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instructions attached  below 

#include <iostream>

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#include <iomanip>

using namespace std;

const int ROWS = 8;

const int COLS = 9;

//P(sense obstacle | obstacle) = 0.8

float probSenseObstacle = 0.8;

//P(senses no obstacle | obstacle) = 1 – 0.8 = 0.2

float probFalseNoObstacle = 0.2;

//P(sense obstacle | no obstacle) = 0.15

float probFalseObstacle = 0.15;

//P(senses no obstacle | no obstacle) = 1 – 0.15 = 0.85

float probSenseNoObstacle = 0.85;

//Puzzle including a border around the edge

int maze[ROWS][COLS] =

{ {1,1,1,1,1,1,1,1,1},

{1,0,0,0,0,0,0,0,1},

{1,0,1,0,0,1,0,0,1},

{1,0,0,0,0,0,0,0,1},

{1,0,1,0,0,1,0,0,1},

{1,0,0,0,0,0,0,0,1},

{1,0,0,0,0,0,0,0,1},

{1,1,1,1,1,1,1,1,1},

};

//Matrix of probabilities

float probs[ROWS][COLS];

//Temporary matrix

float motionPuzzle[ROWS][COLS];

float sensingCalculation(int evidence[4], int row, int col)

{

float result = 1.0;

//If obstacle sensed to the west

if (evidence[0] == 1)

{

//If obstacle to the west in maze

if (maze[row][col – 1] == 1)

result *= probSenseObstacle;

//If no obstacle to the west in maze

else

result *= probFalseObstacle;

}

//If no obstacle sensed to the west

else

{

//If obstacle to the west in maze

if (maze[row][col – 1] == 1)

{

result *= probFalseNoObstacle;

}

//If no obstacle to the west in maze

else

{

result *= probSenseNoObstacle;

}

}

//If obstacle sensed to the north

if (evidence[1] == 1)

{

//If obstacle to the north in maze

if (maze[row – 1][col] == 1)

result *= probSenseObstacle;

//If no obstacle to the north in maze

else

result *= probFalseObstacle;

}

//If no obstacle sensed to the north

else

{

//If obstacle to the north in maze

if (maze[row – 1][col] == 1)

{

result *= probFalseNoObstacle;

}

//If no obstacle to the north in maze

else

{

result *= probSenseNoObstacle;

}

}

//If obstacle sensed to the east

if (evidence[2] == 1)

{

//If obstacle to the east in maze

if (maze[row][col + 1] == 1)

result *= probSenseObstacle;

//If no obstacle to the east in maze

else

result *= probFalseObstacle;

}

//If no obstacle sensed to the east

else

{

//If obstacle to the east in maze

if (maze[row][col + 1] == 1)

{

result *= probFalseNoObstacle;

}

//If no obstacle to the east in maze

else

{

result *= probSenseNoObstacle;

}

}

//If obstacle sensed to the south

if (evidence[3] == 1)

{

//If obstacle to the south in maze

if (maze[row + 1][col] == 1)

result *= probSenseObstacle;

//If no obstacle to the south in maze

else

result *= probFalseObstacle;

}

//If no obstacle sensed to the south

else

{

//If obstacle to the south in maze

if (maze[row + 1][col] == 1)

{

result *= probFalseNoObstacle;

}

//If no obstacle to the south in maze

else

{

result *= probSenseNoObstacle;

}

}

return result;

}

//Use evidence conditional probability P(Zt|St)

void sensing(int evidence[4])

{

float denominator = 0;

//Calculates denominator

for (int r = 0; r < ROWS; r++)

{

for (int c = 0; c < COLS; c++)

{

if (maze[r][c] != 1)

{

denominator += sensingCalculation(evidence, r, c) * probs[r][c];

}

}

}

for (int row = 0; row < ROWS; row++)

{

for (int col = 0; col < COLS; col++)

{

//If the current space isn’t an obstacle

if (maze[row][col] != 1)

{

float currentProbabilty = probs[row][col];

float numerator = sensingCalculation(evidence, row, col) * currentProbabilty;

float result = numerator / denominator;

probs[row][col] = result;

}

}

}

}

//Use transition probability P(St|St-1)

void motion(int direction)

{

for (int row = 0; row < ROWS; row++)

{

for (int col = 0; col < COLS; col++)

{

if (maze[row][col] != 1)

{

float total = 0.0;

//north

if (direction == 1)

{

//checking west

if (maze[row][col – 1] != 1)

{

total += probs[row][col – 1] * 0.1;

}

else

{

total += probs[row][col] * 0.1;

}

//checking north

if (maze[row – 1][col] != 1)

{

total += probs[row – 1][col] * 0;

}

else

{

total += probs[row][col] * 0.8;

}

//checking east

if (maze[row][col + 1] != 1)

{

total += probs[row][col + 1] * 0.1;

}

else

{

total += probs[row][col] * 0.1;

}

//checking south

if (maze[row + 1][col] != 1)

{

total += probs[row + 1][col] * 0.8;

}

else

{

total += probs[row][col] * 0;

}

}

//west

else if (direction == 0)

{

//checking west

if (maze[row][col – 1] != 1)

{

total += probs[row][col – 1] * 0;

}

else

{

total += probs[row][col] * 0.8;

}

//checking north

if (maze[row – 1][col] != 1)

{

total += probs[row – 1][col] * 0.1;

}

else

{

total += probs[row][col] * 0.1;

}

//checking east

if (maze[row][col + 1] != 1)

{

total += probs[row][col + 1] * 0.8;

}

else

{

total += probs[row][col] * 0;

}

//checking south

if (maze[row + 1][col] != 1)

{

total += probs[row + 1][col] * 0.1;

}

else

{

total += probs[row][col] * 0.1;

}

}

motionPuzzle[row][col] = total;

}

else

{

motionPuzzle[row][col] = -1;

}

}

}

for (int r = 0; r < ROWS; r++)

{

for (int c = 0; c < COLS; c++)

{

probs[r][c] = motionPuzzle[r][c];

}

}

}

void printPuzzle(float puzzle[ROWS][COLS])

{

for (int row = 0; row < ROWS; row++)

{

for (int col = 0; col < COLS; col++)

{

if (puzzle[row][col] == -1)

cout << “##### “;

else

cout << setprecision(2) << fixed << puzzle[row][col] * 100.0 << ”  “;

}

cout << endl;

}

}

int main()

{

//Initial probability matrix

for (int row = 0; row < ROWS; row++)

{

for (int col = 0; col < COLS; col++)

{

if (maze[row][col] == 0)

{

probs[row][col] = (1.0 / 38);

}

else

{

probs[row][col] = -1;

}

}

}

printPuzzle(probs);

cout << endl;

int s1[4] = { 0, 0, 0, 0 };

sensing(s1);

printPuzzle(probs);

cout << endl;

//1 = north

motion(1);

printPuzzle(probs);

cout << endl;

int s2[4] = { 1,0,0,0 };

sensing(s2);

printPuzzle(probs);

cout << endl;

//1 = north

motion(1);

printPuzzle(probs);

cout << endl;

int s3[4] = { 0,0,0,0 };

sensing(s3);

printPuzzle(probs);

cout << endl;

//0 = west

motion(0);

printPuzzle(probs);

cout << endl;

int s4[4] = { 0,1,0,1 };

sensing(s4);

printPuzzle(probs);

cout << endl;

//0 = west

motion(0);

printPuzzle(probs);

cout << endl;

int s5[4] = { 1,0,0,0 };

sensing(s5);

printPuzzle(probs);

cout << endl;

return 0;

}

 

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