#### Board Path

A
```package com.thealgorithms.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 final class BoardPath {
private 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];
}
}
```