POJ_2533 Frogger 最小瓶颈路

题目链接：http://poj.org/problem?id=2533

该题其实等价于求两点之间的最小瓶颈路-min(d[i][j], max(d[i][k], d[k][j])),即最短路中的最大值

用Floyd算法可以在O(n3)内求出，鉴于此题n=200，因此直接上Floyd

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <string>
using namespace std;
#define inf 0x3f3f3f3f
#define maxm 30005
#define maxn 205
double d[maxn][maxn];
int n, m;
int x[maxn], y[maxn];

void floyd(){
    for(int k = 0; k < n; k++){
        for(int i = 0; i < n; i++)
            for(int j = 0; j < n; j++)
                d[i][j] = min(d[i][j], max(d[i][k], d[k][j]));
    }
}

int main(){
    int cnt = 1;
    while(scanf("%d", &n) && n){
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(i == j) d[i][j] = 0;
                d[i][j] = inf;
            }
        }
        for(int i = 0; i < n; i++){
            scanf("%d %d", &x[i], &y[i]);
        }
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                d[i][j] = sqrt(pow(x[i] - x[j], 2) + pow(y[i] - y[j], 2));
            }
        }
        floyd();
        printf("Scenario #%d
", cnt++);
        printf("Frog Distance = %.3f

", d[0][1]);
    }
}

题目：

Longest Ordered Subsequence

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 51551		Accepted: 22931

Description

A numeric sequence of a_i is ordered if a₁ < a₂ < ... < a_N. Let the subsequence of the given numeric sequence (a₁, a₂, ..., a_N) be any sequence (a_i1, a_i2, ..., a_iK), where 1 <= i₁ < i₂ < ... < i_K <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).

Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

7
1 7 3 5 9 4 8

Sample Output

4