有关最长上升子序列的详细算法解释在http://www.cnblogs.com/denghaiquan/p/6679952.html
1）51nod 1134
一题裸的最长上升子序列，由于N<=50000，n2算法会超时，只能用nlogn算法。
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <cstdlib>
5 #include <string>
6 #include <vector>
7 #include <map>
8 #include <set>
9 #include <queue>
10 #include <sstream>
11 #include <algorithm>
12 using namespace std;
13 #define pb push_back
14 #define mp make_pair
15 #define ms(a, b) memset((a), (b), sizeof(a))
16 //#define LOCAL
17 typedef long long LL;
18 const int inf = 0x3f3f3f3f;
19 const int maxn = 50000+10;
20 const LL mod = 1000000000+7;
21 int a[maxn];
22 int dp[maxn];
23 int Binary_search(int key, int len)
24 {
25 int l=1, r=len+1;
26 while(l<r)
27 {
28 int middle = (l+r) >> 1;
29 if(key>=dp[middle])
30 l = middle +1;
31 else
32 r = middle;
33 }
34 return l;
35 }
36 int main()
37 {
38 #ifdef LOCAL
39 freopen("input.txt" , "r", stdin);
40 #endif // LOCAL
41 int n, len;
42 scanf("%d", &n);
43 for(int i=0;i<n;i++) scanf("%d", &a[i]);
44 dp[1] = a[0];
45 len = 1;
46 for(int i=1;i<n;i++)
47 {
48 if(a[i] > dp[len])
49 dp[++len] = a[i];
50 else{
51 int j = Binary_search(a[i], len);
52 dp[j] = a[i];
53 }
54 }
55 printf("%d\n", len);
56 return 0;
57 }
2）POJ 2533
裸的最长上升子序列，N<=1000， n2算法可以过。
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <cstdlib>
5 #include <string>
6 #include <vector>
7 #include <map>
8 #include <set>
9 #include <queue>
10 #include <sstream>
11 #include <algorithm>
12 using namespace std;
13 #define pb push_back
14 #define mp make_pair
15 #define ms(a, b) memset((a), (b), sizeof(a))
16 //#define LOCAL
17 typedef long long LL;
18 const int inf = 0x3f3f3f3f;
19 const int maxn = 1000+10;
20 const LL mod = 1000000000+7;
21 int a[maxn];
22 int dp[maxn];
23 int main()
24 {
25 #ifdef LOCAL
26 freopen("input.txt" , "r", stdin);
27 #endif // LOCAL
28 int n;
29 scanf("%d", &n);
30 for(int i=0;i<n;i++) scanf("%d", &a[i]);
31 dp[0]=1;
32 for(int i=1;i<n;i++)
33 {
34 dp[i] = 1;
35 for(int j=0;j<i;j++)
36 {
37 if(a[j]<a[i] && dp[j]+1 > dp[i])
38 dp[i] = dp[j] + 1;
39 }
40 }
41 int ans = 0;
42 for(int i=0;i<n;i++) ans = max(ans, dp[i]);
43 printf("%d\n", ans);
44 return 0;
45 }
3）POJ 1631
一题裸的最长上升子序列，由于N<=50000，n2算法会超时，只能用nlogn算法。
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <cstdlib>
5 #include <string>
6 #include <vector>
7 #include <map>
8 #include <set>
9 #include <queue>
10 #include <sstream>
11 #include <algorithm>
12 using namespace std;
13 #define pb push_back
14 #define mp make_pair
15 #define ms(a, b) memset((a), (b), sizeof(a))
16 //#define LOCAL
17 typedef long long LL;
18 const int inf = 0x3f3f3f3f;
19 const int maxn = 40000+10;
20 const LL mod = 1000000000+7;
21 int a[maxn];
22 int dp[maxn];
23 int Binary_search(int key, int len)
24 {
25 int l=1, r=len+1;
26 while(l<r)
27 {
28 int middle = (l+r) >> 1;
29 if(key>=dp[middle])
30 l = middle +1;
31 else
32 r = middle;
33 }
34 return l;
35 }
36 int main()
