#### Board Path

A
```package com.thealgorithms.dynamicprogramming;

public final class BoardPath {
private BoardPath() {
}

/**
* Recursive solution without memoization
*
* @param start - the current position
* @param end   - the target position
* @return the number of ways to reach the end from the start
*/
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;
}

/**
* Recursive solution with memoization
*
* @param curr - the current position
* @param end  - the target position
* @param strg - memoization array
* @return the number of ways to reach the end from the start
*/
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;
}

/**
* Iterative solution with tabulation
*
* @param curr - the current position (always starts from 0)
* @param end  - the target position
* @param strg - memoization array
* @return the number of ways to reach the end from the start
*/
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 <= end; dice++) {
count += strg[i + dice];
}
strg[i] = count;
}
return strg[curr];
}
}
```