#include <iostream>
#include <queue>
using namespace std;
#define GRID 8
#define ADJMATRIX 64 //(GRID*GRID)
/***************************************************************************
TO find the minimum moves required to move a Knight on a NxN chess board
from position (x,y) to (a,b).
Note:
Assumption =for a 8x8 matrix (x,y) range is (0,0) to (7,7).
Author: Thejas P M
*****************************************************************************/
class Node
{
public:
int Dist;
Node(int d=0)
{
Dist=d;
}
};
void possibleKnightMoves(int x, int y,Node arr[64][64])
{
int xPlus2 = x+2;
int xMinus2 = x-2;
int xPlus1 = x+1;
int xMinus1 = x-1;
int yPlus2 = y+2;
int yMinus2 = y-2;
int yPlus1 = y+1;
int yMinus1 = y-1;
int current = y*GRID+x;
arr[current][current].Dist=0;
if(xPlus2 < GRID && yPlus1 < GRID)
{
int adjVtx = yPlus1*GRID+xPlus2;
arr[current][adjVtx].Dist=1;
}
if(xPlus2 < GRID && yMinus1 >= 0)
{
int adjVtx = yMinus1*GRID+xPlus2;
arr[current][adjVtx].Dist=1;
}
if(xMinus2 >= 0 && yPlus1 < GRID)
{
int adjVtx = yPlus1*GRID+xMinus2;
arr[current][adjVtx].Dist=1;
}
if(xMinus2 >= 0 && yMinus1 >= 0)
{
int adjVtx = yMinus1*GRID+xMinus2;
arr[current][adjVtx].Dist=1;
}
if(xPlus1 < GRID && yPlus2 < GRID)
{
int adjVtx = yPlus2*GRID+xPlus1;
arr[current][adjVtx].Dist=1;
}
if(xPlus1 < GRID && yMinus2 >= 0)
{
int adjVtx = yMinus2*GRID+xPlus1;
arr[current][adjVtx].Dist=1;
}
if(xMinus1 >= 0 && yPlus2 < GRID)
{
int adjVtx = yPlus2*GRID+xMinus1;
arr[current][adjVtx].Dist=1;
}
if(xMinus1 >= 0 && yMinus2 >= 0)
{
int adjVtx = yMinus2*GRID+xMinus1;
arr[current][adjVtx].Dist=1;
}
return;
}
int** BFSAdj(Node arr[64][64], int& vtx,int& vtxCount)
{
/*
Step 1: Colour all the nodes in the Storage structure as White(0) and parents to -1
Step 2: Start with the vtx passed onto the function set its Distance to 0 i.e Storage[vtx][2]=0
Step 3: Initialize a Queue, ENQUE the vtx onto Q
Step 4: While Queue not empty do
Let VtxTemp = DEQUE from Q
Let S array = all Vertexes Adjacent to VtxTemp
For each vertex in S array
if Storage[Si][0] == White
Change colour Storage[Si][0] == Grey
Update Distance Storage[Si][2] == Storage[VtxTemp][2] + 1
Update parent Storage[Si][2] = VtxTemp
ENQUE Si
Storage[VtxTemp][1]=2
Step 5: Done
*/
if(vtxCount <=0 || vtx > vtxCount)
{
cout<<"CHECK the INPUT TO BFS"<<endl;
return NULL;
}
int **Storage = NULL;
Storage = new int*[vtxCount];
int i=0;
for(i=0;i<vtxCount;++i)
{
Storage[i]=new int[3];
Storage[i][0]=0; //holds the colour of the node 0-White,1-Grey,2-Black
Storage[i][1]=-1; //Parent Node
Storage[i][2]=99; //Distance
//cout<<Storage[i][0]<<endl<<Storage[i][1]<<endl<<Storage[i][2]<<endl<<endl;
}
Storage[vtx][2]=0;
