背包问题之前的C语言版本已经将思路解析的差不多，虽然还有些许错误需要改正，但大体思路是正确的，需要的读者请参阅动态规划之背包问题（C语言）
背包问题本身就是典型的动态规划问题，所以这里只给出动态规划的算法。

0-1背包

思路一：常规做法

import java.util.Scanner;public class Main {static Scanner in = new Scanner(System.in);static int[] v,w;static int[][] d;static int n, c;public static void main(String[] args) {n = in.nextInt();c = in.nextInt();v = new int[n+1];w = new int[n+1];d = new int[c+1][c+1];for (int i = 1; i <= n; i++) {v[i] = in.nextInt();w[i] = in.nextInt();}/*** d(i, j) = max{d(i+1, j), d(i+1, j - V[i]) + W[i]}* d(i, j)表示把第i, i+1, i+2...n个物品装到容量为 j 的背包中的最大总重量* 所以i必须逆序， j无所谓* */for(int i = n; i >= 1; i--) {for(int j = 0; j <= c; j++) {d[i][j] = (i==n ? 0 : d[i+1][j]);if(j >= v[i]) {d[i][j] = Math.max(d[i][j],d[i+1][j-v[i]]+w[i]);}}}System.out.println(d[1][c]);}
}

思路二：滚动数组，在输入数据的时候就进行处理

import java.util.Scanner;public class Main {static Scanner in = new Scanner(System.in);static int[] v,w;static int[][] d;static int n, c;public static void main(String[] args) {n = in.nextInt();c = in.nextInt();v = new int[n+1];w = new int[n+1];d = new int[c+1][c+1];/*** d(i, j) = max{d(i-1, j), d(i-1, j - V[i]) + W[i]}* d(i, j)表示把第前 i 个物品物品装到容量为 j 的背包中的最大总重量* */for(int i = 1; i <= n; i++) {int v = in.nextInt();int w = in.nextInt();for(int j = 0; j <= c; j++) {d[i][j] = (i==1 ? 0 : d[i-1][j]);if(j >= v) {d[i][j] = Math.max(d[i][j],d[i-1][j-v]+w);}}}System.out.println(d[n][c]);}
}

思路三：用一维数组实现

import java.util.Scanner;class Main {Scanner in = new Scanner(System.in);static int[] w, v, d;static int n, c;public static void main(String[] args) {/*v为背包容量， n为物品件数*/n = in.nextInt();c = in.nextInt();w = new int[n+1];v = new int[n+1];d = new int[c+1];/*w为物品重量数组， v为物品价值数组*/for (int i = 1; i <= n; i++) {w[i] = in.nextInt();v[i] = in.nextInt();}for(int i = 1; i <= n; i++) {//一维数组实现二次循环中必须用倒序for(int j = c; j >= w[i]; j--) {d[j] = Math.max(d[j], d[j - w[i]] + v[i]);}}System.out.println(d[c]);}
}

思路四：最简单版

import java.util.Scanner;public class Main {static Scanner in = new Scanner(System.in);static int[] v, w, d;static int n, c;public static void main(String[] args) {n = in.nextInt();c = in.nextInt();v = new int[n+1];w = new int[n+1];d = new int[c+1];for (int i = 1; i <= n; i++) {int v = in.nextInt();int w = in.nextInt();for (int j = c; j >= 0; j--) {if (j >= v) {d[j] = Math.max(d[j], d[j-v] + w);}}}System.out.println(d[c]);}
}

完全背包

用二维数组实现

import java.util.Scanner;class Main {public static void main(String[] args) {Scanner input = new Scanner(System.in);/*v为背包容量， n为物品件数*/int v = input.nextInt();int n = input.nextInt();int[] weight = new int[n+1];int[] value = new int[n+1];int[][] fa = new int[n+1][v+1];/*weight为物品重量数组， value为物品价值数组*/for (int i = 1; i <= n; i++) {weight[i] = input.nextInt();value[i] = input.nextInt();}for(int i = 1; i <= n; i++) {for(int j = 1; j <= v; j++) {for(int k = 0; k * weight[i] <= j; k++) {fa[i][j] = Math.max(fa[i][j], fa[i - 1][j - k * weight[i]] + k * value[i]);}}}System.out.println(fa[n][v]);}
}

用一维数组实现

import java.util.Scanner;class Main {public static void main(String[] args) {Scanner input = new Scanner(System.in);/*v为背包容量， n为物品件数*/int v = input.nextInt();int n = input.nextInt();int[] weight = new int[n+1];int[] value = new int[n+1];int[] fa = new int[v+1];/*weight为物品重量数组， value为物品价值数组*/for (int i = 1; i <= n; i++) {weight[i] = input.nextInt();value[i] = input.nextInt();}for(int i = 1; i <= n; i++) {//完全背包问题一维数组实现二次循环必须正序for(int j = weight[i]; j <= v; j++) {fa[j] = Math.max(fa[j], fa[j - weight[i]] + value[i]);}}System.out.println(fa[v]);}
}

多重背包

用二维数组实现

import java.util.Scanner;class Main {public static void main(String[] args) {Scanner input = new Scanner(System.in);/*v为背包容量， n为物品件数*/int v = input.nextInt();int n = input.nextInt();int[] weight = new int[n+1];int[] value = new int[n+1];int[] num = new int[n+1];int[][] fa = new int[n+1][v+1];/*weight为物品重量数组， value为物品价值数组*/for (int i = 1; i <= n; i++) {weight[i] = input.nextInt();value[i] = input.nextInt();num[i] = input.nextInt();}for(int i = 1; i <= n; i++) {for(int j = 1; j <= v; j++) {for(int k = 1; k <= num[i] && k * weight[i] <= j; k++) {fa[i][j] = Math.max(fa[i-1][j], fa[i - 1][j - k * weight[i]] + k * value[i]);}}}System.out.println(fa[n][v]);}
}

用一维数组实现

import java.util.Scanner;class Main {public static void main(String[] args) {Scanner input = new Scanner(System.in);/*v为背包容量， n为物品件数*/int v = input.nextInt();int n = input.nextInt();int[] weight = new int[n+1];int[] value = new int[n+1];int[] num = new int[n+1];int[] fa = new int[v+1];/*weight为物品重量数组， value为物品价值数组*/for (int i = 1; i <= n; i++) {weight[i] = input.nextInt();value[i] = input.nextInt();num[i] = input.nextInt();}for (int i = 1; i <= n; i++) {for (int j = v; j >= 1; j--) {for (int k = 1; k <=num[i] && k * weight[i] <= j; k++) {fa[j] = Math.max(fa[j], fa[j - k * weight[i]] + k * value[i]);}}}System.out.println(fa[v]);}
}