DP[n][m] =

min(

DP[n-1][m]+W(n-1,m,(+1,0),DP[n-1][m]),

DP[n][m-1]+W(n,m-1,(0,+1),DP[n][m-1])

)

DP[n][m] =

1+min(

DP[n-1][m]+W(n-1,m,(+1,0),DP[n-1][m]),

DP[n][m-1]+W(n,m-1,(0,+1),DP[n][m-1])

)

(if n > 1)

(if m > 1)

Base Case

DP[0][0] = 0

Answer

DP[n][m]

DP[n][m][k] =

min(

DP[n-1][m][k]+W(n-1,m,(+1,0),DP[n-1][m]),

DP[n][m-1][k]+W(n,m-1,(0,+1),DP[n][m-1]),

DP[n][m-1][k-1], DP[n-1][m][k-1],

)

DP[n][m][k] =

1+min(

DP[n-1][m][k]+W(n-1,m,(+1,0),DP[n-1][m]),

DP[n][m-1][k]+W(n,m-1,(0,+1),DP[n][m-1]),

DP[n][m-1][k-1], DP[n-1][m][k-1],

)

(if n > 1)

(if m > 1)

(if m > 1 and k > 1)

(if n > 1 and k > 1)

Base Case

DP[0][0][*] = 0

Answer

DP[n][m][k]

According to random d if all green ...

Counter-example

Misunderstanding

Common flaws