Question

T

My question from C++ Plus Data Structures By Nell Dale, Chip Weems, Tim Richards book,page499 question 16.

please if you have solution manual for this book,help me

We want to count the number of possible paths to move from row 1, column 1 to row N,

column N in a two-dimensional grid. Steps are restricted to going up or to the right, but not
diagonally. The illustration followsshows three of many paths, if N = 10.(a) [1] The following function, NumPaths, is supposed to count the number of paths,
but it has some problems. Debug the function.
int NumPaths(int row, int col, int n)
{
if(row == n)
return 1;
else if(col == n)
return NumPaths + 1;
else
return NumPaths(row + 1, col) * NumPaths(row, col + 1);
}
(b) [1] After you have corrected the function, trace the execution of NumPaths with n =
4 by hand.
(c) [1.5] You can improve the efficiency of this operation by keeping intermediate
values of NumPathsin a two-dimensional array of integer values. This approach
keeps the function from having to recalculate values that it has already figured out.
Design and code a version of NumPathsthat uses this approach.
(d) [0.5] Show an invocation of the version of NumPaths you developed in part (c),
including any array initialization necessary.
(e) [1] How do the two versions of NumPaths compare in terms of time efficiency?
Space efficiency?

Answer 1

copyable code

a)

program code debug the function

public class NumPathsval {

protected int calls1 = 0;

public int numPathsval(int rowval, int colval, int n1)

{

    calls1++;

    if (rowval == n1)

      return 1;

    else if (colval == n1)

      return 1;

    else

      return numPathsval(rowval+1, colval, n1) + numPathsval(rowval, colval+1, n1);

}

public static void main(String[] args) {

  

    int n1 = Integer.parseInt(args[0]);

    NumPathsval helperval = new NumPathsval();

    int count11 = helperval.numPathsval(1,1,n1);

    System.out.println(" " + count11 + " paths to (" + n1 + "," + n1 + ")");

    System.out.println(" That " + helperval.calls1 + " calls.");

}

}

a) program code debug the function public class NumPathsval f protected int calls10 public int numPathsval (int rowval, int colval, int nl) calls1++ if (rowvalnl) return 1i return 1; return numPathsval (rowval+l, solal, nl) + else if (colval n1) else numPathsval (rowva, colval+1, n1) public static void main (String [l args) t

public static void main (String[] 큐rag) Integer.parseInt (args NumPathsval helperval new NumPathsval ) int count 11 helperval. numPatnsva1(1, 1, n1); System.out.println(" "+count11 + " paths to ("+nl + "," Svstemoutprintla" That " + help calls.) System. out.printlIn(ThatT hellperval.cal3 T Output NumPaths 4 20 paths to (4,) That 39 calls 3432 paths to (8.8) That 6863 calls. NumPatns 9 12870 paths to (9,g) That 25739 calls

ath3Fromva1 for (int k 0; k < n1 ; ++k) new long [n11 [n1 for (int l= 0; 1 < n1; ++1) pathsEromvalk] [1] -1; if (pathsFromval [rowval-1] [colval-1]1) pathsFromval rowval-11 [colval-11- numPathsval (rowval+1,colval,n1) + numPathsval (rowval,colval+1.n1) // Return return pathsFromval [rowval-11 [colval-11 public static void main (String[] g3) inc n1 = Integer.par 3 e Int (args [0]); NumPathval helperval new NumPathsval) long count1 -helperwal.numPathsval (1. 1,nl System.out.println("+Count1+"paths to (" +nl+", "+ System.out println(" That + helperval.callsl +" calls.");
copyable code

public class NumPathsval {

protected long calls1 = 0;

    protected long[][] pathsFromval;

public long numPathsval(int rowval, int colval, int n1)

{

    calls1++;

    // Base cases:

    if ((rowval == n1) || (colval == n1)) {

     return 1;

    }

    else {

     

      if (pathsFromval == null) {

        pathsFromval = new long[n1][n1];

        for (int k = 0; k < n1; ++k)

          for (int l = 0; l < n1; ++l)

            pathsFromval[k][l] = -1;

      }

      if (pathsFromval[rowval-1][colval-1] == -1) {

        pathsFromval[rowval-1][colval-1] =

          numPathsval(rowval+1,colval,n1) + numPathsval(rowval,colval+1,n1);

      }

      // Return

      return pathsFromval[rowval-1][colval-1];

    }

}

public static void main(String[] args) {

   

    int n1 = Integer.parseInt(args[0]);

    NumPathsval helperval = new NumPathsval();

    long count1 = helperval.numPathsval(1,1,n1);

    System.out.println(" " + count1 + " paths to (" + n1 + "," + n1 + ")");

    System.out.println(" That " + helperval.calls1 + " calls.");

}

}

d) Answe %2umPathSyal 4 20 paths to (4.4) That 1 lls. 3432 paths to (8.8) That 99 calls. 12870 paths to (9) That 129 calls. %NumRathsyal 15 40116600 paths to (15.15) That 33 cals funin b)-1 fun(a+1,b) > f(a+1,b+1) fun(a,b+1)>f(a+1,b+1) write 0 fun(1,1) <-2*u2,2) tun(1,1) (# 2*2*2*-m(4,4)

Space Efficiency It has highly recursive version since it has stach but not O(n) deep Qin 2) space effficency clarity The array value has less clear so it has recursive of array strikes the balance