Python Program for Minimum Cost Path

In this article, we will learn about the solution to the problem statement given below.

Problem statement − We are given a cost matrix and a position (m, n), we need to find the cost of minimum cost path to reach (m, n) from (0, 0). Each cell represents a cost to traverse from one cell to another.

Now let’s observe the solution in the implementation below −

Example

 Live Demo

# dynamic approach
R = 3
C = 3
def minCost(cost, m, n):
   # initialization
   tc = [[0 for x in range(C)] for x in range(R)]
   # base case
   tc[0][0] = cost[0][0]
   # total cost(tc) array
   for i in range(1, m + 1):
      tc[i][0] = tc[i-1][0] + cost[i][0]
   # tc array
   for j in range(1, n + 1):
      tc[0][j] = tc[0][j-1] + cost[0][j]
   # rest tc array
   for i in range(1, m + 1):
      for j in range(1, n + 1):
         tc[i][j] = min(tc[i-1][j-1], tc[i-1][j], tc[i][j-1]) + cost[i][j]
   return tc[m][n]
# main
cost = [[1, 5, 3],
        [7, 7, 4],
        [8, 5, 3]]
print("Total Cost:",minCost(cost, 2, 1))

Output

Total Cost: 13

All the variables are declared in the local scope and their references are seen in the figure above.

Conclusion

In this article, we have learned about how we can make a Python Program for Min Cost Path