HDOJ4374 One hundred layer

Posted 2020-06-14

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()