Rod Cutting: Bottom-Up DP

Filling the revenue table r[0..n] for optimal rod cutting

Click "Next Step" to begin the bottom-up computation

Price Table p[i]

Revenue Table r[j] (being computed)

Best First Cut s[j]

Current j

Comparing (i, j−i)

Using r[j−i]

Filled

Optimal

Algorithm: Bottom-Up-Cut-Rod

let r[0..n] be new array
r[0] = 0
for j = 1 to n
  q = -∞
  for i = 1 to j
    if q < p[i] + r[j-i]
      q = p[i] + r[j-i]
      s[j] = i
  r[j] = q
return r[n]

Price Table p[i]

Revenue Table r[j] (being computed)

Best First Cut s[j]

Optimal Cuts for Rod of Length