Chessboard exploration

explore_chessboard_dp.py

#!/usr/bin/env python

m = 3
n = 4

S = [[None for _ in range(n+1)] for _ in range(m+1)]

for i in range(m):
  for j in range(n):
    if i==0 or j==0:
      S[i][j] = 1
    else:
      S[i][j] = S[i-1][j] + S[i][j-1]
n_paths = S[m-1][n-1]
print(f"Number of unique paths: {n_paths}")