Maximum Multiplication Score

Given four fixed weights a[0..3] and an array b, pick indices i0<i1<i2<i3 to maximize the weighted sum a[0]*b[i0]+a[1]*b[i1]+a[2]*b[i2]+a[3]*b[i3]; the core challenge is choosing four ordered positions in b (considering positive/negative weight effects) which is typically solved by dynamic programming that tracks best scores after each selection.