POJ 2533 Longest Ordered Subsequence(最长上升子序列O(n*n)解法)
2018-01-03 11:02
447 查看
Longest Ordered Subsequence
Description
A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1, a2, ..., aN)
be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence
(1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).
Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.
Input
The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000
Output
Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.
Sample Input
Sample Output
4
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions:56940 | Accepted: 25509 |
A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1, a2, ..., aN)
be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= N. For example, sequence
(1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).
Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.
Input
The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000
Output
Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.
Sample Input
7 1 7 3 5 9 4 8
Sample Output
4
dp[i]为以a[i]为最后一个元素所能组成的最长上升子序列,这样就保证了a[i]为此序列中的最大值
因此在递推时只需a[i]>a[j] 便一定能组成长度为a[j]+1的子序列
#include<iostream> #include<cstdio> #include<algorithm> #include<string.h> using namespace std; int main() { int n; while (scanf("%d", &n) != EOF) { int dp[1002], a[1002]; for (int i = 1; i <= n; i++) scanf("%d", &a[i]); if (n == 1) { printf("1\n"); continue; } for (int j = 0; j <= 1000; j++) dp[j] = 1; int res=0; for (int i = 2; i <= n; i++) { for (int j = 1; j < i; j++) { if (a[i] > a[j]) dp[i] = max(dp[i], dp[j] + 1); } res = max(dp[i], res); } printf("%d\n", res); } return 0; }
相关文章推荐
- 每日三题-Day5-A(POJ 2533 Longest Ordered Subsequence 最长上升子序列O(nlogn)解法)
- POJ-2533 Longest Ordered Subsequence (线性dp 最长上升子序列)
- poj_2533 Longest Ordered Subsequence(最长上升子序列)
- POJ 2533 Longest Ordered Subsequence(最长上升子序列)
- POJ 2533 Longest Ordered Subsequence(最长上升子序列模版)
- poj-2533-Longest Ordered Subsequence-最长上升子序列
- 【dp-LIS】牛客网 --最长上升子序列 POJ 2533--Longest Ordered Subsequence(LIS模板题)
- Longest Ordered Subsequence POJ - 2533(最长上升子序列)
- POJ 2533 Longest Ordered Subsequence 最长上升子序列
- Longest Increasing Subsequence[LIS 最长上升子序列问题] (Longest Ordered Subsequence) POJ - 2533 队列优化
- poj 2533 Longest Ordered Subsequence(最长上升子序列)
- Longest Ordered Subsequence POJ - 2533 (最长上升子序列)
- POJ 2533 Longest Ordered Subsequence(LIS:最长上升子序列)
- POJ2533 -Longest Ordered Subsequence最长上升子序列-动规和nlogn二分算法详解
- POJ 2533 Longest Ordered Subsequence(DP最长上升子序列O(n^2)&&O(nlogn))
- POJ - 2533 Longest Ordered Subsequence(最长上升子序列)
- POJ 2533 Longest Ordered Subsequence(最长上升子序列)
- poj 2533 Longest Ordered Subsequence(最长上升子序列)
- POJ 2533-Longest Ordered Subsequence(dp_最长上升子序列)
- POJ - 2533 Longest Ordered Subsequence —— 最长不连续上升子序列