动态规划-蓝桥杯-健身

这是一个完全背包的题，可以利用完全背包来解决。

//package com.js.datastructure.recursion.蓝桥.国特训练营.动态规划线性DP;

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int[] kkk = new int[21];
        kkk[0] = 1;
        for (int i = 1; i < 21; i++) {
            kkk[i] = kkk[i-1] * 2;
        }
        //1~n天中选择一些日子健身
        //有m个健身计划，第i个健身计划，需要2^ki天，获得健身增益si
        //有q天有其他安排
        //
        
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int q = scanner.nextInt();

        int[] t = new int[q];

        for (int i = 0; i < q; i++) {
            t[i] = scanner.nextInt();
        }
        
        int[] k = new int[m];
        int[] s = new int[m];

        //记录值
        for (int i = 0; i < m; i++) {
            k[i] = kkk[scanner.nextInt()];
            s[i] = scanner.nextInt();
        }
        
        //定义dp[i]为间隔天数为i时的最大收益数，转化为完全背包,正序遍历
        long[] dp = new long[n+1];
        for (int i = 0; i < m; i++) {
            if(k[i] > n){
                continue;
            }
            dp[k[i]] = Math.max(s[i],dp[k[i]]);
            for (int j = 0; j < n+1; j++) {
                if(dp[j] != 0 && j + k[i] < n+1){
                    dp[j + k[i]] = Math.max(dp[j] + s[i],dp[j + k[i]]);
                }
            }
        }

        //处理dp数组，满足题目中的
        int now = 0;
        for (int i = 0; i < n + 1; i++) {
            if(dp[i] != 0){
                now = i;
            }else {
                dp[i] = dp[now];
            }
        }


        //把时间段摘出来，进行填充
        ArrayList<Integer> time = new ArrayList<>();
        time.add(t[0] - 1);
        for (int i = 1; i < q; i++) {
            time.add(t[i] - t[i-1] - 1);
        }
        time.add(n - t[q-1]);

        long ans = 0;
        for(int tt : time){
            ans = ans + dp[tt];
        }
        System.out.println(ans);
    }
}