各种蕴含算法思想的DP - 1

study from:

https://www.cnblogs.com/flashhu/p/9480669.html

 

1.前缀和

https://www.luogu.org/problemnew/show/P2513

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cmath>
 4 #include <cstring>
 5 #include <time.h>
 6 #include <string>
 7 #include <set>
 8 #include <map>
 9 #include <list>
10 #include <stack>
11 #include <queue>
12 #include <vector>
13 #include <bitset>
14 #include <ext/rope>
15 #include <algorithm>
16 #include <iostream>
17 using namespace std;
18 #define ll long long
19 #define minv 1e-6
20 #define inf 1e9
21 #define pi 3.1415926536
22 #define E  2.7182818284
23 const int mod=1e4;//998244353
24 const int maxn=1e3+10;
25 
26 int f[maxn][maxn],tot[maxn];
27 
28 int main()
29 {
30     int n,k,i,j,l;
31     scanf("%d%d",&n,&k);
32     f[1][0]=1;
33     for (i=2;i<=n;i++)
34     {
35         tot[0]=0;
36         l=min(i*(i-1)/2,k);
37         for (j=0;j<=l;j++)
38             tot[j]=(tot[j-1]+f[i-1][j])%mod;
39         for (j=0;j<=l;j++)
40             f[i][j]=(tot[j]-tot[max(j-i,-1)]+mod)%mod;
41     }
42     printf("%d",f[n][k]);
43     return 0;
44 }

 

https://www.luogu.org/problemnew/show/P2511

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cmath>
 4 #include <cstring>
 5 #include <time.h>
 6 #include <string>
 7 #include <set>
 8 #include <map>
 9 #include <list>
10 #include <stack>
11 #include <queue>
12 #include <vector>
13 #include <bitset>
14 #include <ext/rope>
15 #include <algorithm>
16 #include <iostream>
17 using namespace std;
18 #define ll long long
19 #define minv 1e-6
20 #define inf 1e9
21 #define pi 3.1415926536
22 #define E  2.7182818284
23 const int mod=10007;//998244353
24 const int maxn=5e4+10;
25 
26 int a[maxn],t[maxn],tot[maxn],f[maxn][2];
27 
28 int main()
29 {
30     int n,c,x,y,i,j,k,l,r,m,result=0;
31     scanf("%d%d",&n,&c);
32     c++;
33     for (i=1;i<=n;i++)
34         scanf("%d",&a[i]);
35     l=1; r=5e7;
36     while (l<=r)
37     {
38         m=(l+r)>>1;
39         j=1;
40         k=0;
41         for (i=1;i<=n;i++)
42             if (a[i]>m)
43                 break;
44             else if (k+a[i]>m)
45             {
46                 j++;
47                 k=a[i];
48             }
49             else
50                 k+=a[i];
51         if (i==n+1 && j<=c)
52             r=m-1;
53         else
54             l=m+1;
55     }
56     printf("%d ",l);
57 
58     t[0]=0;
59     for (i=1;i<=n;i++)
60         t[i]=t[i-1]+a[i];
61 
62     f[0][0]=1;
63     x=1,y=0;
64     for (j=1;j<=c;j++)
65     {
66         tot[-1]=0;
67         for (i=0;i<=n;i++)
68             tot[i]=(tot[i-1]+f[i][y])%mod;
69         //f[i][j]  f[][j-1]
70         k=0;
71         f[0][x]=0;
72         for (i=1;i<=n;i++)
73         {
74             //[k,i)
75             while (t[i]-t[k]>l)
76                 k++;
77             f[i][x]=(tot[i-1]-tot[k-1])%mod;
78         }
79         result=(result+f[n][x])%mod;
80         x=x^1;
81         y=y^1;
82     }
83     printf("%d",(result+mod)%mod);
84     return 0;
85 }
86 /*
87 5 1
88 3 3 4 5 3
89 
90 5 3
91 1 1 1 1 1
92 */

 

2.单调队列优化

https://www.luogu.org/problemnew/show/P1886

 1 #include <cstdio>
 2 #include <cstdlib>
 3 #include <cmath>
 4 #include <cstring>
 5 #include <time.h>
 6 #include <string>
 7 #include <set>
 8 #include <map>
 9 #include <list>
10 #include <stack>
11 #include <queue>
12 #include <vector>
13 #include <bitset>
14 #include <ext/rope>
15 #include <algorithm>
16 #include <iostream>
17 using namespace std;
18 #define ll long long
19 #define minv 1e-6
20 #define inf 1e9
21 #define pi 3.1415926536
22 #define E  2.7182818284
23 const int mod=10007;//998244353
24 const int maxn=1e6+10;
25 
26 /**
27 n个数字a[1]-a[n],每个大小为m的区间
28 最小值和最大值
29 **/
30 
31 int a[maxn],x[maxn];    ///x:记录下标
32 
33 int main()
34 {
35     int n,m,i,head,tail;
36     scanf("%d%d",&n,&m);
37     for (i=1;i<=n;i++)
38         scanf("%d",&a[i]);
39     ///min
40     head=1,tail=0;
41     ///以i作为末尾的区间
42     for (i=1;i<=n;i++)
43     {
44 
45         while (head1<=tail1 && x[head1]<=i-m)
46             head1++;
47         while (head1<=tail1 && a[x[tail1]]>=a[i])
48             tail1--;
49 
50         ///每个点入队列一次,最多出队列一次
51         while (head<=tail && x[head]<=i-m)   ///在区间外的数字被剔除,(i-m,i]
52             head++;
53         while (head<=tail && a[x[tail]]>=a[i])   ///求区间最小/大值,对于在前面的数,只有数值小/大于后面才有用,否则从右往左被剔除(符号相反,大于等于/小于等于),类似单调栈
54             tail--;
55         tail++;
56         x[tail]=i;
57         if (i>=m)
58             printf("%d%c",a[x[head]],i==n?'\n':' ');
59     }
60 
61     ///max
62     head=1,tail=0;
63     for (i=1;i<=n;i++)
64     {
65         while (head<=tail && x[head]<=i-m)
66             head++;
67         while (head<=tail && a[x[tail]]<=a[i])
68             tail--;
69         tail++;
70         x[tail]=i;
71         if (i>=m)
72             printf("%d%c",a[x[head]],i==n?'\n':' ');
73     }
74     return 0;
75 }

 

posted @ 2018-08-29 21:56  congmingyige  阅读(146)  评论(0编辑  收藏  举报