensions of the matrix #define M 5 #define N 5 // An Data Structure for queue used in BFS struct queueNode {  // i j and distance stores x and y-coordinates  // of a matrix cell and its distance from guard  // respectively  int i j distance; }; // These arrays are used to get row and column // numbers of 4 neighbors of a given cell int row[] = { -1 0 1 0}; int col[] = { 0 1 0 -1 }; // return true if row number and column number // is in range bool isValid(int i int j) {  if ((i < 0 || i > M - 1) || (j < 0 || j > N - 1))  return false;  return true; } // return true if current cell is an open area and its // distance from guard is not calculated yet bool isSafe(int i int j char matrix[][N] int output[][N]) {  if (matrix[i][j] != 'O' || output[i][j] != -1)  return false;  return true; } // Function to replace all of the O's in the matrix // with their shortest distance from a guard void findDistance(char matrix[][N]) {  int output[M][N];  queue<queueNode> q;  // finding Guards location and adding into queue  for (int i = 0; i < M; i++)  {  for (int j = 0; j < N; j++)  {  // initialize each cell as -1  output[i][j] = -1;  if (matrix[i][j] == 'G')  {  queueNode pos = {i j 0};  q.push(pos);  // guard has 0 distance  output[i][j] = 0;  }  }  }  // do till queue is empty  while (!q.empty())  {  // get the front cell in the queue and update  // its adjacent cells  queueNode curr = q.front();  int x = curr.i y = curr.j dist = curr.distance;  // do for each adjacent cell  for (int i = 0; i < 4; i++)  {  // if adjacent cell is valid has path and  // not visited yet en-queue it.  if (isSafe(x + row[i] y + col[i] matrix output)  && isValid(x + row[i] y + col[i]))  {  output[x + row[i]][y + col[i]] = dist + 1;  queueNode pos = {x + row[i] y + col[i] dist + 1};  q.push(pos);  }  }  // dequeue the front cell as its distance is found  q.pop();  }  // print output matrix  for (int i = 0; i < M; i++)  {  for (int j = 0; j < N; j++)  cout << std::setw(3) << output[i][j];  cout << endl;  } } // Driver code int main() {  char matrix[][N] =  {  {'O' 'O' 'O' 'O' 'G'}  {'O' 'W' 'W' 'O' 'O'}  {'O' 'O' 'O' 'W' 'O'}  {'G' 'W' 'W' 'W' 'O'}  {'O' 'O' 'O' 'O' 'G'}  };  findDistance(matrix);  return 0; } 
Java
// Java program to replace all of the O's // in the matrix with their shortest  // distance from a guard  package Graphs; import java.util.LinkedList; import java.util.Queue; public class MinDistanceFromaGuardInBank{   // Store dimensions of the matrix  int M = 5; int N = 5; class Node  {  int i j dist;  Node(int i int j int dist)  {  this.i = i;  this.j = j;  this.dist = dist;  } } // These arrays are used to get row // and column numbers of 4 neighbors // of a given cell  int row[] = { -1 0 1 0 }; int col[] = { 0 1 0 -1 }; // Return true if row number and  // column number is in range  boolean isValid(int i int j) {  if ((i < 0 || i > M - 1) ||  (j < 0 || j > N - 1))  return false;  return true; } // Return true if current cell is  // an open area and its distance  // from guard is not calculated yet  boolean isSafe(int i int j char matrix[][]  int output[][]) {  if (matrix[i][j] != 'O' ||   output[i][j] != -1)  return false;    return true; } // Function to replace all of the O's  // in the matrix with their shortest // distance from a guard  void findDistance(char matrix[][]) {  int output[][] = new int[M][N];  Queue<Node> q = new LinkedList<Node>();    // Finding Guards location and  // adding into queue   for(int i = 0; i < M; i++)  {  for(int j = 0; j < N; j++)  {    // Initialize each cell as -1   output[i][j] = -1;    if (matrix[i][j] == 'G')  {  q.add(new Node(i j 0));    // Guard has 0 distance   output[i][j] = 0;  }  }  }    // Do till queue is empty   while (!q.isEmpty())  {    // Get the front cell in the queue  // and update its adjacent cells   Node curr = q.peek();  int x = curr.i;  int y = curr.j;  int dist = curr.dist;    // Do