37 {
38 #ifdef LOCAL
39 freopen("input.txt" , "r", stdin);
40 #endif // LOCAL
41 int T;
42 scanf("%d", &T);
43 while(T--)
44 {
45 ms(dp, 0);
46 ms(a, 0);
47 int n, len;
48 scanf("%d", &n);
49 for(int i=0;i<n;i++) scanf("%d", &a[i]);
50 dp[1] = a[0];
51 len = 1;
52 for(int i=1;i<n;i++)
53 {
54 if(a[i] > dp[len])
55 dp[++len] = a[i];
56 else{
57 int j = Binary_search(a[i], len);
58 dp[j] = a[i];
59 }
60 }
61 printf("%d\n", len);
62 }
63 return 0;
64 }
4）POJ 1887
这题是找最长下不上升子序列。发现n2算法可以过。不过要注意输出。
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <cstdlib>
5 #include <string>
6 #include <vector>
7 #include <map>
8 #include <set>
9 #include <queue>
10 #include <sstream>
11 #include <algorithm>
12 using namespace std;
13 #define pb push_back
14 #define mp make_pair
15 #define ms(a, b) memset((a), (b), sizeof(a))
16 //#define LOCAL
17 typedef long long LL;
18 const int inf = 0x3f3f3f3f;
19 const int maxn = 32767+10;
20 const LL mod = 1000000000+7;
21 int a[maxn];
22 int dp[maxn];
23 int main()
24 {
25 #ifdef LOCAL
26 freopen("input.txt" , "r", stdin);
27 #endif // LOCAL
28 int t=1;
29 while(scanf("%d", &a[0])&&a[0]!=-1)
30 {
31 if(t>1) printf("\n");
32 int n =1, ans = 0 ;
33 while(scanf("%d", &a[n])&&a[n]!=-1) n++;
34 dp[0] = 1;
35 for(int i=1;i<n;i++)
36 {
37 dp[i] = 1;
38 for(int j=0;j<n;j++)
39 {
40 if(a[j] > a[i] && dp[j]+1 > dp[i])
41 dp[i] = dp[j] + 1;
42 }
43 }
44 for(int i=0;i<n;i++) ans = max(ans, dp[i]);
45 printf("Test #%d:\n",t++);
46 printf(" maximum possible interceptions: %d\n", ans);
47 ms(a, 0);
48 ms(dp, 0);
49 }
50 return 0;
51 }
5）POJ 1609
这题同样是最长不上升子序列，不过是2个关键词，先排序一个，再在另一个里面找最长不上升子序列。
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #include <cstdlib>
5 #include <string>
6 #include <vector>
7 #include <map>
8 #include <set>
9 #include <queue>
10 #include <sstream>
11 #include <algorithm>
12 using namespace std;
13 #define pb push_back
14 #define mp make_pair
15 #define ms(a, b) memset((a), (b), sizeof(a))
16 //#define LOCAL
17 typedef long long LL;
18 const int inf = 0x3f3f3f3f;
19 const int maxn = 10000+10;
20 const LL mod = 1000000000+7;
21 int a[maxn];
22 int dp[maxn];
23 struct node
24 {
25 int l, m;
26 };
27 bool cmp(node x1, node x2)
28 {
29 if(x1.l != x2.l)
30 return x1.l > x2.l;
31 return x1.m > x2.m;//当第一个关键字相同的时候，第2个关键字要从大到小排序
32 }
33 int main()
34 {
35 #ifdef LOCAL
36 freopen("input.txt" , "r", stdin);
37 #endif // LOCAL
38 int n;
39 while(scanf("%d", &n))
40 {
41 if(n == 0) {printf("*\n");break;}
42 node blocks[maxn];
43 for(int i = 0;i < n;i++) scanf("%d%d", &blocks[i].l, &blocks[i].m);
44 sort(blocks, blocks+n, cmp);
45 dp[0] = 1;
46 for(int i=1;i<n;i++)
47 {
48 dp[i] = 1;
49 for(int j = 0;j<i;j++)
50 {
51 if(blocks[j].m >= blocks[i].m && dp[j] + 1 > dp[i])
52 dp[i] = dp[j]+1;
53 }
54 }
55 int ans = 0;
56 for(int i=0;i<n;i++) ans = max(ans, dp[i]);
57 printf("%d\n", ans);
58 ms(dp, 0);
59 }
60 return 0;
61 }
时间： 2024-12-18 17:36:43