ACQUIRE  Land Acquisition
Gold Problem Land Acquisition [Paul Christiano, 2007]
Farmer John is considering buying more land for the farm and has his eye on N (1 <= N <= 50,000) additional rectangular plots, each with integer dimensions (1 <= width_i <= 1,000,000; 1 <= length_i <= 1,000,000).
If FJ wants to buy a single piece of land, the cost is $1/square unit, but savings are available for large purchases. He can buy any number of plots of land for a price in dollars that is the width of the widest plot times the length of the longest plot. Of course, land plots cannot be rotated, i.e., if Farmer John buys a 3x5 plot and a 5x3 plot in a group, he will pay 5x5=25.
FJ wants to grow his farm as much as possible and desires all the plots of land. Being both clever and frugal, it dawns on him that he can purchase the land in successive groups, cleverly minimizing the total cost by grouping various plots that have advantageous width or length values.
Given the number of plots for sale and the dimensions of each, determine the minimum amount for which Farmer John can purchase all
Input
 Line 1: A single integer: N
 Lines 2..N+1: Line i+1 describes plot i with two spaceseparated integers: width_i and length_i
Output
 Line 1: The minimum amount necessary to buy all the plots.
Sample
Input: 4 100 1 15 15 20 5 1 100 Output: 500
Explanation
There are four plots for sale with dimensions as shown.
The first group contains a 100x1 plot and costs 100. The next group contains a 1x100 plot and costs 100. The last group contains both the 20x5 plot and the 15x15 plot and costs 300. The total cost is 500, which is minimal.
hide comments
ppap_1264589:
20211219 16:59:12
DP with Convex Hull Trick !


sherlockvanh:
20201202 16:26:57
why do i get " runtime error (SIGSEGV) " ? anyone can show me some testcases? 

aarustark:
20200518 21:42:24
its giving tle with O(n*n) solution in c++14 

Rishabh:
20200510 15:19:30
O(n^2) not getting AC. Need to will convex hull trick 

lnxdx:
20190925 17:59:45
Why problem tags are always visible? There is no way to hide them? :/


lnxdx:
20190924 22:00:26
This problem can be solved in O(n.log(n)) using Convex Hull or 1D/1D optimizations. But should not be solvable in O(n^2). The site admin should decrease the time complexity of this problem. Last edit: 20190925 17:58:45 

lnxdx:
20190924 21:57:24
For the sake of god, please do not write "in one go". 

prodipdatta7:
20190720 06:30:32
after removing irrelevant rectangles, O(n * n) solution passed 

minhtri5302:
20181114 05:31:43
Bruteforce  > AC 

vishesh197:
20181109 04:11:48
Getting TLE even after removing irrelevant rectangles and applying dp solution O(n^2).

Added by:  Hasan Jaddouh 
Date:  20130531 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  USACO Mar08 