USACO humble, USACO humble

USACO humble, USACO humble

Constructed with set, priority queue and heap can also be

/*ID:kevin_s1PROG:humbleLANG:C++*/#include <iostream>#include <cstdio>#include <string>#include <cstring>#include <vector>#include <map>#include <set>#include <algorithm>#include <cstdlib>#include <list>#include <cmath>using namespace std;#define MAXK 110//gobal variable====int K, N;long int S[MAXK];set<long int> humble;//==================//function==========//==================int main(){freopen("humble.in","r",stdin);freopen("humble.out","w",stdout);cin>>K>>N;for(int i = 1; i <= K; i++){cin>>S[i];humble.insert(S[i]);}for(int i = 1; i <= K; i++){set<long int>::iterator iter = humble.begin();while(1){long int tmp = (*iter) * S[i];if(tmp < 0)break;if(humble.size() > N){humble.erase(--humble.end());if(tmp > (*(--humble.end())))break;}humble.insert(tmp);iter++;}}cout<< *(--humble.end())<<endl;return 0;}

Usaco 313 has no simple algorithm and does not time out.

Humble?
We calculate the first n ugly numbers in the array hum. To make it easier to implement, we also use 1 as an ugly number, so we need to slightly adjust the algorithm.
When we know the first k ugly numbers and want to get the k + 1 number, we can do this: Find the smallest ugly number for each prime number p, h makes h * p bigger than the last ugly number
Take the smallest one in h * p we found: it is the next ugly number in order to make the search faster, we can maintain an index "pindex" for each prime number, which indicates the ugly number that each prime number has received, starting from there every time instead of starting from scratch.

ACM solution report

Category of a poj question
Mainstream algorithms:
1. Search // trace back
2. DP (Dynamic Planning)
3. Greedy
4. Graph Theory // Dijkstra, Minimum Spanning Tree, and network stream
5. Number Theory // solves the modulus linear equation
6. Calculate the area and perimeter of the joint of the geometric/Convex Shell with the same placement of the rectangle
7. Composite math // Polya Theorem
8. Simulation
9. Data Structure // check the collection and heap
10. Game Theory
1. Sorting
1423,169 4, 1723,172 7, 1763,178 8, 1828,183 8, 1840,220 1, 2376,
2377,238 0, 1318,187 1971,197, 1990,200 4, 2002,209 1, 2379 2,
1002 (character processing is required, and sorting can be done in a fast way) 1007 (stable sorting) 2159 (difficult to understand)
2231 2371 (simple sorting) 2388 (sequence statistics algorithm) 2418 (Binary sorting tree)
2. Search, backtracking, and traversal
2329
Simple: 1128,116 6, 1176,123 1, 1256,127 0, 1321,154 3, 1606,166 4,
1731,174 2, 1745,184, 1950,203, 2157,218 8, 2183,238 2, 2386,242 1, 6
Not easy: 1024,105 4, 1117,116 7, 1708,174 6, 1775,187 8, 1903,196 6, 2046,
2197,234 9
Recommended: 1011,119 0, 1191,141 6, 1579,163 2, 1639,165 9, 1680,168 3, 1691,
1709,171 4, 1753,1771, 1826,185 5, 1856,189 0, 1924,193 5, 1948,197 9, 1980,217 2331,233 1979, 1980 9, (similar to the maze), (higher requirements for pruning)
3. Calendar
1008 2080 (Be careful with such questions)
4. Enumeration
1387,141, 2245,232, 2363,238 1, 1650 6, (higher pruning requirements), (decimal precision problem)
5. Typical data structure Algorithms
Easy: 1182,165 6, 2021,202 3, 2051,215 3, 2227,223 6, 2247,235 2,
2395
Not easy: 1145,117 7, 1195,122 7, 1661,183 4
Recommended: 1330,133 8, 1451,147 0, 1634,168 9, 1693,170 3, 1724,198 8, 2004,
2010,211 9, 2274
1125 (fresh algorithm), 2421 (Minimum Spanning Tree of the graph)
6. Dynamic Planning
1037 A decorative fence,
1050 To the Max,
1088 skiing,
1125 Stockbroker Grapevine,
1141 Brackets Sequence,
1159 Palindrom ...... remaining full text>