Vzhľadom na obdĺžnikovú matricu sa môžeme pohybovať z aktuálnej bunky v 4 smeroch s rovnakou pravdepodobnosťou. 4 smery sú vľavo vľavo hore alebo dole. Vypočítajte pravdepodobnosť, že po N sa presunie z danej polohy (I j) v matrici, v žiadnom momente nebudeme krížiť hranice matrice.
analógová komunikácia
Dôrazne vám odporúčame, aby ste minimalizovali váš prehliadač a vyskúšali si to najskôr sami.
Cieľom je vykonať niečo podobné DFS. Rekurzívne prechádzame v každom zo 4 povolených smerov a pre každú bunku, s ktorou sa vyskytol, vypočítame požadovanú pravdepodobnosť s jedným menším pohybom. Pretože každý smer má rovnakú pravdepodobnosť, že každý smer prispeje k 1/4 celkovej pravdepodobnosti tejto bunky, t. J. 0,25. Vrátime sa 0, ak vstúpime mimo maticu a vrátime sa 1, ak sú n kroky dokončené bez hraníc matice matice.
Nižšie je uvedená implementácia vyššie uvedenej myšlienky:
C++/// C++ program to find the probability // that we do not cross boundary of a // matrix after N moves. #include
/// C program to find the probability // that we do not cross boundary of a // matrix after N moves. #include
// Java program to find the probability // that we do not cross boundary // of a matrix after N moves. import java.io.*; class GFG { // check if (x y) is valid // matrix coordinate static boolean isSafe(int x int y int m int n) { return (x >= 0 && x < m && y >= 0 && y < n); } // Function to calculate probability // that after N moves from a given // position (x y) in m x n matrix // boundaries of the matrix will // not be crossed. static double findProbability(int m int n int x int y int N) { // boundary crossed if (! isSafe(x y m n)) return 0.0; // N steps taken if (N == 0) return 1.0; // Initialize result double prob = 0.0; // move up prob += findProbability(m n x - 1 y N - 1) * 0.25; // move right prob += findProbability(m n x y + 1 N - 1) * 0.25; // move down prob += findProbability(m n x + 1 y N - 1) * 0.25; // move left prob += findProbability(m n x y - 1 N - 1) * 0.25; return prob; } // Driver code public static void main (String[] args) { // matrix size int m = 5 n = 5; // coordinates of starting point int i = 1 j = 1; // Number of steps int N = 2; System.out.println('Probability is ' + findProbability(m n i j N)); } } // This code is contributed by KRV.
# Python3 program to find the probability # that we do not cross boundary of a # matrix after N moves. # check if (x y) is valid matrix coordinate def isSafe(x y m n): return (x >= 0 and x < m and y >= 0 and y < n) # Function to calculate probability # that after N moves from a given # position (x y) in m x n matrix # boundaries of the matrix will # not be crossed. def findProbability(m n x y N): # boundary crossed if (not isSafe(x y m n)): return 0.0 # N steps taken if (N == 0): return 1.0 # Initialize result prob = 0.0 # move up prob += findProbability(m n x - 1 y N - 1) * 0.25 # move right prob += findProbability(m n x y + 1 N - 1) * 0.25 # move down prob += findProbability(m n x + 1 y N - 1) * 0.25 # move left prob += findProbability(m n x y - 1 N - 1) * 0.25 return prob # Driver code if __name__ == '__main__': # matrix size m = 5 n = 5 # coordinates of starting po i = 1 j = 1 # Number of steps N = 2 print('Probability is' findProbability(m n i j N)) # This code is contributed by PranchalK
// C# program to find the probability // that we do not cross boundary // of a matrix after N moves. using System; class GFG { // check if (x y) is valid // matrix coordinate static bool isSafe(int x int y int m int n) { return (x >= 0 && x < m && y >= 0 && y < n); } // Function to calculate probability // that after N moves from a given // position (x y) in m x n matrix // boundaries of the matrix will // not be crossed. static double findProbability(int m int n int x int y int N) { // boundary crossed if (! isSafe(x y m n)) return 0.0; // N steps taken if (N == 0) return 1.0; // Initialize result double prob = 0.0; // move up prob += findProbability(m n x - 1 y N - 1) * 0.25; // move right prob += findProbability(m n x y + 1 N - 1) * 0.25; // move down prob += findProbability(m n x + 1 y N - 1) * 0.25; // move left prob += findProbability(m n x y - 1 N - 1) * 0.25; return prob; } // Driver code public static void Main () { // matrix size int m = 5 n = 5; // coordinates of starting point int i = 1 j = 1; // Number of steps int N = 2; Console.Write('Probability is ' + findProbability(m n i j N)); } } // This code is contributed by nitin mittal.
// PHP program to find the probability // that we do not cross boundary of a // matrix after N moves. // check if (x y) is valid // matrix coordinate function isSafe($x $y $m $n) { return ($x >= 0 && $x < $m && $y >= 0 && $y < $n); } // Function to calculate probability // that after N moves from a given // position (x y) in m x n matrix // boundaries of the matrix will // not be crossed. function findProbability($m $n $x $y $N) { // boundary crossed if (!isSafe($x $y $m $n)) return 0.0; // N steps taken if ($N == 0) return 1.0; // Initialize result $prob = 0.0; // move up $prob += findProbability($m $n $x - 1 $y $N - 1) * 0.25; // move right $prob += findProbability($m $n $x $y + 1 $N - 1) * 0.25; // move down $prob += findProbability($m $n $x + 1 $y $N - 1) * 0.25; // move left $prob += findProbability($m $n $x $y - 1 $N - 1) * 0.25; return $prob; } // Driver code // matrix size $m = 5; $n = 5; // coordinates of starting point $i = 1; $j = 1; // Number of steps $N = 2; echo 'Probability is ' findProbability($m $n $i $j $N); // This code is contributed by nitin mittal. ?> <script> // JavaScript program to find the probability // that we do not cross boundary of a // matrix after N moves. // check if (x y) is valid matrix coordinate function isSafe(x y m n){ return (x >= 0 && x < m && y >= 0 && y < n); } // Function to calculate probability // that after N moves from a given // position (x y) in m x n matrix // boundaries of the matrix will not be crossed. function findProbability( m n x y N){ // boundary crossed if (!isSafe(x y m n)) return 0.0; // N steps taken if (N == 0) return 1.0; // Initialize result let prob = 0.0; // move up prob += findProbability(m n x - 1 y N - 1) * 0.25; // move right prob += findProbability(m n x y + 1 N - 1) * 0.25; // move down prob += findProbability(m n x + 1 y N - 1) * 0.25; // move left prob += findProbability(m n x y - 1 N - 1) * 0.25; return prob; } // Driver code // matrix size let m = 5 n = 5; // coordinates of starting point let i = 1 j = 1; // Number of steps let N = 2; document.write( 'Probability is ' +findProbability(m n i j N)); </script>
Výstup
Probability is 0.875