[ 0/1 Knapsack] Book example 5.6
Let gj(y) be the value of an optimal solution to KNAP(j+1,n,y). Clearly, g0(m) is the value of an optimal solution to KNAP(l,n,m). The possible Decisions for xi are 0 and 1 (D1 = {0,1}). From the principle of optimality it follows that
g0(m) = max {g1(m), g1(m- w1) + p1}
Now, while the principle of optimality has been stated only with respect to the initial state and decision, it can be applied equally well to intermediate states and decisions. (example 5.10)