Why does the following code returns wrong value of count?

Question

Problem: Given a 2D matrix of n x m. The matrix contained integers. Given a destination position, find the number of ways in which that person can reach the destination from source(origin) fulfilling the following conditions- (i) Movement can be only in north, south, east or west direction. (ii) A person can move from one cell to other if and only if that cell has value less than the value in the current cell.

#include<iostream>
using namespace std;
void printSolution(int** solution, int n, int m)
{
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<m;j++)
        {
            cout<<solution[i][j]<<" ";
        }
        cout<<endl;
    }
    cout<<endl;
}
int mazeHelp(int** maze, int** solution, int x, int y, int desx, int desy, int n, int m)
{
    int count = 0;
    if(x==desx-1 && y==desy-1)
    {
        solution[x][y] = 1;
        printSolution(solution, n, m);
        count++;
        solution[x][y]=0;
        //cout<<"Return 1"<<endl;
        return count;

    }
    if(x<0 || y<0 || x>=desx || y>=desy || solution[x][y]==1)
    {
        //cout<<"Return 2"<<endl;
        return count;   
    }
    solution[x][y] = 1;
    if(x+1<desx && solution[x+1][y]!=1 && maze[x+1][y]>maze[x][y])
    {
        count = mazeHelp(maze, solution, x+1, y, desx, desy, n, m); 
    }
    if(x-1>0 && solution[x-1][y]!=1 && maze[x-1][y]>maze[x][y])
    {
        count = mazeHelp(maze, solution, x-1, y, desx, desy, n, m);
    }
    if(y+1<desy && solution[x][y+1]!=1 && maze[x][y+1]>maze[x][y])
    {
        count = mazeHelp(maze, solution, x, y+1, desx, desy, n, m);
    }
    if(y-1>0 && solution[x][y-1]!=1 && maze[x][y-1]>maze[x][y])
    {
        count = mazeHelp(maze, solution, x, y-1, desx, desy, n, m);
    }
    solution[x][y] = 0;
}
int printPaths(int** maze, int desx, int desy, int** solution, int n, int m)
{
    int count = 0;
    count = mazeHelp(maze, solution, 0, 0, desx, desy, n, m);
    return count;
}

int main()
{
    int desx, desy, n, m;
    cout<<"Enter number of rows : ";
    cin>>n;
    cout<<"Enter number of columns : ";
    cin>>m;
    cout<<"Enter matrix : "<<endl;
    int** solution = new int*[n];
  for(int i=0;i<n;i++){
    solution[i] = new int[m];
  }
    int** maze = new int*[m];
    for(int i=0;i<n;i++){
    maze[i] = new int[m];
  }
  for(int i=0;i<n;i++)
    {
        for(int j=0;j<m;j++)
        {
            cin>>maze[i][j];
        }
    }
    for(int i=0; i<n; i++)
    {
        for(int j=0;j<m;j++)
        {
            solution[i][j] = 0;
        }
    }
    cout<<"Enter destination address (x,y) : ";
    cin>>desx>>desy;
    int res = printPaths(maze, desx, desy, solution, n, m);
    cout<<"Total number of paths : "<<res;
    return 0;
}

My code prints correct paths for every input but return wrong value of count every time. Is there any error in calculating the number of paths?

Answer 1

As already mentioned in the comments, in the mazeHelp function, you recursively call mazeHelp at several places. Each call returns a number of found paths. You have to cumulate them in the count variable, and return that count at the end, for parent recursive calls.

int mazeHelp(int** maze, int** solution, int x, int y, int desx, int desy, int n, int m)
{
    int count = 0;
    if(x==desx-1 && y==desy-1)
    {
        solution[x][y] = 1;
        printSolution(solution, n, m);
        count++;
        solution[x][y]=0;
        //cout<<"Return 1"<<endl;
        return count;

    }
    if(x<0 || y<0 || x>=desx || y>=desy || solution[x][y]==1)
    {
        //cout<<"Return 2"<<endl;
        return count;   
    }
    solution[x][y] = 1;
    if(x+1<desx && solution[x+1][y]!=1 && maze[x+1][y]>maze[x][y])
    {
        count += mazeHelp(maze, solution, x+1, y, desx, desy, n, m); 
    }
    if(x-1>0 && solution[x-1][y]!=1 && maze[x-1][y]>maze[x][y])
    {
        count += mazeHelp(maze, solution, x-1, y, desx, desy, n, m);
    }
    if(y+1<desy && solution[x][y+1]!=1 && maze[x][y+1]>maze[x][y])
    {
        count += mazeHelp(maze, solution, x, y+1, desx, desy, n, m);
    }
    if(y-1>0 && solution[x][y-1]!=1 && maze[x][y-1]>maze[x][y])
    {
        count += mazeHelp(maze, solution, x, y-1, desx, desy, n, m);
    }
    solution[x][y] = 0;
    return count;
}