最长升序子序列

Description

Given a sequence a[1],a[2],a[3]......a[n], your job is to calculate the max sum of a sub-sequence. For example, given (6,-1,5,4,-7), the max sum in this sequence is 6 + (-1) + 5 + 4 = 14. 

 

Input

The first line of the input contains an integer T(1<=T<=20) which means the number of test cases. Then T lines follow, each line starts with a number N(1<=N<=100000), then N integers followed(all the integers are between -1000 and 1000). 

 

Output

For each test case, you should output two lines. The first line is "Case #:", # means the number of the test case. The second line contains three integers, the Max Sum in the sequence, the start position of the sub-sequence, the end position of the sub-sequence. If there are more than one result, output the first one. Output a blank line between two cases. 

 

Sample Input

2

5 6 -1 5 4 -7

7 0 6 -1 1 -6 7 -5

 

Sample Output

Case 1: 14 1 4

Case 2: 7 1 6

 

 

 

思路：

       用二分法（避免超时）找最小的数放在子序列里面，比如最开始的序列是 2 3 4，但是后面又发现了一个1，就把1代替之前的2，以免后面出现更长的子序列

 

 

#include<iostream>
#include<cstdio>
using namespace std;
#define  maxn 100000+10
int al[maxn], cl[maxn];
int main()
{
    int n,len,left,right,mid;
    while (scanf("%d",&n)!= EOF){
        for (int i = 0; i < n; i++)
            scanf("%d", &al[i]);
        len = 0, cl[0] = -1;
        for (int i = 0; i < n; i++)
        {
            if (al[i]>cl[len])
                cl[++len] = al[i];    //把大的数放进去
            else
            {
                left = 1, right = len;    //二分法找后面小的数放在这个子序列的前面，以免有更长的子序列
                
                while (left <= right)
                {
                    mid = (left + right) / 2;
                    if (al[i]>cl[mid])
                        left = mid + 1;
                    else
                       right = mid - 1;
                }
                cl[left] = al[i];
            }
        }
        printf("%d
", len);
    }
    
    return 0;
}