背包问题
- 01背包(不需要装满)
- 01背包(需要装满)
- 完全背包
- 多重背包（一维空间）
- 多重背包（二进制）
- 混合背包
- 二维费用
- 分组背包
01背包(不需要装满)
import java.util.Scanner;
public class ZeroOnePack {
static int N = 1010;
static int INF = 0x3f3f3f3f;
static int[] dp = new int[N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int v = sc.nextInt();
for (int i = 1; i <= n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
for (int j = v; j >= weight; j--) {
dp[j] = Math.max(dp[j], dp[j - weight] + value);
}
}
System.out.println(dp[v]);
sc.close();
}
}
01背包(需要装满)
import java.util.Scanner;
public class ZeroOnePack {
static int N = 1010;
static int INF = 0x3f3f3f3f;
static int[] dp = new int[N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int v = sc.nextInt();
Arrays.fill(dp, -INF);
dp[0] = 0;
for (int i = 1; i <= n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
for (int j = v; j >= weight; j--) {
dp[j] = Math.max(dp[j], dp[j - weight] + value);
}
}
System.out.println(dp[v]);
sc.close();
}
}
完全背包
import java.util.Scanner;
public class CompletePack {
static int N=1010;
static int[] dp = new int[N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int v = sc.nextInt();
for (int i = 1; i <= n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
for (int j = weight; j <=v; j++) {
dp[j] = Math.max(dp[j], dp[j - weight] + value);
}
}
System.out.println(dp[v]);
sc.close();
}
}
多重背包（一维空间）
import java.util.Scanner;
public class MultiPack {
static int N = 110;
static int[] dp = new int[N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int v = sc.nextInt();
for (int i = 1; i <= n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
int amount = sc.nextInt();
for (int j = v; j >=0; j--) {
for (int k = 0; k <= amount && j >= k * weight; k++) {
dp[j] = Math.max(dp[j], dp[j - k * weight] + k * value);
}
}
}
System.out.println(dp[v]);
sc.close();
}
}
多重背包（二进制）
import java.util.ArrayList;
import java.util.Scanner;
class goods {
int weight, value;
public goods(int weight, int value) {
this.weight = weight;
this.value = value;
}
}
public class MultiPack {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
var Good = new ArrayList<goods>();
int[] dp = new int[2010];
int n = sc.nextInt();
int v = sc.nextInt();
for (int i = 1; i <= n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
int amont = sc.nextInt();
for (int j = 1; j <= amont; j *= 2) {
amont -= j;
Good.add(new goods(weight * j, value * j));
}
if (amont > 0) {
Good.add(new goods(weight * amont, value * amont));
}
}
for (var good :
Good) {
for (int i = v; i >= good.weight; i--) {
dp[i] = Math.max(dp[i], dp[i - good.weight] + good.value);
}
}
System.out.println(dp[v]);
sc.close();
}
}
混合背包
import java.util.ArrayList;
import java.util.Scanner;
class goods {
int weight, value, kind;
public goods(int weight, int value, int kind) {
this.weight = weight;
this.value = value;
this.kind = kind;
}
}
public class Main {
static int n, v;
static int[] dp = new int[2010];
static ArrayList<goods> GOOD = new ArrayList<>();
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
n = sc.nextInt();
v = sc.nextInt();
for (int i = 0; i < n; i++) {
int weight = sc.nextInt();
int value = sc.nextInt();
int kind = sc.nextInt();
GOOD.add(new goods(weight, value, kind));
}
for (var good :
GOOD) {
if (good.kind == -1) {
ZeroOnePack(good.weight, good.value);
} else if (good.kind == 0) {
CompletePack(good.weight, good.value);
} else {
MultiplePack(good.weight, good.value, good.kind);
}
}
System.out.println(dp[v]);
sc.close();
}
static void ZeroOnePack(int weight, int value) {
for (int i = v; i >= weight; i--) {
dp[i] = Math.max(dp[i], dp[i - weight] + value);
}
}
static void CompletePack(int weight, int value) {
for (int i = weight; i <= v; i++) {
dp[i] = Math.max(dp[i], dp[i - weight] + value);
}
}
static void MultiplePack(int weight, int value, int amount) {
if (amount * weight >= v) {
CompletePack(weight, value);
return;
}
int k = 1;
while (k < amount) {
ZeroOnePack(k * weight, k * value);
amount = amount - k;
k = k * 2;
}
ZeroOnePack(amount * weight, amount * value);
}
}
二维费用
import java.util.Scanner;
public class Main {
static int N = 1010;
static int n, v, m;
static int[][] dp = new int[N][N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
n = sc.nextInt();
v = sc.nextInt();
m = sc.nextInt();
for (int i = 1; i <= n; i++) {
int volume = sc.nextInt();
int weight = sc.nextInt();
int value = sc.nextInt();
for (int j = v; j >= volume; j--) {
for (int k = m; k >= weight; k--) {
dp[j][k] = Math.max(dp[j][k], dp[j - volume][k - weight] + value);
}
}
}
System.out.println(dp[v][m]);
sc.close();
}
}
分组背包
import java.util.Scanner;
public class Main {
static int N = 110;
static int[] dp = new int[N];
static int[] s = new int[N];
static int[][] weight = new int[N][N];
static int[][] value = new int[N][N];
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int v = sc.nextInt();
for (int i = 1; i <= n; i++) {
s[i] = sc.nextInt();
for (int j = 1; j <= s[i]; j++) {
weight[i][j]=sc.nextInt();
value[i][j]=sc.nextInt();
}
}
for (int i = 1; i <=n ; i++) {
for (int j = v; j >=0 ; j--) {
for (int k = 1; k <=s[i] ; k++) {
if (j>=weight[i][k]) {
dp[j] = Math.max(dp[j], dp[j - weight[i][k]] + value[i][k]);
}
}
}
}
System.out.println(dp[v]);
sc.close();
}
}
