題面好難找：嘟嘟嘟

貪心 + dp。

首先要按bi的降序排序，讓每一次減少大的數盡量靠前。為啥咧？於是我們就需要證明：令sum = a₁ - (1 - 1) * b₁ + a₂ - (2 - 1) * b₂ + a₃ - (3 - 1) * b₃ + ……+ a_n - (n - 1) * b_n，整理得：sum = (a₁ + a₂ + a₃ + ……+ a_n) + (0 * b₁ + 1 * b₂ + 2 * b₃ + ……+ (n - 1) * b_n)。因為Σa_n是定值，所以讓sum最大就是讓bi降序排序。

然後dp。

令dp[i][j]第 j 回合取ai的最大得分，仿照01背包：dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1] + a[i] - (j - 1) * b[i])。

於是這道題就做完啦。

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<cmath>
 4 #include<algorithm>
 5 #include<cstring>
 6 #include<cstdlib>
 7 #include<cctype>
 8 #include<vector>
 9 #include<stack>
10 #include<queue>
11 using namespace std;
 
12 #define enter puts("") 
13 #define space putchar(‘ ‘)
14 #define Mem(a, x) memset(a, x, sizeof(a))
15 #define rg register
16 typedef long long ll;
17 typedef double db;
18 const int INF = 0x3f3f3f3f;
19 const db eps = 1e-8;
20 const int maxn = 205;
21 inline ll read()
22 {
23   ll ans = 0;
24   char ch = getchar(), last = ‘
 
 ‘;
25   while(!isdigit(ch)) {last = ch; ch = getchar();}
26   while(isdigit(ch)) {ans = ans * 10 + ch - ‘0‘; ch = getchar();}
27   if(last == ‘-‘) ans = -ans;
28   return ans;
29 }
30 inline void write(ll x)
31 {
32   if(x < 0) x = -x, putchar(‘-‘);
33   if(x >= 10) write(x / 10);
34   putchar(x % 10 + ‘0‘);
35 }
36 
37 int n, m;
38 struct Node
39 {
40   int a, b;
41   bool operator < (const Node &oth)const
42   {
43     return b > oth.b;
44   }
45 }t[maxn];
46 ll dp[maxn][maxn];
47 
48 int main()
49 { 
50   n = read(); m = read();
51   for(int i = 1; i <= n; ++i) t[i].a = read();
52   for(int i = 1; i <= n; ++i) t[i].b = read();
53   sort(t + 1, t + n + 1);
54   for(int i = 1; i <= n; ++i)
55     for(int j = 1; j <= m; ++j)
56       dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1] + t[i].a - (j - 1) * t[i].b);
57   write(dp[n][m]), enter;
58   return 0;
59 }

數字遊戲II