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N-Puzzle IDA-Star.cpp
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N-Puzzle IDA-Star.cpp
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/****************************************************************************************************************************************************************
Author:
Dhairya Dhondiyal
Description:
The program solves N-Puzzle using IDA* algorithm with manhattan distance + linear conflict as heuristics.
Disclaimer:
Copyright (C) - All Rights Reserved
Unauthorized copying of this file, via any medium is strictly prohibited
Proprietary and confidential
Written by Dhairya Dhondiyal, February 2016
****************************************************************************************************************************************************************/
#include<iostream>
#include<math.h>
#include<vector>
#include<time.h>
#include<stack>
#define N 4
using namespace std;
int grid[N][N]= {{10,11,6,12}, //65 Moves
{15,13,0,9},
{8,14,2,3},
{7,4,1,5}};
/*int grid[N][N]={{2,8,7,11}, //42 Moves
{5,0,4,15},
{13,9,14,3},
{1,10,6,12}};*/
struct Node //Basic Node
{
char from;
int Grid[N][N],x0,y0,manhattan_h,h;
Node(int x=0,int y=0,char direction='X')
{
x0=x;
y0=y;
from=direction;
}
}Start;
int i,j,threshhold,linear_horizontal_conflicts=0,linear_vertical_conflicts=0,maxi,maxj,original_h,exchanged_h,global_g;
clock_t tStart,tEnd;
bool found=false;
stack<char> path;
showmoves()
{
while(!path.empty())
{
if(path.top()=='R')
{
swap(Start.Grid[Start.y0-1][Start.x0-1],Start.Grid[Start.y0-1][Start.x0-2]);
Start.x0--;
}
if(path.top()=='L')
{
swap(Start.Grid[Start.y0-1][Start.x0-1],Start.Grid[Start.y0-1][Start.x0]);
Start.x0++;
}
if(path.top()=='D')
{
swap(Start.Grid[Start.y0-1][Start.x0-1],Start.Grid[Start.y0-2][Start.x0-1]);
Start.y0--;
}
if(path.top()=='U')
{
swap(Start.Grid[Start.y0-1][Start.x0-1],Start.Grid[Start.y0][Start.x0-1]);
Start.y0++;
}
cout<<path.top()<<endl;
for(i=0;i<N;i++)
{
for(j=0;j<N;j++)
{
cout<<Start.Grid[i][j]<<"\t";
}
cout<<endl<<endl;
}
system("pause");
cout<<endl;
path.pop();
}
}
vector<Node> Neighbors(Node* temp_Node) //Uses Manhattan Heuristics and linear conflict
{
int ctr=0;
vector<Node> neighbors;
linear_horizontal_conflicts=0;linear_vertical_conflicts=0;
if(temp_Node->x0+1<=N&&temp_Node->from!='L') //Space->Right, Move=Left;
{
neighbors.push_back(Node(temp_Node->x0+1,temp_Node->y0,'R'));
for(i=0;i<N;i++)
{
maxi=-1;
maxj=-1;
for(j=0;j<N;j++)
{
if(i==temp_Node->y0-1&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j+1];
else if(i==temp_Node->y0-1&&j==temp_Node->x0)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j-1];
else
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j];
if((i==temp_Node->y0-1&&j==temp_Node->x0-1))
{
if(temp_Node->Grid[i][j+1]!=0&&(temp_Node->Grid[i][j+1]-1)/N==i)
if(temp_Node->Grid[i][j+1]>maxi)
maxi=temp_Node->Grid[i][j+1];
else
linear_horizontal_conflicts++;
}
else if(i==temp_Node->y0-1&&j==temp_Node->x0)
{
if(temp_Node->Grid[i][j-1]!=0&&(temp_Node->Grid[i][j-1]-1)/N==i)
if(temp_Node->Grid[i][j-1]>maxi)
maxi=temp_Node->Grid[i][j-1];
