Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.
How many routes are there through a 2020 grid?
2 using namespace std;
3
4 #define num 41
5 long long PascalTriangle[num][num];
6
7 void CalcPascalTriangle()
8 {
9 PascalTriangle[0][0] = 1;
10 PascalTriangle[1][0] = 1;
11 PascalTriangle[1][1] = 1;
12 for(int i=2; i<num; i++)
13 {
14 for(int j=0; j<=i; j++)
15 {
16 if(j == 0 || j == i)
17 {
18 PascalTriangle[i][j] = 1;
19 }
20 else
21 {
22 PascalTriangle[i][j] = PascalTriangle[i-1][j-1] + PascalTriangle[i-1][j];
23 }
24 }
25 }
26 }
27
28 int main()
29 {
30 CalcPascalTriangle();
31 cout << PascalTriangle[40][20];
32 cin.get();
33 }