nyoj 01背包 289苹果 325zb的生日 456邮票分你一半
2015-05-02 22:30
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</pre>记录自己的成长,避免重复学习!<p></p><p>今天我研究了一下01背包,下面是我做的三道题,比较起来更容易理解、总结。</p><p>题目链接:<a target=_blank target="_blank" href="http://acm.nyist.net/JudgeOnline/problem.php?pid=289">苹果</a></p><p>题目链接:<a target=_blank target="_blank" href="http://acm.nyist.net/JudgeOnline/problem.php?pid=325">zb的生日</a></p><p>题目链接:<a target=_blank target="_blank" href="http://acm.nyist.net/JudgeOnline/problem.php?pid=456">邮票分你一半</a></p><p><span style="white-space:pre"></span>动态规划:避免重复计算,记录下计算过的值,用空间换取时间;</p><p><span style="white-space:pre"></span>01背包:是动态规划应用的一种,就是一系列的物品<span style="font-size:14px">n</span>1,<span style="font-size:14px">n</span>2,<span style="font-size:14px">n</span>3...,<span style="font-size:14px">n</span>n的大小分别是<span style="font-size:14px">c</span>1,<span style="font-size:14px">c</span>2,<span style="font-size:14px">c</span>3,...,<span style="font-size:14px">c</span>n,价值分别是<span style="font-size:14px">w</span>1,<span style="font-size:14px">w</span>2,<span style="font-size:14px">w</span>3,...,<span style="font-size:14px">w</span>n,有一个大小为<span style="font-size:14px">v</span>的背包,现在要在背包里放入价值最大是多少?</p><p>苹果代码:</p><p><span style="white-space:pre">// 这里的<span style="font-size:14px">v题目有告诉,n是不定的</span></span></p><p><span style="white-space:pre"><span style="font-size:14px">//pricep[i]:背包剩余i是时,装载的最大价值是prince[i]</span></span></p><pre name="code" class="java">import java.io.BufferedInputStream; import java.io.PrintStream; import java.util.Arrays; public class Main { static BufferedInputStream bis = new BufferedInputStream(System.in); static PrintStream out = System.out; public static void main(String[] args) throws Exception { int n, v, c, w, price[] = new int[1005];//1005=1000+5 while (true) { n = getInt(); v = getInt(); if (n + v == 0) { break; } Arrays.fill(price, 0);//每次初始化dp数组 for (int j = 0; j < n; j++) { c = getInt(); w = getInt(); for (int i = v; i >= c; i--) {//如果过程不清楚,最好在纸上模拟一下 price[i] = Math.max(price[i], price[i - c] + w); } } out.println(price[v]); } out.close(); bis.close(); } <span style="white-space:pre"> </span>//用BufferedInputStream来优化int输入 static int getInt() throws Exception { int i, temp = 0, mark = 1; while ((i = bis.read()) < 45) ; if (i == 45) { mark = -1; i = bis.read(); } while (i > 47) { temp = temp * 10 + i - 48; i = bis.read(); } return temp * mark; } }
zb的生日、邮票分你一半是一样的!
代码:(zb的生日ac代码)
import java.io.BufferedInputStream; import java.io.PrintStream; import java.util.Arrays; import java.util.Scanner; public class Main { static int[] arr = new int[25], dp = new int[100005];//100005=(20*1000)/2+5 public static void main(String[] args) { Scanner in = new Scanner(new BufferedInputStream(System.in)); PrintStream out = System.out; while (in.hasNextInt()) { int n = in.nextInt(), sum = 0, halfSum; Arrays.fill(dp, 0); for (int i = 1; i <= n; i++) { arr[i] = in.nextInt(); sum += arr[i]; } halfSum = sum >> 1; for (int i = 1; i <= n; i++) {//n给定,苹果的是不给定 for (int j = halfSum; j >= arr[i]; j--) { dp[j] = Math.max(dp[j], dp[j - arr[i]] + arr[i]); } } out.println(sum - 2 * dp[halfSum]); } out.close(); in.close(); } }
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