else
linear_horizontal_conflicts++;
}
else
{
if(temp_Node->Grid[i][j]!=0&&(temp_Node->Grid[i][j]-1)/N==i)
if(temp_Node->Grid[i][j]>maxi)
maxi=temp_Node->Grid[i][j];
else
linear_horizontal_conflicts++;
}
if((j==temp_Node->y0-1&&i==temp_Node->x0-1))
{
if(temp_Node->Grid[j][i+1]!=0&&(temp_Node->Grid[j][i+1]-1)%N==i)
if(temp_Node->Grid[j][i+1]>maxj)
maxj=temp_Node->Grid[j][i+1];
else
linear_vertical_conflicts++;
}
else if(j==temp_Node->y0-1&&i==temp_Node->x0)
{
if(temp_Node->Grid[j][i-1]!=0&&(temp_Node->Grid[j][i-1]-1)%N==i)
if(temp_Node->Grid[j][i-1]>maxj)
maxj=temp_Node->Grid[j][i-1];
else
linear_vertical_conflicts++;
}
else
if(temp_Node->Grid[j][i]!=0&&(temp_Node->Grid[j][i]-1)%N==i)
if(temp_Node->Grid[j][i]>maxj)
maxj=temp_Node->Grid[j][i];
else
linear_vertical_conflicts++;
}
}
original_h=abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0]-1)/N)+abs(temp_Node->x0-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0]-1)%N);
exchanged_h=+abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0]-1)%N);
neighbors[ctr].manhattan_h=temp_Node->manhattan_h+exchanged_h-original_h;
neighbors[ctr].h=neighbors[ctr].manhattan_h+2*linear_vertical_conflicts+2*linear_horizontal_conflicts;
ctr++;
}
if(temp_Node->x0-1>0&&temp_Node->from!='R') //Space->Left, Move=Right;
{
linear_horizontal_conflicts=0;linear_vertical_conflicts=0;
neighbors.push_back(Node(temp_Node->x0-1,temp_Node->y0,'L'));
for(i=0;i<N;i++)
{
maxi=-1;
maxj=-1;
for(j=0;j<N;j++)
{
if(i==temp_Node->y0-1&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j-1];
else if(i==temp_Node->y0-1&&j==temp_Node->x0-2)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j+1];
else
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j];
if((i==temp_Node->y0-1&&j==temp_Node->x0-1))
{
if(temp_Node->Grid[i][j-1]!=0&&(temp_Node->Grid[i][j-1]-1)/N==i)
if(temp_Node->Grid[i][j-1]>maxi)
maxi=temp_Node->Grid[i][j-1];
else
linear_horizontal_conflicts++;
}
else if(i==temp_Node->y0-1&&j==temp_Node->x0-2)
{
if(temp_Node->Grid[i][j+1]!=0&&(temp_Node->Grid[i][j+1]-1)/N==i)
if(temp_Node->Grid[i][j+1]>maxi)
maxi=temp_Node->Grid[i][j+1];
else
linear_horizontal_conflicts++;
}
else
{
if(temp_Node->Grid[i][j]!=0&&(temp_Node->Grid[i][j]-1)/N==i)
if(temp_Node->Grid[i][j]>maxi)
maxi=temp_Node->Grid[i][j];
else
linear_horizontal_conflicts++;
}
if((j==temp_Node->y0-1&&i==temp_Node->x0-1))
{
if(temp_Node->Grid[j][i-1]!=0&&(temp_Node->Grid[j][i-1]-1)%N==i)
if(temp_Node->Grid[j][i-1]>maxj)
maxj=temp_Node->Grid[j][i-1];
else
linear_vertical_conflicts++;
}
else if(j==temp_Node->y0-1&&i==temp_Node->x0-2)
{
if(temp_Node->Grid[j][i+1]!=0&&(temp_Node->Grid[j][i+1]-1)%N==i)
if(temp_Node->Grid[j][i+1]>maxj)
maxj=temp_Node->Grid[j][i+1];
else
linear_vertical_conflicts++;
}
else
if(temp_Node->Grid[j][i]!=0&&(temp_Node->Grid[j][i]-1)%N==i)
if(temp_Node->Grid[j][i]>maxj)
maxj=temp_Node->Grid[j][i];
else
linear_vertical_conflicts++;
}
}
original_h=abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0-2]-1)/N)+abs(temp_Node->x0-2-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0-2]-1)%N);
