UVA - 10239 The Book-shelver's Problem

最新推荐文章于 2020-02-01 18:16:00 发布

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本文探讨了如何在给定书籍尺寸和书架宽度的情况下，通过优化布局策略，找到能够容纳所有书籍的最小高度书架。通过采用记忆化搜索算法，解决了此问题，并提供了实例演示。

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Description

Problem D
The Book-shelver’s Problem
Input: standard input
Output: standard output
Time Limit: 5 seconds
Memory Limit: 32 MB

You are given a collection of books, which must be shelved in a library bookcase ordered (from top to bottom in the bookcase and from left to right in each shelf) by the books’ catalogue numbers. The bookcase has a fixed width, but you may have any height you like. The books are placed on shelves in the bookcase in the usual upright manner (i.e., you cannot lay a book on its side). You may use as many shelves as you like, placed wherever you like up to the height of the bookcase, and you may put as many books on each shelf as you like up to the width of the bookcase. You may assume that the shelves have negligible thickness.

Now, given an ordered (by catalogue numbers) list of the heights and widths of the books and the width of the bookcase, you are expected to determine what is the minimum height bookcase that can shelve all those books.

Input

The input file may contain multiple test cases. The first line of each test case contains an integer N (1 £ N £ 1000) that denotes the number of books to shelve, and a floating-point number W (0 < W £ 1000) that denotes the width of the bookcase in centimeters. Then follow N lines where the i-th (1 £ i £ N) line contains two floating-point numbers h_i (0 < h_i £ 100) and w_i (0 < w_i £ W) indicating the height and width (both in centimeters) of the i-th book in the list ordered by catalogue numbers. Each floating-point number will have four digits after the decimal point.

A test case containing two zeros for N and W terminates the input.

Output

For each test case in the input print a line containing the minimum height (in centimeters, up to four digits after the decimal point) of the bookcase that can shelve all the books in the list.

Sample Input
5 30.0000
30.0000 20.0000
20.0000 10.0000
25.0000 10.0000
30.0000 15.0000
10.0000 5.0000
10 20.0000
10.0000 2.0000
15.0000 10.0000
20.0000 5.0000
6.0000 2.0000
10.0000 3.0000
30.0000 6.0000
5.0000 3.0000
35.0000 2.0000
32.0000 4.0000
10.0000 6.0000
0 0.0000

Sample Output
60.0000

65.0000

题意：n本书，有宽和高，要你依次放到书架上，可以用木板隔层，每层最多不超过m的宽度

思路：竟然要求是依次放，那么每本书有放这层和不放这层的两种可能，记忆化搜索，注意要考虑全都放一层的情况

#include <iostream>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <cstdlib>
using namespace std;
const int maxn = 1005;
const double inf = 0x3f3f3f3f3f3f3f3f;
double m, h[maxn], w[maxn], dp[maxn];
int n, vis[maxn];

double dfs(int cur) {
	if (cur >= n+1)
		return 0;
	if (vis[cur])
		return dp[cur];
	double &ans = dp[cur];
	ans = inf;
	vis[cur] = 1;
	double H = h[cur], W = w[cur];
	for (int u = cur+1; u <= n+1; u++) {
		ans = min(ans, dfs(u)+H);
		W += w[u];
		H = max(H, h[u]);
		if (W-m > 1e-9)
			break;
	}
	return ans;
}

int main() {
	while (scanf("%d%lf", &n, &m) != EOF && n) {
		memset(vis, 0, sizeof(vis));
		for (int i = 1; i <= n; i++)
			scanf("%lf%lf", &h[i], &w[i]);
		double ans = dfs(1);
		printf("%.4lf\n", ans);
	}
	return 0;
}