N Queens Problem

Solved using Hill Climbing Heuristic Search technique. This searching is implemented using simple HCS, so it may get stuck on Local Maxima.

Random Restart HC will restart every time if the HC gets stuck, the default no of iterations can be determined by the iterations parameter

Algorithm

Simple Hill Climbing Search

heurisitc = h(currentState)
while True
    neighbours = currentState
    neighbour = min(h(nieghbours))
    newHeurisitc = h(neighbour)

    if newHeuristic >= heuristic
        exit

    currentState = neighbour

Random Restart Hill Climbing Search

for 0 --> iterations
    heurisitc = h(currentState)
    while True
        neighbours = currentState
        neighbour = min(h(nieghbours))
        newHeurisitc = h(neighbour)
    
        if newHeuristic >= heuristic
            exit
    
        currentState = neighbour

    if stuck in local maxima
        restart --> new currentState

Examples

n = 4

Starting Board :: 
Q  -  -  -  
-  Q  -  -  
-  -  -  Q  
-  Q  -  -  


Final Board :: 
-  -  Q  -  
Q  -  -  -  
-  -  -  Q  
-  Q  -  -  


Steps climbed :: 2

n = 5

Starting Board :: 
-  -  -  Q  -  
-  -  -  -  Q  
-  -  -  -  Q  
Q  -  -  -  -  
-  -  -  Q  -  

Final Board :: 
-  Q  -  -  -  
-  -  -  -  Q  
-  -  Q  -  -  
Q  -  -  -  -  
-  -  -  Q  -  

Steps climbed :: 2

Local Maxima Case

Starting Board :: 
Q  -  -  -  -  
Q  -  -  -  -  
-  -  -  Q  -  
-  -  -  Q  -  
Q  -  -  -  -  

Final Board :: 
-  -  Q  -  -  
Q  -  -  -  -  
-  -  -  Q  -  
-  -  -  Q  -  
Q  -  -  -  -  

Steps climbed :: 1
Stuck at Local Maxima State