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Added "Find shortest safe route in a path with landmines" Question #6714
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## Find shortest safe route in a path with landmines | ||
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184 changes: 184 additions & 0 deletions
184
code/backtracking/src/find_safe_path/find_safe_path.cpp
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// C++ program to find shortest safe Route in | ||
// the matrix with landmines | ||
#include <bits/stdc++.h> | ||
using namespace std; | ||
#define R 12 | ||
#define C 10 | ||
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// These arrays are used to get row and column | ||
// numbers of 4 neighbours of a given cell | ||
int rowNum[] = { -1, 0, 0, 1 }; | ||
int colNum[] = { 0, -1, 1, 0 }; | ||
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// A function to check if a given cell (x, y) | ||
// can be visited or not | ||
bool isSafe(int mat[R][C], int visited[R][C], | ||
int x, int y) | ||
{ | ||
if (mat[x][y] == 0 || visited[x][y]) | ||
return false; | ||
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return true; | ||
} | ||
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// A function to check if a given cell (x, y) is | ||
// a valid cell or not | ||
bool isValid(int x, int y) | ||
{ | ||
if (x < R && y < C && x >= 0 && y >= 0) | ||
return true; | ||
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return false; | ||
} | ||
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// A function to mark all adjacent cells of | ||
// landmines as unsafe. Landmines are shown with | ||
// number 0 | ||
void markUnsafeCells(int mat[R][C]) | ||
{ | ||
for (int i = 0; i < R; i++) | ||
{ | ||
for (int j = 0; j < C; j++) | ||
{ | ||
// if a landmines is found | ||
if (mat[i][j] == 0) | ||
{ | ||
// mark all adjacent cells | ||
for (int k = 0; k < 4; k++) | ||
if (isValid(i + rowNum[k], j + colNum[k])) | ||
mat[i + rowNum[k]][j + colNum[k]] = -1; | ||
} | ||
} | ||
} | ||
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// mark all found adjacent cells as unsafe | ||
for (int i = 0; i < R; i++) | ||
{ | ||
for (int j = 0; j < C; j++) | ||
{ | ||
if (mat[i][j] == -1) | ||
mat[i][j] = 0; | ||
} | ||
} | ||
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// Uncomment below lines to print the path | ||
/*for (int i = 0; i < R; i++) | ||
{ | ||
for (int j = 0; j < C; j++) | ||
{ | ||
cout << std::setw(3) << mat[i][j]; | ||
} | ||
cout << endl; | ||
}*/ | ||
} | ||
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// Function to find shortest safe Route in the | ||
// matrix with landmines | ||
// mat[][] - binary input matrix with safe cells marked as 1 | ||
// visited[][] - store info about cells already visited in | ||
// current route | ||
// (i, j) are coordinates of the current cell | ||
// min_dist --> stores minimum cost of shortest path so far | ||
// dist --> stores current path cost | ||
void findShortestPathUtil(int mat[R][C], int visited[R][C], | ||
int i, int j, int &min_dist, int dist) | ||
{ | ||
// if destination is reached | ||
if (j == C-1) | ||
{ | ||
// update shortest path found so far | ||
min_dist = min(dist, min_dist); | ||
return; | ||
} | ||
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// if current path cost exceeds minimum so far | ||
if (dist > min_dist) | ||
return; | ||
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// include (i, j) in current path | ||
visited[i][j] = 1; | ||
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// Recurse for all safe adjacent neighbours | ||
for (int k = 0; k < 4; k++) | ||
{ | ||
if (isValid(i + rowNum[k], j + colNum[k]) && | ||
isSafe(mat, visited, i + rowNum[k], j + colNum[k])) | ||
{ | ||
findShortestPathUtil(mat, visited, i + rowNum[k], | ||
j + colNum[k], min_dist, dist + 1); | ||
} | ||
} | ||
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// Backtrack | ||
visited[i][j] = 0; | ||
} | ||
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// A wrapper function over findshortestPathUtil() | ||
void findShortestPath(int mat[R][C]) | ||
{ | ||
// stores minimum cost of shortest path so far | ||
int min_dist = INT_MAX; | ||
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// create a boolean matrix to store info about | ||
// cells already visited in current route | ||
int visited[R][C]; | ||
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// mark adjacent cells of landmines as unsafe | ||
markUnsafeCells(mat); | ||
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// start from first column and take minimum | ||
for (int i = 0; i < R; i++) | ||
{ | ||
// if path is safe from current cell | ||
if (mat[i][0] == 1) | ||
{ | ||
// initialize visited to false | ||
memset(visited, 0, sizeof visited); | ||
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// find shortest route from (i, 0) to any | ||
// cell of last column (x, C - 1) where | ||
// 0 <= x < R | ||
findShortestPathUtil(mat, visited, i, 0, | ||
min_dist, 0); | ||
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// if min distance is already found | ||
if(min_dist == C - 1) | ||
break; | ||
} | ||
} | ||
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// if destination can be reached | ||
if (min_dist != INT_MAX) | ||
cout << "Length of shortest safe route is " | ||
<< min_dist; | ||
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else // if the destination is not reachable | ||
cout << "Destination not reachable from " | ||
<< "given source"; | ||
} | ||
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// Driver code | ||
int main() | ||
{ | ||
// input matrix with landmines shown with number 0 | ||
int mat[R][C] = | ||
{ | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 }, | ||
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 } | ||
}; | ||
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// find shortest path | ||
findShortestPath(mat); | ||
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return 0; | ||
} |
198 changes: 198 additions & 0 deletions
198
code/backtracking/src/find_safe_path/find_safe_path.java
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// Java program to find shortest safe Route | ||
// in the matrix with landmines | ||
import java.util.Arrays; | ||
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class GFG{ | ||