for each adjacent cell   for (int i = 0; i < 4; i++)   {    // If adjacent cell is valid has  // path and not visited yet  // en-queue it.   if (isValid(x + row[i] y + col[i]))  {  if (isSafe(x + row[i] y + col[i]  matrix output))   {  output[x + row[i]][y + col[i]] = dist + 1;  q.add(new Node(x + row[i]  y + col[i]  dist + 1));  }  }  }    // Dequeue the front cell as   // its distance is found   q.poll();  }    // Print output matrix   for(int i = 0; i < M; i++)   {  for(int j = 0; j < N; j++)  {  System.out.print(output[i][j] + ' ');  }  System.out.println();  } } // Driver code public static void main(String args[]) {  char matrix[][] = { { 'O' 'O' 'O' 'O' 'G' }  { 'O' 'W' 'W' 'O' 'O' }  { 'O' 'O' 'O' 'W' 'O' }  { 'G' 'W' 'W' 'W' 'O' }  { 'O' 'O' 'O' 'O' 'G' } };    MinDistanceFromaGuardInBank g =   new MinDistanceFromaGuardInBank();    g.findDistance(matrix); } } // This code is contributed by Shobhit Yadav 
Python3
# Python3 program to replace all of the O's in the matrix # with their shortest distance from a guard from collections import deque as queue # store dimensions of the matrix M = 5 N = 5 # These arrays are used to get row and column # numbers of 4 neighbors of a given cell row = [-1 0 1 0] col = [0 1 0 -1] # return true if row number and column number # is in range def isValid(i j): if ((i < 0 or i > M - 1) or (j < 0 or j > N - 1)): return False return True # return true if current cell is an open area and its # distance from guard is not calculated yet def isSafe(i jmatrix output): if (matrix[i][j] != 'O' or output[i][j] != -1): return False return True # Function to replace all of the O's in the matrix # with their shortest distance from a guard def findDistance(matrix): output = [[ -1 for i in range(N)]for i in range(M)] q = queue() # finding Guards location and adding into queue for i in range(M): for j in range(N): # initialize each cell as -1 output[i][j] = -1 if (matrix[i][j] == 'G'): pos = [i j 0] q.appendleft(pos) # guard has 0 distance output[i][j] = 0 # do till queue is empty while (len(q) > 0): # get the front cell in the queue and update # its adjacent cells curr = q.pop() x y dist = curr[0] curr[1] curr[2] # do for each adjacent cell for i in range(4): # if adjacent cell is valid has path and # not visited yet en-queue it. if isValid(x + row[i] y + col[i]) and isSafe(x + row[i] y + col[i] matrix output) : output[x + row[i]][y + col[i]] = dist + 1 pos = [x + row[i] y + col[i] dist + 1] q.appendleft(pos) # print output matrix for i in range(M): for j in range(N): if output[i][j] > 0: print(output[i][j] end=' ') else: print(output[i][j]end=' ') print() # Driver code matrix = [['O' 'O' 'O' 'O' 'G'] ['O' 'W' 'W' 'O' 'O'] ['O' 'O' 'O' 'W' 'O'] ['G' 'W' 'W' 'W' 'O'] ['O' 'O' 'O' 'O' 'G']] findDistance(matrix) # This code is contributed by mohit kumar 29 
C#
// C# program to replace all of the O's // in the matrix with their shortest  // distance from a guard  using System; using System.Collections.Generic; public class Node  {  public int i j dist;  public Node(int i int j int dist)  {  this.i = i;  this.j = j;  this.dist = dist;  } } public class MinDistanceFromaGuardInBank {  // Store dimensions of the matrix   static int M = 5;  static int N = 5;  // These arrays are used to get row  // and column numbers of 4 neighbors  // of a given cell   static int[] row = { -1 0 1 0 };  static int[] col = { 0 1 0 -1 };  // Return true if row number and   // column number is in range   static bool isValid(int i int j)  {  if ((i < 0 || i > M - 1) || (j < 0 || j > N - 1))  return false;  return true;  }  // Return true if current cell is   // an open area and its distance   // from guard is not calculated yet   static bool isSafe(int i int j char[] matrixint[] output)  {  if (matrix[ij] != 'O' || output[ij] != -1)  {  return false;  }  return true;  }  // Function to replace all of the O's   // in the matrix with