HDU Problem 1051 Wooden Sticks 【LIS】

Wooden Sticks

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 18561    Accepted Submission(s): 7569

Problem Description

There is a pile of n wooden sticks. The length and weight of each stick are known in advance. The sticks are to be processed by a woodworking machine in one by one fashion. It needs some time, called setup time, for the machine to prepare processing a stick. The setup times are associated with cleaning operations and changing tools and shapes in the machine. The setup times of the woodworking machine are given as follows: 

(a) The setup time for the first wooden stick is 1 minute. 
(b) Right after processing a stick of length l and weight w , the machine will need no setup time for a stick of length l' and weight w' if l<=l' and w<=w'. Otherwise, it will need 1 minute for setup. 

You are to find the minimum setup time to process a given pile of n wooden sticks. For example, if you have five sticks whose pairs of length and weight are (4,9), (5,2), (2,1), (3,5), and (1,4), then the minimum setup time should be 2 minutes since there is a sequence of pairs (1,4), (3,5), (4,9), (2,1), (5,2).

 

Input

The input consists of T test cases. The number of test cases (T) is given in the first line of the input file. Each test case consists of two lines: The first line has an integer n , 1<=n<=5000, that represents the number of wooden sticks in the test case, and the second line contains n 2 positive integers l1, w1, l2, w2, ..., ln, wn, each of magnitude at most 10000 , where li and wi are the length and weight of the i th wooden stick, respectively. The 2n integers are delimited by one or more spaces.

 

Output

The output should contain the minimum setup time in minutes, one per line.

 

Sample Input

3 5 4 9 5 2 2 1 3 5 1 4 3 2 2 1 1 2 2 3 1 3 2 2 3 1

 

Sample Output

2 1 3

 

Source

Asia 2001, Taejon (South Korea)

 

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对比贪心

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
const int MAXN = 5010;
const int INF = 1e8;
struct node{
    int l, w;
}S[MAXN];
bool cmp(node x, node y) {
    if (x.l == y.l) return x.w > y.w;
    return x.l > y.l;
}
int g[MAXN], dp[MAXN];
int main() {
    int t = 1, n;
    scanf("%d", &t);
    //freopen("data.txt", "r", stdin);
    //freopen("1.txt", "w", stdout);
    while (t--) {
        scanf("%d", &n); //printf("%d ", n);
        for (int i = 1; i <= n; i++) {
            scanf("%d%d", &S[i].l, &S[i].w);
            //printf("%d %d ", S[i].l, S[i].w);
            g[i] = INF;
        }
        int ans = 0;
        /*
        将木棒的重量升序排，如果一个木棒会占用时间
        他的长度必定要大于dp中最大的，这时把他接在后面，这样就转换成了
        LIS的模板。
        */
        sort(S + 1, S + 1 + n, cmp);
        for (int i = 1; i <= n; i++) {
            int k = lower_bound(g+1, g+1+n, S[i].w) - g;
            dp[i] = k; g[k] = min(S[i].w, g[k]);
            ans = max(ans, dp[i]);
        }
        printf("%d
", ans);
    }
    return 0;
}