exchanged_h=abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0-2]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0-1][temp_Node->x0-2]-1)%N);
neighbors[ctr].manhattan_h=temp_Node->manhattan_h+exchanged_h-original_h;
neighbors[ctr].h=neighbors[ctr].manhattan_h+2*linear_vertical_conflicts+2*linear_horizontal_conflicts;
ctr++;
}
if(temp_Node->y0+1<=N&&temp_Node->from!='U') //Space->Down Move=Up
{
linear_horizontal_conflicts=0;linear_vertical_conflicts=0;
neighbors.push_back(Node(temp_Node->x0,temp_Node->y0+1,'D'));
for(i=0;i<N;i++)
{
maxi=-1;
maxj=-1;
for(j=0;j<N;j++)
{
if(i==temp_Node->y0-1&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i+1][j];
else if(i==temp_Node->y0&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i-1][j];
else
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j];
if((i==temp_Node->y0-1&&j==temp_Node->x0-1))
{
if(temp_Node->Grid[i+1][j]!=0&&(temp_Node->Grid[i+1][j]-1)/N==i)
if(temp_Node->Grid[i+1][j]>maxi)
maxi=temp_Node->Grid[i+1][j];
else
linear_horizontal_conflicts++;
}
else if(i==temp_Node->y0&&j==temp_Node->x0-1)
{
if(temp_Node->Grid[i-1][j]!=0&&(temp_Node->Grid[i-1][j]-1)/N==i)
if(temp_Node->Grid[i-1][j]>maxi)
maxi=temp_Node->Grid[i-1][j];
else
linear_horizontal_conflicts++;
}
else
{
if(temp_Node->Grid[i][j]!=0&&(temp_Node->Grid[i][j]-1)/N==i)
if(temp_Node->Grid[i][j]>maxi)
maxi=temp_Node->Grid[i][j];
else
linear_horizontal_conflicts++;
}
if((j==temp_Node->y0-1&&i==temp_Node->x0-1))
{
if(temp_Node->Grid[j+1][i]!=0&&(temp_Node->Grid[j+1][i]-1)%N==i)
if(temp_Node->Grid[j+1][i]>maxj)
maxj=temp_Node->Grid[j+1][i];
else
linear_vertical_conflicts++;
}
else if(j==temp_Node->y0&&i==temp_Node->x0-1)
{
if(temp_Node->Grid[j-1][i]!=0&&(temp_Node->Grid[j-1][i]-1)%N==i)
if(temp_Node->Grid[j-1][i]>maxj)
maxj=temp_Node->Grid[j-1][i];
else
linear_vertical_conflicts++;
}
else
if(temp_Node->Grid[j][i]!=0&&(temp_Node->Grid[j][i]-1)%N==i)
if(temp_Node->Grid[j][i]>maxj)
maxj=temp_Node->Grid[j][i];
else
linear_vertical_conflicts++;
}
}
original_h=abs(temp_Node->y0-(temp_Node->Grid[temp_Node->y0][temp_Node->x0-1]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0][temp_Node->x0-1]-1)%N);
exchanged_h=abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0][temp_Node->x0-1]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0][temp_Node->x0-1]-1)%N);
neighbors[ctr].manhattan_h=temp_Node->manhattan_h+exchanged_h-original_h;
neighbors[ctr].h=neighbors[ctr].manhattan_h+2*linear_vertical_conflicts+2*linear_horizontal_conflicts;
ctr++;
}
if(temp_Node->y0-1>0&&temp_Node->from!='D') //Space->Up Move=Down
{
linear_horizontal_conflicts=0;linear_vertical_conflicts=0;
neighbors.push_back(Node(temp_Node->x0,temp_Node->y0-1,'U'));
for(i=0;i<N;i++)
{
maxi=-1;
maxj=-1;
for(j=0;j<N;j++)
{
if(i==temp_Node->y0-1&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i-1][j];
else if(i==temp_Node->y0-2&&j==temp_Node->x0-1)
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i+1][j];
else
neighbors[ctr].Grid[i][j]=temp_Node->Grid[i][j];
if((i==temp_Node->y0-1&&j==temp_Node->x0-1))
{
if(temp_Node->Grid[i-1][j]!=0&&(temp_Node->Grid[i-1][j]-1)/N==i)
if(temp_Node->Grid[i-1][j]>maxi)
maxi=temp_Node->Grid[i-1][j];
else