their shortest  // distance from a guard   static void findDistance(char[] matrix)  {  int[] output = new int[MN];  Queue<Node> q = new Queue<Node>();  // Finding Guards location and  // adding into queue   for(int i = 0; i < M; i++)  {  for(int j = 0; j < N; j++)  {  // Initialize each cell as -1   output[i j] = -1;  if (matrix[i j] == 'G')  {  q.Enqueue(new Node(i j 0));  // Guard has 0 distance   output[i j] = 0;  }  }  }  // Do till queue is empty   while (q.Count != 0)  {  // Get the front cell in the queue  // and update its adjacent cells   Node curr = q.Peek();   int x = curr.i;  int y = curr.j;  int dist = curr.dist;  // Do for each adjacent cell   for (int i = 0; i < 4; i++)   {  // If adjacent cell is valid has  // path and not visited yet  // en-queue it.   if (isValid(x + row[i] y + col[i]))  {  if (isSafe(x + row[i] y + col[i]matrix output))   {  output[x + row[i]  y + col[i]] = dist + 1;  q.Enqueue(new Node(x + row[i]y + col[i]dist + 1));  }  }  }  // Dequeue the front cell as   // its distance is found   q.Dequeue();  }  // Print output matrix   for(int i = 0; i < M; i++)  {  for(int j = 0; j < N; j++)  {  Console.Write(output[ij] + ' ');  }  Console.WriteLine();  }  }  // Driver code  static public void Main ()  {  char[] matrix ={ { 'O' 'O' 'O' 'O' 'G' }  { 'O' 'W' 'W' 'O' 'O' }  { 'O' 'O' 'O' 'W' 'O' }  { 'G' 'W' 'W' 'W' 'O' }  { 'O' 'O' 'O' 'O' 'G' } };  findDistance(matrix);  } } // This code is contributed by avanitrachhadiya2155 
JavaScript
<script> // Javascript program to replace all of the O's // in the matrix with their shortest // distance from a guard // Store dimensions of the matrix let M = 5; let N = 5; class Node {  constructor(ijdist)  {  this.i = i;  this.j = j;  this.dist = dist;  } } // These arrays are used to get row // and column numbers of 4 neighbors // of a given cell let row=[-1 0 1 0]; let col=[0 1 0 -1 ]; // Return true if row number and // column number is in range function isValid(ij) {  if ((i < 0 || i > M - 1) ||  (j < 0 || j > N - 1))  return false;    return true; } // Return true if current cell is // an open area and its distance // from guard is not calculated yet function isSafe(ijmatrixoutput) {  if (matrix[i][j] != 'O' ||  output[i][j] != -1)  return false;    return true; } // Function to replace all of the O's // in the matrix with their shortest // distance from a guard function findDistance(matrix) {  let output = new Array(M);    for(let i=0;i<M;i++)  {  output[i]=new Array(N);  }  let q = [];    // Finding Guards location and  // adding into queue  for(let i = 0; i < M; i++)  {  for(let j = 0; j < N; j++)  {    // Initialize each cell as -1  output[i][j] = -1;    if (matrix[i][j] == 'G')  {  q.push(new Node(i j 0));    // Guard has 0 distance  output[i][j] = 0;  }  }  }    // Do till queue is empty  while (q.length!=0)  {    // Get the front cell in the queue  // and update its adjacent cells  let curr = q[0];  let x = curr.i;  let y = curr.j;  let dist = curr.dist;    // Do for each adjacent cell  for (let i = 0; i < 4; i++)  {    // If adjacent cell is valid has  // path and not visited yet  // en-queue it.  if (isValid(x + row[i] y + col[i]))  {  if (isSafe(x + row[i] y + col[i]  matrix output))  {  output[x + row[i]][y + col[i]] = dist + 1;  q.push(new Node(x + row[i]  y + col[i]  dist + 1));  }  }  }    // Dequeue the front cell as  // its distance is found  q.shift();  }    // Print output matrix  for(let i = 0; i < M; i++)  {  for(let j = 0; j < N; j++)  {  document.write(output[i][j] + ' ');  }  document.write('  
'
); } } // Driver code let matrix=[[ 'O' 'O' 'O' 'O' 'G' ] [ 'O' 'W' 'W' 'O' 'O' ] [ 'O' 'O' 'O' 'W' 'O' ] [ 'G' 'W' 'W' 'W' 'O' ] [ 'O' 'O' 'O' 'O' 'G' ]]; findDistance(matrix); // This code is contributed by ab2127 </script>

Produktion
 3 3 2 1 0 2 -1 -1 2 1 1 2 3 -1 2 0 -1 -1 -1 1 1 2 2 1 0 

Tidskompleksitet: O(n*m)
Hjælpeplads: O(n*m)