JavaAlgorithms/DynamicProgramming/BoardPath.java

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];
  }
}