HDOJ4343 Interval query

Posted 2020-06-13

最大不相交集合的数量。
思路是dp[i][j]表示已经有i个不相交集合下一个不相交集合的最右边界。
离散化后，通过贪心解。

  1 /* 4343 */
  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 typedef struct node_t {
 44     int l, r;
 45     
 46     friend bool operator< (const node_t& a, const node_t& b) {
 47         if (a.l == b.l)
 48             return a.r < b.r;
 49         return a.l < b.l;
 50     }
 51 } node_t;
 52 
 53 const int maxn = 1e5+5;
 54 int n, q;
 55 int dp[18][maxn*2];
 56 int X[maxn*2], nx;
 57 node_t nd[maxn];
 58 
 59 int getId(int x, bool flag) {
 60     if (flag)
 61         return lower_bound(X, X+nx, x) - X;
 62     else
 63         return upper_bound(X, X+nx, x) - X - 1;
 64 }
 65 
 66 int calc(int l, int r) {
 67     if (l > r)
 68         return 0;
 69     
 70     if (l==nx || r==-1)
 71         return 0;
 72     
 73     int ret = 0;
 74     per(i, 0, 18) {
 75         if (dp[i][l] <= r) {
 76             ret += (1<<i);
 77             l = dp[i][l];
 78         }
 79     }
 80     
 81     return ret;
 82 }
 83 
 84 void solve() {
 85     nx = 0;
 86     rep(i, 0, n) {
 87         X[nx++] = nd[i].l;
 88         X[nx++] = nd[i].r;
 89     }
 90     sort(nd, nd+n);
 91     sort(X, X+nx);
 92     nx = unique(X, X+nx) - X;
 93     rep(i, 0, n) {
 94         nd[i].l = getId(nd[i].l, true);
 95         nd[i].r = getId(nd[i].r, false);
 96     }
 97     
 98     int mn = nx, l, r = n-1;
 99     per(i, 0, nx) {
100         while (r>=0 && nd[r].l>=i) {
101             mn = min(mn, nd[r].r);
102             --r;
103         }
104         dp[0][i] = mn;
105     }
106     rep(i, 0, 18)
107         dp[i][nx] = nx;
108     rep(i, 1, 18) {
109         rep(j, 0, nx) {
110             dp[i][j] = dp[i-1][dp[i-1][j]];
111         }
112     }
113     
114     int ans;
115     
116     while (q--) {
117         scanf("%d %d", &l, &r);
118         l = getId(l, true);
119         r = getId(r, false);
120         ans = calc(l, r);
121         printf("%d\n", ans);
122     }
123 }
124 
125 int main() {
126     ios::sync_with_stdio(false);
127     #ifndef ONLINE_JUDGE
128         freopen("data.in", "r", stdin);
129         freopen("data.out", "w", stdout);
130     #endif
131     
132     while (scanf("%d %d", &n, &q)!=EOF) {
133         rep(i, 0, n)
134             scanf("%d %d", &nd[i].l, &nd[i].r);
135         solve();
136     }
137     
138     #ifndef ONLINE_JUDGE
139         printf("time = %d.\n", (int)clock());
140     #endif
141     
142     return 0;
143 }

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         ld = list(string.digits)
12         # fout.write("%d\n" % (t))
13         for tt in xrange(t):
14             n = randint(40, 50)
15             q = randint(20, 30)
16             fout.write("%d %d\n" % (n, q))
17             for i in xrange(n+q):
18                 l = randint(1, bound-1)
19                 r = randint(l, bound)
20                 fout.write("%d %d\n" % (l, r))
21                 
22             
23                 
24 def MovDataIn():
25     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
26     shutil.copyfile("data.in", desFileName)
27 
28     
29 if __name__ == "__main__":
30     GenDataIn()
31     MovDataIn()