linear_horizontal_conflicts++;
}
else if(i==temp_Node->y0-2&&j==temp_Node->x0-1)
{
if(temp_Node->Grid[i+1][j]!=0&&(temp_Node->Grid[i+1][j]-1)/N==i)
if(temp_Node->Grid[i+1][j]>maxi)
maxi=temp_Node->Grid[i+1][j];
else
linear_horizontal_conflicts++;
}
else
{
if(temp_Node->Grid[i][j]!=0&&(temp_Node->Grid[i][j]-1)/N==i)
if(temp_Node->Grid[i][j]>maxi)
maxi=temp_Node->Grid[i][j];
else
linear_horizontal_conflicts++;
}
if((j==temp_Node->y0-1&&i==temp_Node->x0-1))
{
if(temp_Node->Grid[j-1][i]!=0&&(temp_Node->Grid[j-1][i]-1)%N==i)
if(temp_Node->Grid[j-1][i]>maxj)
maxj=temp_Node->Grid[j-1][i];
else
linear_vertical_conflicts++;
}
else if(j==temp_Node->y0-2&&i==temp_Node->x0-1)
{
if(temp_Node->Grid[j+1][i]!=0&&(temp_Node->Grid[j+1][i]-1)%N==i)
if(temp_Node->Grid[j+1][i]>maxj)
maxj=temp_Node->Grid[j+1][i];
else
linear_vertical_conflicts++;
}
else
if(temp_Node->Grid[j][i]!=0&&(temp_Node->Grid[j][i]-1)%N==i)
if(temp_Node->Grid[j][i]>maxj)
maxj=temp_Node->Grid[j][i];
else
linear_vertical_conflicts++;
}
}
original_h=abs(temp_Node->y0-2-(temp_Node->Grid[temp_Node->y0-2][temp_Node->x0-1]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0-2][temp_Node->x0-1]-1)%N);
exchanged_h=abs(temp_Node->y0-1-(temp_Node->Grid[temp_Node->y0-2][temp_Node->x0-1]-1)/N)+abs(temp_Node->x0-1-(temp_Node->Grid[temp_Node->y0-2][temp_Node->x0-1]-1)%N);
neighbors[ctr].manhattan_h=temp_Node->manhattan_h+exchanged_h-original_h;
neighbors[ctr].h=neighbors[ctr].manhattan_h+2*linear_vertical_conflicts+2*linear_horizontal_conflicts;
}
return neighbors;
}
int searching(Node* node,int g)
{
int f,t;
f=g+node->h;
if(f>threshhold||found==true)
return f;
if(g>global_g)
{
system("cls");
cout<<"Moves:\t"<<g;
global_g=g;
}
if(node->h==0)
{
tEnd=clock()-tStart;
system("cls");
if(node->from=='L')
path.push('R');
if(node->from=='R')
path.push('L');
if(node->from=='U')
path.push('D');
if(node->from=='D')
path.push('U');
found=true;
cout<<"Moves required:\t"<<g<<endl;
return 0;
}
int minimum=INT_MAX;
for(auto &neighbor:Neighbors(node))
{
t=searching(&neighbor,g+1);
if(t<minimum)
minimum=t;
}
if(found==true)
{
if(node->from=='L')
path.push('R');
if(node->from=='R')
path.push('L');
if(node->from=='U')
path.push('D');
if(node->from=='D')
path.push('U');
}
return minimum;
}
Idastar()
{
tStart=clock();
while(1)
{
if(found==true)
break;
int t;
t=searching(&Start,0);
threshhold=t;
/*if(clock()-(double)tStart/CLOCKS_PER_SEC>10000)
{
cout<<"Time limit exceeded";
exit(0);
}*/
}
}
int main()
{
for(i=0;i<N;i++) //Start Recognition and filling 'Start' members.
{
maxi=-1;
maxj=-1;
for(j=0;j<N;j++)
{
if(grid[i][j]!=0&&(grid[i][j]-1)/N==i)
if(grid[i][j]>maxi)
maxi=grid[i][j];
else
linear_horizontal_conflicts++;
if(grid[j][i]!=0&&(grid[j][i]-1)%N==i)
if(grid[j][i]>maxj)
maxj=grid[j][i];
else
linear_vertical_conflicts++;
if(grid[i][j]==0)
{
Start.x0=j+1;
Start.y0=i+1;
}
else
Start.manhattan_h+=abs(i-(grid[i][j]-1)/N)+abs(j-(grid[i][j]-1)%N);
Start.Grid[i][j]=grid[i][j];
}
}
Start.h+=Start.manhattan_h+2*linear_horizontal_conflicts+2*linear_vertical_conflicts;
threshhold=Start.h;
Idastar();
showmoves();
cout<<"Time Taken:\t"<<(double)tEnd/CLOCKS_PER_SEC<<endl;
}