HDOJ4261 Estimation

Posted 2020-06-13

挺不错的一道题，基本思路是dp。关键点是如何求区间内的Sigma|A_i-B_i|。
线段树做TLE了，优先队列可以过。

  1 /* 4261 */
  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 = 1e9;
 44 const int maxn = 2005;
 45 const int maxm = 30;
 46 int n, m;
 47 int a[maxn];
 48 int dp[maxm][maxn];
 49 int dif[maxn][maxn];
 50 
 51 void solve() {
 52     int tmp;
 53     
 54     rep(i, 1, n+1) {
 55         priority_queue<int> q;
 56         priority_queue<int, vi, greater<int> > Q;
 57         
 58         int ls, rs;
 59         int ln, rn;
 60         int x, xx;
 61         int l = 0;
 62         
 63         ln = rn = 0;
 64         ls = rs = 0;
 65         rep(j, i, n+1) {
 66             ++l;
 67             x = a[j];
 68             if (l & 1) {
 69                 ++ln;
 70                 if (rn && Q.top()<x) {
 71                     xx = Q.top();
 72                     Q.pop();
 73                     q.push(xx);
 74                     ls += xx;
 75                     Q.push(x);
 76                     rs += x - xx;
 77                 } else {
 78                     q.push(x);
 79                     ls += x;
 80                 }
 81                 
 82                 x = q.top();
 83                 tmp = rs - ls + x;
 84                 dif[i][j] = tmp;
 85             } else {
 86                 ++rn;
 87                 if (q.top() > x) {
 88                     xx = q.top();
 89                     q.pop();
 90                     Q.push(xx);
 91                     rs += xx;
 92                     q.push(x);
 93                     ls += x - xx;
 94                 } else {
 95                     Q.push(x);
 96                     rs += x;
 97                 }
 98                 
 99                 x = q.top();
100                 tmp = rs - ls;
101                 dif[i][j] = tmp;
102             }
103         }
104     }
105     
106     rep(j, 1, n+1) {
107         dp[1][j] = dif[1][j];
108     }
109     
110     rep(i, 2, m+1) {
111         rep(j, i, n+1) {
112             dp[i][j] = INF;
113             rep(k, i-1, j) {
114                 dp[i][j] = min(dp[i][j], dp[i-1][k]+dif[k+1][j]);
115             }
116         }
117     }
118     
119     printf("%d\n", dp[m][n]);
120 }
121 
122 int main() {
123     ios::sync_with_stdio(false);
124     #ifndef ONLINE_JUDGE
125         freopen("data.in", "r", stdin);
126         freopen("data.out", "w", stdout);
127     #endif
128     
129     while (scanf("%d %d", &n, &m)!=EOF && (n||m)) {
130         rep(i, 1, n+1) {
131             scanf("%d", &a[i]);
132         }
133         solve();
134     }
135     
136     #ifndef ONLINE_JUDGE
137         printf("time = %d.\n", (int)clock());
138     #endif
139     
140     return 0;
141 }

数据生成器。

 1 from random import randint, shuffle
 2 import shutil
 3 import string
 4 
 5 
 6 def GenDataIn():
 7     with open("data.in", "w") as fout:
 8         t = 22
 9         bound = 10**4
10         for tt in xrange(t):
11             n = randint(1800, 2000)
12             k = randint(1, 25)
13             fout.write("%d %d\n" % (n, k))
14             dataList = []
15             for i in xrange(n):
16                 x = randint(-bound, bound)
17                 dataList.append(x)
18             fout.write(" ".join(map(str, dataList)) + "\n")
19         fout.write("0 0\n")        
20         
21                 
22 def MovDataIn():
23     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
24     shutil.copyfile("data.in", desFileName)
25 
26     
27 if __name__ == "__main__":
28     GenDataIn()
29     MovDataIn()