AcWing 3. 完全背包问题JAVA题解
原题链接
简单
作者:
巴韭特
,
2021-05-19 20:38:42
,
所有人可见
,
阅读 2
朴素写法
import java.util.*;
public class Main {
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int N = scan.nextInt();
int V = scan.nextInt();
int[] v = new int[N + 1];
int[] w = new int[N + 1];
for (int i = 1; i <= N; i++) {
v[i] = scan.nextInt();
w[i] = scan.nextInt();
}
int[][] dp = new int[N + 1][V + 1];
for (int i = 1; i <= N; i++) {
for (int j = 0; j <= V; j++) {
for (int k = 0; k * v[i] <= j; k++) {
// k = 0时,相当于没选第i个物品
dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - v[i] * k] + w[i] * k);
}
}
}
System.out.println(dp[N][V]);
}
}
优化成二层循环的写法
import java.util.*;
public class Main {
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int N = scan.nextInt();
int V = scan.nextInt();
int[] v = new int[N + 1];
int[] w = new int[N + 1];
for (int i = 1; i <= N; i++) {
v[i] = scan.nextInt();
w[i] = scan.nextInt();
}
int[][] dp = new int[N + 1][V + 1];
for (int i = 1; i <= N; i++) {
for (int j = 0; j <= V; j++) {
dp[i][j] = dp[i-1][j];
if (j >= v[i]) {
dp[i][j] = Math.max(dp[i][j], dp[i][j - v[i]] + w[i]);
}
}
}
/*
for (int i = 1; i <= N; i++) {
for (int j = v[i]; j <= V; j++) {
dp[i][j] = Math.max(dp[i-1][j], dp[i][j - v[i]] + w[i]);
}
}
for循环内部不能这么写,因为这样会导致j < v[i]这一部分的
dp[i][j]为0, 而不是dp[i-1][j]
*/
System.out.println(dp[N][V]);
}
}
优化成一维DP的写法
import java.util.*;
public class Main {
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
int N = scan.nextInt();
int V = scan.nextInt();
int[] v = new int[N];
int[] w = new int[N];
for (int i = 0; i < N; i++) {
v[i] = scan.nextInt();
w[i] = scan.nextInt();
}
int[] dp = new int[V + 1];
for (int i = 0; i < N; i++) {
for (int j = v[i]; j <= V; j++) {
dp[j] = Math.max(dp[j], dp[j - v[i]] + w[i]);
}
}
System.out.println(dp[V]);
}
}