2.6-Java普及组 蓝桥算法训练营

[Feishi11]

采药：背包01 完全背包

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        int m = sc.nextInt();
        int[] dp = new int[1005];
        int[] w = new int[m + 1];
        int[] v = new int[m + 1];
        for (int i = 1; i <= m; i++) {
            w[i] = sc.nextInt();
            v[i] = sc.nextInt();
        }
        for (int i = 1; i <= m; i++) {
            //这里改for (int j = w[i]; j <=t; j++)就是完全背包
            for (int j = t; j >= w[i]; j--) {
                dp[j] = Math.max(dp[j], dp[j - w[i]] + v[i]);
            }
        }
        System.out.println(dp[t]);
    }
}

摘花生：二维做法

状态转移 (i-1, j)即上面来,(i, j-1)即左边来两两取最大值加上当前的值就好了

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int[][] a = new int[n + 1][m + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= m; j++) {
                    a[i][j] = sc.nextInt();
                }
            }
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= m; j++) {
                    a[i][j] = Math.max(a[i][j - 1], a[i - 1][j]) + a[i][j];
                }
            }
            System.out.println(a[n][m]);
        }
    }
}

摘花生：一维做法

dp[i][j]只需要用到这一层和上一层的元素可以压缩成一维

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int m = sc.nextInt();
            int[] a = new int[1005];
            int max = -1;
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= m; j++) {
                    int x = sc.nextInt();
                    a[j] = Math.max(a[j - 1], a[j]) + x;
                    max = Math.max(a[j], max);
                }
            }
            System.out.println(max);
        }
    }
}

摆花： 

//i表示有多少种花，j表示有多少盆花，k表示某种花放多少盆

import java.util.Scanner;

public class 摆花 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int mod = (int) (1e6 + 7);
        int[][] dp = new int[n + 1][m + 1];
        dp[0][0] = 1;
        for (int i = 1; i <= n; i++) {
            int a = sc.nextInt();
            for (int j = 0; j <= m; j++) {
                //注意这里要j-k>=0
                for (int k = 0; k <= a && j - k >= 0; k++) {
                    dp[i][j] = (dp[i][j] + dp[i - 1][j - k]) % mod;
                }
            }
        }
        System.out.println(dp[n][m]);
    }
}