Dynamic Programming - Iteration

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Iteration in the recurrence relation

When the recurrence relation is a static equation - there is no iteration.

• Min Cost Climbing Stairs

• climb 1 or 2 steps at a time. $$ dp(i) = \min(dp(i - 1) + \text{cost}[i - 1], \, dp(i - 2) + \text{cost}[i - 2]) $$

• if the question is to take k steps at a time, the recurrence relation would become dynamic $$ dp(i) = \min_{(i - k) \leq j < i} (dp(j) + \text{cost}[j]) $$