线性DP，使用单调队列优化。
1 /* 4374 */
2 #include <iostream>
3 #include <sstream>
4 #include <string>
5 #include <map>
6 #include <queue>
7 #include <set>
8 #include <stack>
9 #include <vector>
10 #include <deque>
11 #include <algorithm>
12 #include <cstdio>
13 #include <cmath>
14 #include <ctime>
15 #include <cstring>
16 #include <climits>
17 #include <cctype>
18 #include <cassert>
19 #include <functional>
20 #include <iterator>
21 #include <iomanip>
22 using namespace std;
23 //#pragma comment(linker,"/STACK:102400000,1024000")
24
25 #define sti set<int>
26 #define stpii set<pair<int, int> >
27 #define mpii map<int,int>
28 #define vi vector<int>
29 #define pii pair<int,int>
30 #define vpii vector<pair<int,int> >
31 #define rep(i, a, n) for (int i=a;i<n;++i)
32 #define per(i, a, n) for (int i=n-1;i>=a;--i)
33 #define clr clear
34 #define pb push_back
35 #define mp make_pair
36 #define fir first
37 #define sec second
38 #define all(x) (x).begin(),(x).end()
39 #define SZ(x) ((int)(x).size())
40 #define lson l, mid, rt<<1
41 #define rson mid+1, r, rt<<1|1
42
43 const int INF = 0x3f3f3f3f;
44 const int maxn = 105;
45 const int maxm = 10005;
46 int n, m, x, t;
47 int score[maxn][maxm];
48 int dp[maxn][maxm];
49 int P[maxm], Q[maxm];
50 int sum[maxm];
51
52 void solve() {
53 int i, j, k;
54 int lpos, rpos;
55 int l, r, tmp;
56
57 for (i=1; i<=n; ++i)
58 for (j=1; j<=m; ++j)
59 dp[i][j] = -INF;
60
61 for (j=1; j<=m; ++j)
62 sum[j] = sum[j-1] + score[1][j];
63 for (lpos=max(1,x-t),j=lpos; j<=x; ++j)
64 dp[1][j] = sum[x] - sum[j-1];
65 for (rpos=min(m,x+t),j=rpos; j>x; --j)
66 dp[1][j] = sum[j] - sum[x-1];
67
68 for (i=2; i<=n; ++i) {
69 for (j=1; j<=m; ++j)
70 sum[j] = sum[j-1] + score[i][j];
71
72 // k <= j
73 l = 1, r =0;
74 for (j=1; j<=m; ++j) {
75 lpos = max(1, j-t);
76 tmp = dp[i-1][j] - sum[j-1];
77 while (l<=r && Q[r]<=tmp)
78 --r;
79 Q[++r] = tmp;
80 P[r] = j;
81 while (P[l] < lpos)
82 ++l;
83 dp[i][j] = max(dp[i][j], Q[l] + sum[j]);
84 }
85
86 // k>=j
87 l = 1, r =0;
88 for (j=m; j>=1; --j) {
89 rpos = min(m, j+t);
90 tmp = dp[i-1][j] + sum[j];
91 while (l<=r && Q[r]<=tmp)
92 --r;
93 Q[++r] = tmp;
94 P[r] = j;
95 while (P[l] > rpos)
96 ++l;
97 dp[i][j] = max(dp[i][j], Q[l] - sum[j-1]);
98 }
99 }
100
101 int ans = -INF;
102
103 rep(j, 1, m+1)
104 ans = max(ans, dp[n][j]);
105
106 printf("%d\n", ans);
107 }
108
109 int main() {
110 ios::sync_with_stdio(false);
111 #ifndef ONLINE_JUDGE
112 freopen("data.in", "r", stdin);
113 freopen("data.out", "w", stdout);
114 #endif
115
116 while (scanf("%d %d %d %d", &n, &m, &x, &t)!=EOF) {
117 rep(i, 1, n+1)
118 rep(j, 1, m+1)
119 scanf("%d", &score[i][j]);
120 solve();
121 }
122
123 #ifndef ONLINE_JUDGE
124 printf("time = %d.\n", (int)clock());
125 #endif
126
127 return 0;
128 }
数据发生器。
1 from copy import deepcopy
2 from random import randint, shuffle
3 import shutil
4 import string
5
6
7 def GenDataIn():
8 with open("data.in", "w") as fout:
9 t = 10
10 bound = 10**5
11 # fout.write("%d\n" % (t))
12 for tt in xrange(t):
13 n = randint(1, 100)
14 m = randint(1, 10000)
15 x = randint(1, m)
16 t = randint(1, m)
17 fout.write("%d %d %d %d\n" % (n, m, x, t))
18 for i in xrange(n):
19 L = []
20 for j in xrange(m):
21 x = randint(-500, 500)
22 L.append(x)
23 fout.write(" ".join(map(str, L)) + "\n")
24
25
26 def MovDataIn():
27 desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
28 shutil.copyfile("data.in", desFileName)
29
30
31 if __name__ == "__main__":
32 GenDataIn()
33 MovDataIn()
时间： 2024-10-04 02:19:57