package DynamicProgramming;
/*
* this is an important Algo in which 
* we have starting and ending of board and we have to reach 
* we have to count no. of ways 
* that help to reach end point i.e number by rolling dice
* which have 1 to 6 digits

Test Case:
here target is 10

int n=10;
		startAlgo();
		System.out.println(bpR(0,n));
		System.out.println(endAlgo()+"ms");
		int[] strg=new int [n+1];
		startAlgo();
		System.out.println(bpRS(0,n,strg));
		System.out.println(endAlgo()+"ms");
		startAlgo();
		System.out.println(bpIS(0,n,strg));
		System.out.println(endAlgo()+"ms");
		


*/
public class BoardPath {
	public static long startTime;
	public static long endTime;
	public static void startAlgo() {
		startTime=System.currentTimeMillis();
	}
	public static long endAlgo() {
		endTime=System.currentTimeMillis();
		return endTime-startTime;
	}
	public static int bpR(int start,int end){
		if(start==end) {
			return 1;
		}
		else if(start>end)
			return 0;
		int count=0;
		for(int dice=1;dice<=6;dice++) {
			count+=bpR(start+dice,end);
		}
		return count;
	}
	public static int bpRS(int curr,int end,int strg[]){
		if(curr==end) {
			return 1;
		}
		else if(curr>end)
			return 0;
		if(strg[curr]!=0)
			return strg[curr];
		int count=0;
		for(int dice=1;dice<=6;dice++) {
			count+=bpRS(curr+dice,end,strg);
		}
		strg[curr]=count;
		return count;
	}
	public static int bpIS(int curr,int end,int[]strg){
		strg[end]=1;
		for(int i=end-1;i>=0;i--) {
			int count=0;
			for(int dice=1;dice<=6&&dice+i<strg.length;dice++) {
				count+=strg[i+dice];
			}
			strg[i]=count;
		}
		return strg[0];
	}


}