int array[64];
int temp_count=0;
std::queue<int> bfsQ;
bfsQ.push(vtx);
while(bfsQ.size() > 0)
{
int vtxTemp = bfsQ.front();
array[temp_count++]=vtxTemp;
bfsQ.pop();
/* Node *sArray =arr[vtxTemp-1].next;
while (sArray != NULL)
{
if(Storage[sArray->value-1][0] == 0)//white
{cout<<"sArray->value="<<sArray->value<<endl;
Storage[sArray->value-1][0]=1;
Storage[sArray->value-1][1]=vtxTemp;
Storage[sArray->value-1][2]=Storage[vtxTemp-1][2] + 1;
bfsQ.push(sArray->value);
cout<<Storage[sArray->value-1][0]<<" "<<Storage[sArray->value-1][1]<<" "<<Storage[sArray->value-1][2]<<endl<<endl;
}
sArray=sArray->next;
}
*/
for(int j=0;j<ADJMATRIX;++j)
{
if(arr[vtxTemp][j].Dist==1)
{
if(Storage[j][0] == 0)//white
{
cout<<"vtxTemp,j="<<vtxTemp<<","<<j<<endl;
Storage[j][0]=1;
Storage[j][1]=vtxTemp;
Storage[j][2]=Storage[vtxTemp][2] + 1;
bfsQ.push(j);
//cout<<" "<<j;
// cout<<"-----"<<j<<"------"<<endl<<Storage[j][0]<<"\n"<<Storage[j][1]<<" \n"<<Storage[j][2]<<endl<<endl;
}
}
}
Storage[vtxTemp][0]=2;
}
//Print nodes the entered the Q
/*cout<<"\nPOP ORDER\n";
for(int i=0;i<temp_count;++i)
cout<<" "<<array[i];
cout<<"\n";*/
return Storage;
}
int getMove(int** res,int vtxSource,int vtxDst)
{
cout<<"\n PATH = "<<vtxDst<<"<==";
if(res[vtxDst][2]==99)
{
return -1;
}
int result=res[vtxDst][2];
while(res[vtxDst][1]!=-1)
{
vtxDst=res[vtxDst][1];
cout<<vtxDst<<"<==";
}
cout<<endl;
return result;
}
/*NxN Knight shortest path / Min moves
There are NxN nodes in total
two nodes [(x,y) and (a,b)] are connected
if a,b < GRID and (a,b) is in
{(x+1,y+2),(x+1,y-2),(x+2,y+1),(x+2,y-1),(x-2,y-1),(x-2,y+1),(x+2,y+1),(x+1,y-1)}
the nodes are numbered in this order
00 01 02 03 04 05 06 07
08 09 10 11 12 13 14 15
16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63
The conversion from the x,y cordinates to the nodes Formula [vertex = (x*GRID+j)]
similarly x,y =
*/
int main()
{
Node arr[ADJMATRIX][ADJMATRIX];
for(int i=0;i<GRID;++i)
{
for(int j=0;j<GRID;++j)
{
possibleKnightMoves(i,j,arr);
}
}
int x = 7, y = 3,vtxSource = y*GRID+x;
int xa = 7,ya=7,vtxDst=ya*GRID+xa,count =ADJMATRIX;
int** resultSet= BFSAdj(arr,vtxSource,count);
// Find min moves
cout<<"ANSWER = "<<getMove(resultSet,vtxSource,vtxDst);
//Print adjacencyMatrix
/*for(int i=0;i<count;++i)
{
cout<<""<<i<<"\t";
}
cout<<endl<<endl;
for(int i=0;i<count;++i)
{
for(int j=0;j<count;++j)
{
cout<<arr[i][j].Dist<<"\t";
}
cout<<endl;
}*/
//PRINT BFS MATRIX
/* cout<<" --- Result --"<<endl;
for(int i=0;i<count;++i)
{
cout<<"a["<<i<<"]\t";
}
cout<<endl;
for(int j=0;j<3;++j)
{
for(int i=0;i<count;++i)
{
cout<<resultSet[i][j]<<"\t\t";
}
cout<<endl;
}
*/
return 0;
}
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