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static final int R = 12; | ||
static final int C = 10; | ||
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// These arrays are used to get row and column | ||
// numbers of 4 neighbours of a given cell | ||
static int rowNum[] = { -1, 0, 0, 1 }; | ||
static int colNum[] = { 0, -1, 1, 0 }; | ||
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static int min_dist; | ||
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// A function to check if a given cell (x, y) | ||
// can be visited or not | ||
static boolean isSafe(int[][] mat, boolean[][] visited, | ||
int x, int y) | ||
{ | ||
if (mat[x][y] == 0 || visited[x][y]) | ||
return false; | ||
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return true; | ||
} | ||
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// A function to check if a given cell (x, y) is | ||
// a valid cell or not | ||
static boolean isValid(int x, int y) | ||
{ | ||
if (x < R && y < C && x >= 0 && y >= 0) | ||
return true; | ||
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return false; | ||
} | ||
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// A function to mark all adjacent cells of | ||
// landmines as unsafe. Landmines are shown with | ||
// number 0 | ||
static void markUnsafeCells(int[][] mat) | ||
{ | ||
for(int i = 0; i < R; i++) | ||
{ | ||
for(int j = 0; j < C; j++) | ||
{ | ||
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// If a landmines is found | ||
if (mat[i][j] == 0) | ||
{ | ||
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// Mark all adjacent cells | ||
for(int k = 0; k < 4; k++) | ||
if (isValid(i + rowNum[k], j + colNum[k])) | ||
mat[i + rowNum[k]][j + colNum[k]] = -1; | ||
} | ||
} | ||
} | ||
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// Mark all found adjacent cells as unsafe | ||
for(int i = 0; i < R; i++) | ||
{ | ||
for(int j = 0; j < C; j++) | ||
{ | ||
if (mat[i][j] == -1) | ||
mat[i][j] = 0; | ||
} | ||
} | ||
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// Uncomment below lines to print the path | ||
/* | ||
* for (int i = 0; i < R; i++) { | ||
* for (int j = 0; j < C; j++) { cout << | ||
* std::setw(3) << mat[i][j]; } cout << endl; } | ||
*/ | ||
} | ||
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// Function to find shortest safe Route in the | ||
// matrix with landmines | ||
// mat[][] - binary input matrix with safe cells marked as 1 | ||
// visited[][] - store info about cells already visited in | ||
// current route | ||
// (i, j) are coordinates of the current cell | ||
// min_dist --> stores minimum cost of shortest path so far | ||
// dist --> stores current path cost | ||
static void findShortestPathUtil(int[][] mat, | ||
boolean[][] visited, | ||
int i, int j, int dist) | ||
{ | ||
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// If destination is reached | ||
if (j == C - 1) | ||
{ | ||
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// Update shortest path found so far | ||
min_dist = Math.min(dist, min_dist); | ||
return; | ||
} | ||
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// If current path cost exceeds minimum so far | ||
if (dist > min_dist) | ||
return; | ||
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// include (i, j) in current path | ||
visited[i][j] = true; | ||
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// Recurse for all safe adjacent neighbours | ||
for(int k = 0; k < 4; k++) | ||
{ | ||
if (isValid(i + rowNum[k], j + colNum[k]) && | ||
isSafe(mat, visited, i + rowNum[k], | ||
j + colNum[k])) | ||
{ | ||
findShortestPathUtil(mat, visited, i + rowNum[k], | ||
j + colNum[k], dist + 1); | ||
} | ||
} | ||
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// Backtrack | ||
visited[i][j] = false; | ||
} | ||
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// A wrapper function over findshortestPathUtil() | ||
static void findShortestPath(int[][] mat) | ||
{ | ||
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// Stores minimum cost of shortest path so far | ||
min_dist = Integer.MAX_VALUE; | ||
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// Create a boolean matrix to store info about | ||
// cells already visited in current route | ||
boolean[][] visited = new boolean[R][C]; | ||
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// Mark adjacent cells of landmines as unsafe | ||
markUnsafeCells(mat); | ||
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// Start from first column and take minimum | ||
for(int i = 0; i < R; i++) | ||
{ | ||
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// If path is safe from current cell | ||
if (mat[i][0] == 1) | ||
{ | ||
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// Initialize visited to false | ||
for(int k = 0; k < R; k++) | ||
{ | ||
Arrays.fill(visited[k], false); | ||
} | ||
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// Find shortest route from (i, 0) to any | ||
// cell of last column (x, C - 1) where | ||
// 0 <= x < R | ||
findShortestPathUtil(mat, visited, i, 0, 0); | ||
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// If min distance is already found | ||
if (min_dist == C - 1) | ||
break; | ||
} | ||
} | ||
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// If destination can be reached | ||
if (min_dist != Integer.MAX_VALUE) | ||
System.out.println("Length of shortest " + | ||
"safe route is " + min_dist); | ||
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else | ||
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// If the destination is not reachable | ||
System.out.println("Destination not " + | ||
"reachable from given source"); | ||
} | ||
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// Driver code | ||
public static void main(String[] args) | ||
{ | ||
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// Input matrix with landmines shown with number 0 | ||
int[][] mat = { | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 }, | ||
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, | ||
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 } }; | ||
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// Find shortest path | ||
findShortestPath(mat); | ||
} | ||
} | ||
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// This code is contributed by sanjeev2552 | ||
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