Nyoj 214 monotonic incrementing subsequence (2)

Monotonic incrementing subsequence (2)Time Limit: 1000 MS | memory limit: 65535 kb difficulty: 4

Description

Given an integer series {A1, a2..., an} (0 <n <= 100000), locate the monotonic incrementing oldest sequence and obtain its length.

For example, the longest monotonic increasing subsequence of 1 9 10 5 11 2 13 is 1 9 10 11 13 with a length of 5.

 

Input

Multiple groups of test data (<= 7)
The first row of each group of test data is an integer N, indicating a total of N integers in the sequence, followed by N integers in the next row, indicating all elements in the series. separate each integer with spaces (0 <n <= 100000 ).
Data ends with EOF.
The input data must be valid (all are int integers )!

Output

For each group of test data, the length of the output integer sequence is the longest incrementing sub-sequence. Each output occupies one row.

Sample Input

71 9 10 5 11 2 1322 -1

Sample output

51

Solution: The data volume is large, and the O (N ^ 2) method does not work! Only the O (nlogn) algorithm is available.

Attach the Tle code first.

 1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cstdlib> 5 #include <vector> 6 #include <climits> 7 #include <algorithm> 8 #include <cmath> 9 #define LL long long10 using namespace std;11 int d[100010],dp[100010];12 int main(){13     int n,i,j,ans;14     while(~scanf("%d",&n)){15         for(i = 1; i <= n; i++){16             scanf("%d",d+i);17             dp[i] = 1;18         }19         ans = 1;20         for(i = 2; i <= n; i++){21             for(j = i-1; j; j--){22                 if(d[j] < d[i] && dp[i] < dp[j]+1) dp[i] = dp[j]+1;23             }24             if(dp[i] > ans) ans = dp[i];25         }26         printf("%d\n",ans);27     }28     return 0;29 }

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Okay, the AC code and the O (nlogn) algorithm are exquisite in half-lookup and fast. Oh, the last top? Top: 1 can be removed. It's funny! The loss is 4 ms.

 1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cstdlib> 5 #include <vector> 6 #include <climits> 7 #include <algorithm> 8 #include <cmath> 9 #define LL long long10 using namespace std;11 int stk[100010],top;12 void bsearch(int lt,int rt,int val) {13     int mid;14     while(lt <= rt) {15         mid = (lt+rt)>>1;16         if(val < stk[mid]) rt = mid-1;17         else lt = mid+1;18     }19     stk[lt] = val;20 }21 int main() {22     int n,i,temp;23     while(~scanf("%d",&n)) {24         top = 0;25         for(i = 1; i <= n; i++) {26             scanf("%d",&temp);27             if(!top || stk[top-1] < temp)28                 stk[top++] = temp;29             else bsearch(0,top-1,temp);30         }31         printf("%d\n",top?top:1);32     }33     return 0;34 }

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