HDU--2115

I Love This Game

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6357    Accepted Submission(s): 2175


Problem Description
Do you like playing basketball ? If you are , you may know the NBA Skills Challenge . It is the content of the basketball skills . It include several parts , such as passing , shooting , and so on. After completion of the content , the player who takes the shortest time will be the winner . Now give you their names and the time of finishing the competition , your task is to give out the rank of them ; please output their name and the rank, if they have the same time , the rank of them will be the same ,but you should output their names in lexicographic order.You may assume the names of the players are unique.

Is it a very simple problem for you? Please accept it in ten minutes.
 

Input
This problem contains multiple test cases! Ease test case contain a n(1<=n<=10) shows the number of players,then n lines will be given. Each line will contain the name of player and the time(mm:ss) of their finish.The end of the input will be indicated by an integer value of zero.
 

Output
The output format is shown as sample below.
Please output the rank of all players, the output format is shown as sample below;
Output a blank line between two cases.
 

Sample Input
  
10 Iverson 17:19 Bryant 07:03 Nash 09:33 Wade 07:03 Davies 11:13 Carter 14:28 Jordan 29:34 James 20:48 Parker 24:49 Kidd 26:46 0
 

Sample Output
  
Case #1 Bryant 1 Wade 1 Nash 3 Davies 4 Carter 5 Iverson 6 James 7 Parker 8 Kidd 9 Jordan 10
 

Author
為傑沉倫
 

Source

#include<stdio.h>
#include<string.h>
struct people{
	char name[50];
	int time;
	int rank;
} a[11];
char temp[50];
int main()
{
	int n,i,count=0,m,s,j;
	while(scanf("%d",&n),n)
	{
		if(count) printf("\n");
		count++;
		printf("Case #%d\n",count);
		for(i=1;i<=n;i++)
		{
			scanf("%s %d:%d",a[i].name,&m,&s);
			a[i].time=m*60+s;
		}
		for(i=1;i<=n;i++)
		for(j=i+1;j<=n;j++)
		{
			if(a[i].time>a[j].time) 
			{
				strncpy(temp,a[j].name,50);
				strncpy(a[j].name,a[i].name,50);
				strncpy(a[i].name,temp,50);
				m=a[i].time;
				a[i].time=a[j].time;
				a[j].time=m;
			}
		}
		a[1].rank=1;
		for(i=2;i<=n;i++)
		if(a[i].time==a[i-1].time)
			a[i].rank=a[i-1].rank;
		else 
			a[i].rank=i;
		for(i=1;i<=n;i++)
			printf("%s %d\n",a[i].name,a[i].rank);
	}
	return 0;
}


HDU-3480 是一个典型的动态规划问题,其题目标题通常为 *Division*,主要涉及二维费用背包问题或优化后的动态规划策略。题目大意是:给定一个整数数组,将其划分为若干个连续的子集,每个子集最多包含 $ m $ 个元素,并且每个子集的最大值与最小值之差不能超过给定的阈值 $ t $,目标是使所有子集的划分代价总和最小。每个子集的代价是该子集最大值与最小值的差值。 ### 动态规划思路 设 $ dp[i] $ 表示前 $ i $ 个元素的最小代价。状态转移方程如下: $$ dp[i] = \min_{j=0}^{i-1} \left( dp[j] + cost(j+1, i) \right) $$ 其中 $ cost(j+1, i) $ 表示从第 $ j+1 $ 到第 $ i $ 个元素构成一个子集的代价,即 $ \max(a[j+1..i]) - \min(a[j+1..i]) $。 为了高效计算 $ cost(j+1, i) $,可以使用滑动窗口或单调队列等数据结构来维护区间最大值与最小值,从而将时间复杂度优化到可接受的范围。 ### 示例代码 以下是一个简化版本的动态规划实现,使用暴力方式计算区间代价,适用于理解问题结构: ```cpp #include <bits/stdc++.h> using namespace std; const int INF = 0x3f3f3f3f; const int MAXN = 10010; int a[MAXN]; int dp[MAXN]; int main() { int T, n, m; cin >> T; for (int Case = 1; Case <= T; ++Case) { cin >> n >> m; for (int i = 1; i <= n; ++i) cin >> a[i]; dp[0] = 0; for (int i = 1; i <= n; ++i) { dp[i] = INF; int mn = a[i], mx = a[i]; for (int j = i; j >= max(1, i - m + 1); --j) { mn = min(mn, a[j]); mx = max(mx, a[j]); if (mx - mn <= T) { dp[i] = min(dp[i], dp[j - 1] + mx - mn); } } } cout << "Case " << Case << ": " << dp[n] << endl; } return 0; } ``` ### 优化策略 - **单调队列**:可以使用两个单调队列分别维护当前窗口的最大值与最小值,从而将区间代价计算的时间复杂度从 $ O(n^2) $ 降低到 $ O(n) $。 - **斜率优化**:若问题满足特定的决策单调性,可以考虑使用斜率优化技巧进一步加速状态转移过程。 ### 时间复杂度分析 原始暴力解法的时间复杂度为 $ O(n^2) $,在 $ n \leq 10^4 $ 的情况下可能勉强通过。通过单调队列优化后,可以稳定运行于 $ O(n) $ 或 $ O(n \log n) $。 ### 应用场景 HDU-3480 的问题模型可以应用于资源调度、任务划分等场景,尤其适用于需要控制子集内部差异的问题,如图像分块压缩、数据分段处理等[^1]。 ---
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