Lattice path

lattice.cpp

#include <map>
#include <iostream>
#include <algorithm>
unsigned long long moveto(const std::pair<int, int> &p, std::map< std::pair<int, int>, unsigned long long> &memo)
{
	if(memo.find(p) != memo.end()) return memo[p];
	
  /*
    (0, 0) -> (0, 0) => We are already at our destiny so, no of ways we can reach our destiny is '0'
    (0, 0) -> (a, 0) => Only '1' way to reach any point on X-axis from origin
    (0, 0) -> (0, b) => Only '1' way to reach any point on Y-axis from origin
  */
  
  int x = p.first, y = p.second;
	if(x == 0 && y == 0) return 0;
	if(x == 0 && y != 0) return 1;
	if(x != 0 && y == 0) return 1;
	unsigned long long path;
	path = moveto(std::pair<int, int>(x - 1, y), memo) + moveto(std::pair<int, int>(x, y - 1), memo);
	memo[p] = path;
	return path;
}

unsigned long long moveto(const std::pair<int, int> &p)
{
	std::map< std::pair<int, int>, unsigned long long> memo;
	return moveto(p, memo);
}

int main()
{
    
    for(int i = 0; i <= 20; ++i)
    {
    	    for(int j = 0; j <= 20; ++j)
    	    {
            std::cout << "(" << i << ", " << j << "): " << moveto(std::pair<int, int>(i, j)) << '\n';
        }
    }
    return 0;
}