Codeforces 712 D. Memory and Scores (DP+滚动数组+前缀和优化)

 1 //#pragma comment(linker, "/STACK:102400000, 102400000")
 2 #include <algorithm>
 3 #include <iostream>
 4 #include <cstdlib>
 5 #include <cstring>
 6 #include <cstdio>
 7 #include <vector>
 8 #include <cmath>
 9 #include <ctime>
10 #include <list>
11 #include <set>
12 #include <map>
13 using namespace std;
14 typedef long long LL;
15 typedef pair <int, int> P;
16 const int N = 2e5 + 205;
17 LL dp[2][N], mod = 1e9 + 7, sum[N], dpA[2][N], sumA[N];
18 
19 int main()
20 {
21     int a, b, k, t;
22     scanf("%d %d %d %d", &a, &b, &k, &t);
23     a += 1e5, b += 1e5;
24     dp[0][b] = 1;
25     dpA[0][a] = 1;
26     sum[b] = 1, sumA[a] = 1;
27     for(int i = 1; i <= t; ++i) {
28         for(int j = 1; j < N; ++j) {
29             dp[i%2][j] = dpA[i%2][j] = 0;
30         }
31         for(int j = -k*i; j <= k*i; ++j) {
32             int l = max(-k*(i - 1), j - k), r = min(k*(i - 1), j + k);
33             dp[i % 2][b + j] = ((sum[r + b] - sum[l - 1 + b] + dp[i % 2][b + j]) % mod + mod) % mod;
34             dpA[i % 2][a + j] = ((sumA[r + a] - sumA[l - 1 + a] + dpA[i % 2][a + j]) % mod + mod) % mod;
35         }
36         for(int j = 1; j < N; ++j) { //在每轮中sum都会重新更新
37             sum[j] = (sum[j - 1] + dp[i % 2][j]) % mod;
38             sumA[j] = (sumA[j - 1] + dpA[i % 2][j]) % mod;
39         }
40     }
41     LL ans = 0;
42     for(int i = 1; i < N; ++i) {
43         ans = (ans + sum[i - 1]*dpA[t % 2][i] % mod) % mod;
44     }
45     printf("%lld\n", ans);
46     return 0;
47 }