nyoj 01背包 289苹果 325zb的生日 456邮票分你一半

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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+5while (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+5public 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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