问题
Grid Walking (Score 50 points):
You are situated in an N dimensional grid at position (x_1,x2,...,x_N). The dimensions of the grid are (D_1,D_2,...D_N). In one step, you can walk one step ahead or behind in any one of the N dimensions. (So there are always 2N possible different moves). In how many ways can you take M steps such that you do not leave the grid at any point? You leave the grid if you for any x_i, either x_i <= 0 or x_i > D_i.
Input:
The first line contains the number of test cases T. T test cases follow. For each test case, the first line contains N and M, the second line contains x_1,x_2...,x_N and the 3rd line contains D_1,D_2,...,D_N.
So, in the above solution I'm trying to take one dimensional array.
The website claims 38753340 to be the answer, but I'm not getting it.
public class GridWalking {
/**
* @param args
*/
public static void main(String[] args) {
try {
long arr[] = new long[78];
long pos = 44;
long totake = 287;
/*
* Double arr[] = new Double[3]; Double pos = 0; Double totake = 5;
*/
Double val = calculate(arr, pos, totake);
System.out.println(val % 1000000007);
} catch (Exception e) {
System.out.println(e);
e.printStackTrace();
}
}
public static HashMap<String, Double> calculated = new HashMap<String, Double>();
private static Double calculate(long[] arr, long pos, long totake) {
if (calculated.containsKey(pos + "" + totake)) {
return calculated.get(pos + "" + totake);
}
if (0 == totake) {
calculated.put(pos + "" + totake, new Double(1));
return new Double(1);
}
if (pos == arr.length - 1) {
Double b = calculate(arr, pos - 1, totake - 1);
Double ret = b;
calculated.put(pos + "" + totake, new Double(ret));
return ret;
}
if (pos == 0) {
Double b = calculate(arr, pos + 1, totake - 1);
Double ret = b;
calculated.put(pos + "" + totake, new Double(ret));
return ret;
}
Double a = calculate(arr, pos + 1, totake - 1);
Double b = calculate(arr, pos - 1, totake - 1);
Double ret = (a + b);
calculated.put(pos + "" + totake, ret);
return ret;
}
}
回答1:
You need to change key values as for pos + "_" + totake.
I have rewritten it but I'm not sure it working or not. It takes too much time to complete if ever.
public class GridWalking {
static long arr_length = 78;
static long pos = 44;
static long totake = 287;
static long count = 0;
/**
* @param args
*/
public static void main(String[] args) {
try {
calculate(pos, totake);
System.out.println(count % 1000000007);
} catch (Exception e) {
System.out.println(e);
e.printStackTrace();
}
}
private static void calculate(long pos, long totake) {
if (pos < 0 || pos > arr_length - 1)
return;
if (0 == totake) {
count++;
return;
}
calculate(pos + 1, totake - 1);
calculate(pos - 1, totake - 1);
}
}
回答2:
I have tried solving that Grid walking problem in Hackerrank. this is the code that had worked(in ecclipse atleast). but i donno why it does not match with given answers. Nut i think you can get the idea from it. Since it does not use recursion, no problem with execution time..
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Solution {
static int count=0;
public static void main(String[] args) throws FileNotFoundException {
String filename = "src/testcases.txt";//testcases is just a file containing input
File file = new File(filename);
Scanner in = new Scanner(file);
//in.useDelimiter("[^0-9]+");
//-----------------------------------------------------------------
int T=in.nextInt();
for(int t=0;t<1;t++){
int N=in.nextInt();
int M=in.nextInt();System.out.println("M="+M);
int[] X=new int[N];
long max=1000000007;
int[] D=new int[N];
for(int i=0;i<N;i++) X[i]=in.nextInt();
for(int i=0;i<N;i++) D[i]=in.nextInt();
int Dmax=D[0];
int Dtotal=1;
for(int i=0;i<N;i++) if(Dmax<D[i]) Dmax=D[i];
for(int i=0;i<N;i++) X[i]--;
for(int i=0;i<N;i++) Dtotal*=D[i];//total number of fields
long[] mainarray= new long[Dtotal];
long[] mainarraynext=new long[Dtotal];
int[][] ways=new int[N][Dmax];
set( X, mainarray,D, 1);
int temp[]=new int[N];
for(int h=0;h<10;h++){
for(int j=0;j<Dtotal;j++){
mainarraynext[j]=getsum(inverse(j,D),mainarray, D );
}
for(int j=0;j<Dtotal;j++){
mainarray[j]=mainarraynext[j];
mainarray[j]%=max;
}
System.out.println(Arrays.toString(mainarray));
}
long finalsum=0;
for(int j=0;j<Dtotal;j++){
finalsum+=mainarray[j];
//System.out.println(finalsum);
}
System.out.println(finalsum);
//System.out.println(Arrays.toString(inverse(44,D)));
}
}
public static long get(int[] x, long[] mainarray, int[] D){
for(int i=0;i<x.length;i++){
if(x[i]>=D[i]) return 0;
if(x[i]<0) return 0;
}
int index=0;
for(int i=0;i<D.length;i++){
index=(index*D[i])+x[i];
}
return mainarray[index];
}
public static int[] inverse(int index,int[] D){
int[] temp=new int[D.length];
for(int i=D.length-1;i>=0;i--){
temp[i]=index%D[i];
index=index/D[i];
}
return temp;
}
public static void set(int[] x, long[] mainarray, int[] D, int value){
int index=0;
for(int i=0;i<D.length;i++){
index=(index*D[i])+x[i];
}
mainarray[index]=value;
}
public static long getsum(int[] x,long[] mainarray, int[] D ){
int[] temp=new int[x.length];
long sum=0;
//for 2n different sides
for(int j=0;j<x.length;j++){//sum in each side
temp[j]=x[j];
}
for(int j=0;j<x.length;j++){//sum in each side
temp[j]--;
sum+=get(temp, mainarray, D);
temp[j]+=2;
sum+=get(temp, mainarray, D);
temp[j]--;
}
return sum;
}
}
回答3:
Here's a Java solution I've built for the original hackerrank problem. For big grids runs forever. Probably some smart math is needed.
long compute(int N, int M, int[] positions, int[] dimensions) {
if (M == 0) {
return 1;
}
long sum = 0;
for (int i = 0; i < N; i++) {
if (positions[i] < dimensions[i]) {
positions[i]++;
sum += compute(N, M - 1, positions, dimensions);
positions[i]--;
}
if (positions[i] > 1) {
positions[i]--;
sum += compute(N, M - 1, positions, dimensions);
positions[i]++;
}
}
return sum % 1000000007;
}
来源：https://stackoverflow.com/questions/11921616/grid-walking-algorithm-code-correction