HDU 1051 二维排序安排时间 (贪心||STL_set 水过)

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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
 



题目大意:

给n根木棍的长度和重量。根据要求求出制作木棍的最短时间。建立第一个木棍需要1分钟,若是接着要制作的木棍重量和长度都比此木棍长就不需要建立的时间,若是没有,则再需要建立时间。求时间最小为多少

先将一维的顺序固定,在贪心安排第二维的时间。


#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<set>
using namespace std;
set<int>ss;
set<int>::iterator it;

struct node
{
	int l,w;
}a[55555];

bool cmp(node t1,node t2)
{
	if(t1.l<t2.l) return true;
	else if(t1.l==t2.l && t1.w<t2.w) return true;
	return false;
}

int main()
{
  
	int t,n,i,j;
	scanf("%d",&t);
//	cin>>t;
	while(t--) {
		scanf("%d",&n);
		ss.clear();
		for(i=1;i<=n;i++) scanf("%d%d",&a[i].l,&a[i].w);
		sort(a+1,a+1+n,cmp);
		ss.insert(a[1].w);
		for(i=2;i<=n;i++) {
			it=upper_bound(ss.begin(),ss.end(),a[i].w);
			if(it==ss.begin()) {
				ss.insert(a[i].w);
				continue;
			}
			it--;
			ss.erase(*it);
			ss.insert(a[i].w);
		}
		printf("%d\n",ss.size());
	}
	return 0;
} 



贪心

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

struct stick
{
    int l;
    int w;
}s[5000];

bool cmp(stick a,stick b)
{
    if(a.l<b.l)
        return true;
    else if(a.l>b.l)
        return false;
    else
        return a.w<b.w;
}

int main()
{
    int t,n,minute,ti,number;
    int mark[5000];
    cin>>t;
    while(t--)
    {
        cin>>n;
        for(int i=0;i<n;i++)
            cin>>s[i].l>>s[i].w;
        sort(s,s+n,cmp);
        memset(mark,0,sizeof(mark));
        number=0;
        minute=0;
        int pl;
        while(number!=n)
        {
            for(int i=0;i<n;i++)
                if(!mark[i])
                {
                    pl=i;
                    minute++;
                    break;
                }
            for(int i=0;i<n;i++)
            {
                if(!mark[i]&&s[i].l>=s[pl].l&&s[i].w>=s[pl].w)
                {
                    mark[i]=1;
                    number++;
                    pl=i;
                }
            }
        }
        cout<<minute<<endl;
    }
    return 0;
}






### HDU OJ Problem 2566 Coin Counting Solution Using Simple Enumeration and Generating Function Algorithm #### 使用简单枚举求解硬币计数问题 对于简单的枚举方法,可以通过遍历所有可能的组合方式来计算给定面额下的不同硬币组合数量。这种方法虽然直观但效率较低,在处理较大数值时性能不佳。 ```java import java.util.Scanner; public class Main { public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int[] coins = {1, 2, 5}; // 定义可用的硬币种类 while (scanner.hasNext()) { int targetAmount = scanner.nextInt(); int countWays = findNumberOfCombinations(targetAmount, coins); System.out.println(countWays); } } private static int findNumberOfCombinations(int amount, int[] denominations) { if (amount == 0) return 1; if (amount < 0 || denominations.length == 0) return 0; // 不使用当前面值的情况 int excludeCurrentDenomination = findNumberOfCombinations(amount, subArray(denominations)); // 使用当前面值的情况 int includeCurrentDenomination = findNumberOfCombinations(amount - denominations[0], denominations); return excludeCurrentDenomination + includeCurrentDenomination; } private static int[] subArray(int[] array) { if (array.length <= 1) return new int[]{}; return java.util.Arrays.copyOfRange(array, 1, array.length); } } ``` 此代码实现了通过递归来穷尽每一种可能性并累加结果的方式找到满足条件的不同组合数目[^2]。 #### 利用母函数解决硬币计数问题 根据定义,可以将离散列中的每一个元素映射到幂级数的一个项上,并利用这些多项式的乘积表示不同的组合情况。具体来说: 设 \( f(x)=\sum_{i=0}^{+\infty}{a_i*x^i}\),其中\( a_i \)代表当总金额为 i 时能够组成的方案总数,则有如下表达式: \[f_1(x)=(1+x+x^2+...)\] 这实际上是一个几何级数,其封闭形式可写作: \[f_1(x)=\frac{1}{(1-x)}\] 同理,对于其他类型的硬币也存在类似的生成函数。因此整个系统的生成函数就是各个单独部分之积: \[F(x)=f_1(x)*f_2(x)...*f_n(x)\] 最终目标是从 F(x) 中提取系数即得到所需的结果。下面给出基于上述理论的具体实现: ```cpp #include<iostream> using namespace std; const int MAXN = 1e4 + 5; int dp[MAXN]; void solve() { memset(dp, 0, sizeof(dp)); dp[0] = 1; // 初始化基础状态 int values[] = {1, 2, 5}, size = 3; for (int j = 0; j < size; ++j){ for (int k = values[j]; k <= 10000; ++k){ dp[k] += dp[k-values[j]]; } } } int main(){ solve(); int T; cin >> T; while(T--){ int n; cin>>n; cout<<dp[n]<<endl; } return 0; } ``` 这段 C++ 程展示了如何应用动态规划技巧以及生成函数的概念高效地解决问题实例[^1]。
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