a/usaco-guide
Archived
1
0
Fork 0
Code Issues Pull requests Packages Projects Releases Wiki Activity

upd slope a bit

Browse source
This commit is contained in:
Benjamin Qi 2020-07-02 15:03:09 -04:00
parent f03c118930
commit 2068a71c79
1 changed files with 17 additions and 7 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

24
content/6_Plat/Slope.mdx
View file

@ -12,20 +12,24 @@ import { Problem } from "../models";
export const metadata = {
problems: {
ex: [
new Problem("CF", "Problem Without a Legend", "contest/713/problem/C", "Easy", false, ["Slope Trick"], ""),
],
buy: [
new Problem("CF", "Buy Low Sell High", "contest/866/problem/D", "Normal", false, ["Slope Trick"], ""),
new Problem("CF", "Buy Low Sell High", "contest/866/problem/D", "Easy", false, ["Slope Trick"], ""),
],
potatoes: [
new Problem("ojuz", "LMIO - Potatoes & Fertilizers", "LMIO19_bulves", "Hard", false, ["Slope Trick"], "[Equivalent Problem](https://atcoder.jp/contests/kupc2016/tasks/kupc2016_h)"),
new Problem("ojuz", "LMIO - Potatoes & Fertilizers", "LMIO19_bulves", "Normal", false, ["Slope Trick"], "[Equivalent Problem](https://atcoder.jp/contests/kupc2016/tasks/kupc2016_h)"),
],
landscaping: [
new Problem("Plat", "Landscaping", "650", "Very Hard", false, ["Slope Trick"], "Equivalent Problem: GP of Wroclaw 20 J"),
new Problem("Plat", "Landscaping", "650", "Hard", false, ["Slope Trick"], "Equivalent Problem: GP of Wroclaw 20 J"),
],
general: [
new Problem("CF", "Bookface", "gym/102576/problem/C", "Normal", false, ["Slope Trick"], ""),
new Problem("CC", "CCDSAP Exam", "CCDSAP", "Normal", false, ["Slope Trick"], ""),
new Problem("CF", "Farm of Monsters", "gym/102538/problem/F", "Hard", false, ["Slope Trick"], ""),
new Problem("CF", "Moving Walkways", "contest/1209/problem/H", "Hard", false, ["Slope Trick"], ""),
new Problem("ojuz", "APIO - Fireworks", "APIO16_fireworks", "Hard", false, [], ""),
new Problem("CF", "April Fools' Problem", "contest/802/problem/O", "Very Hard", false, ["Slope Trick"], "binary search on top of slope trick"),
new Problem("ICPC World Finals", "Conquer the World", "https://icpc.kattis.com/problems/conquertheworld", "Very Hard", false, ["Slope Trick"], "ICPC world finals, 0 solves in contest - \"Potatoes\" on tree!!"),
],
@ -35,8 +39,8 @@ export const metadata = {
## Tutorials
<resources>
<resource source="CF" title="zscoder - Slope Trick" url="blog/entry/47821"></resource>
<resource source="CF" title="Kuroni - Slope Trick Explained" url="blog/entry/77298"></resource>
<resource source="CF" title="zscoder - Slope Trick" url="blog/entry/47821">3 problems using this trick</resource>
<resource source="CF" title="Kuroni - Slope Trick Explained" url="blog/entry/77298">clarifying the above and another example problem</resource>
</resources>
From the latter link (modified):
@ -46,7 +50,7 @@ From the latter link (modified):
> - It can be divided into multiple sections, where each section is a linear function (usually) with an integer slope.
> - It is a convex/concave function. In other words, the slope of each section is non-decreasing or non-increasing when scanning the function from left to right.
It's generally applicable as a DP optimization. The rest of this module assumes that you are somewhat familiar with at least one of the tutorials mentioned above.
It's generally applicable as a DP optimization.
<info-block title="Pro Tip">
@ -54,6 +58,12 @@ Usually you can come up with a slower (usually $O(N^2)$) DP first and then optim
</info-block>
The rest of this module assumes that you know the basic idea of this trick. In particular, you should be at least somewhat familiar with the $O(N\log N)$ time solution to the first problem in zscoder's tutorial:
<problems-list problems={metadata.problems.ex} />
It's ok if you found the explanations confusing; the example below should help clarify.
## Buy Low Sell High
<problems-list problems={metadata.problems.buy} />
@ -158,7 +168,7 @@ dp[5] = { 3, -2, -9, -16, -25, -35}
dif[5] = { 5, 7, 7, 9, 10}
```
Again, we can choose to sell one share at price $9$. The last three DP values remain the same while the others change.
Again, we can choose to sell one share at price $9$. The last three DP values remain the same while the others change. $dif$ is still in increasing order!
```
dp[5] = { 7, 0, -7, -16, -25, -35}