Let ~A_1, A_2, \dots, A_N~ denote the sets of tasks with weights ~1, 2, \dots, N~, respectively. Additionally, let ~B_2, B_3, \dots, B_N~ denote the sets of tasks with weights ~1~ or ~2~, ~2~ or ~3~, …, ~N-1~ or ~N~, respectively. Finally, let ~B_1 = 0~.

The problem can now be solved using a dynamic programming approach; starting from the first weight (the least one) we choose a task for each weight. When choosing a task with the weight equal to ~T~, we need to check whether another task from the set ~B_T~ has already been taken. Therefore, it is sufficient to have a table of the form ~dp[t][b]~.

This yields the following relations:

$$\displaystyle \begin{align*} dp[0][0] &= 1 \\ dp[0][1] &= 0 \\ dp[i][0] &= dp[i-1][0] \times (A_i+B_i) + dp[i-1][1] \times (A_i+B_i-1) \\ dp[i][1] &= dp[i-1][0] \times B_i + dp[i-1][1] \times B_{i+1} \end{align*}$$