Editing Convex hull trick
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print cost[N] | print cost[N] | ||
</pre> | </pre> | ||
− | Notice that the lines are already being given in descending order of slope, so that each line is added "at the right"; this is because we already sorted them by width. The query step can be performed in logarithmic time, as discussed, and the addition step in amortized constant time, giving a <math>\Theta(N\lg N)</math> solution. We can modify our data structure slightly to take advantage of the fact that query values are non-decreasing | + | Notice that the lines are already being given in descending order of slope, so that each line is added "at the right"; this is because we already sorted them by width. The query step can be performed in logarithmic time, as discussed, and the addition step in amortized constant time, giving a <math>\Theta(N\lg N)</math> solution. We can modify our data structure slightly to take advantage of the fact that query values are non-decreasing, and replace the binary search with a [[pointer walk]], reducing query time to amortized constant as well and giving a <math>\Theta(N)</math> solution for the DP step. The overall complexity, however, is still <math>O(N\lg N)</math>, due to the sorting step. |
==Another example: APIO 2010 Commando== | ==Another example: APIO 2010 Commando== |