從一列數中篩除儘量少的數使得從左往右看，這些數是從小到大再從大到小的（網易）。

題目描述：

　　從一列數中篩除儘量少的數使得從左往右看，這些數是從小到大再從大到小的（網易）。

分析：

　　這能夠用雙端LIS方法來解決，先求一遍從左到右的，再求一遍從右到左的。最後從裏面選出和最大的便可。

 

代碼實現：

#include <iostream>

using namespace std;

int DoubleEndLIS(int *arr, int len)
{
    int *LIS = new int[len];
    int *lefToRight = new int[len];        //leftToRight[i]表示0~i最長子序列長度-1
    int *rightToLeft = new int[len];
    int maxLen = 0;        //記錄總共的(上升+降低)最長子序列長度
    int low, high, mid;

    for (int i = 0; i < len; ++i)
    {
        lefToRight[i]  = 0;
        LIS[i] = 0;
    }

    LIS[0] = arr[0];
    for (int i = 1; i < len; i++)
    {
        low = 0; high = lefToRight[i-1];
        while (low <= high)
        {
            mid = (low + high)/2;
            if (LIS[mid] < arr[i])
            {
                low = mid + 1;
            } 
            else
            {
                high = mid -1;
            }
        }

        LIS[low] = arr[i];
        if (low > lefToRight[i-1])
        {
            lefToRight[i] = lefToRight[i-1] + 1;    //最長子序列長度加1
        }
        else
        {
            lefToRight[i] = lefToRight[i-1];
        }
    }

    //leftToRight的每一個值增長1，由於他們是最長子序列值-1
    //此時leftToRight表示的是最長子序列的真正值。
    for (int i = 0; i < len; i++)
    {
        lefToRight[i]++;
    }

    //從右到左
    for (int i = 0; i < len; i++)
    {
        rightToLeft[i] = 0;
        LIS[i] = 0;
    }

    int k = 0;
    LIS[0] = arr[len-1];
    for (int i = len -2; i >= 0; --i)
    {
        low = 0; high = rightToLeft[k];
        while (low <= high)
        {
            mid = (low + high)/2;
            if (LIS[mid] < arr[i])
            {
                low = mid + 1;
            } 
            else
            {
                high = mid - 1;
            }
        }

        LIS[low] = arr[i];
        if (low > rightToLeft[k])
        {
            rightToLeft[k+1] = rightToLeft[k] + 1;
        }
        else
        {
            rightToLeft[k+1] = rightToLeft[k];
        }
        ++k;
    }

    for (int i = 0; i < k; ++i)
    {
        rightToLeft[i]++;
    }

    //求最大值即爲要求的
    for (int i = 0; i < len; ++i)
    {
        cout<<"i: "<<i<<" "<<lefToRight[i]<<"  "<<rightToLeft[len-i-1]<<endl;
        if (lefToRight[i] + rightToLeft[len-i-1] > maxLen)
            maxLen = lefToRight[i] + rightToLeft[len-i-1];
    }
    cout<<"maxLen:"<<maxLen<<endl;

    delete LIS;
    delete lefToRight;
    delete rightToLeft;

    return len - maxLen + 1;
}

int main()
{
    int arr[] = {1,5,7,6,9,3,8,4,2};
    int ret;
    ret = DoubleEndLIS(arr, 9);
    cout<<ret<<endl;

    return 0;
}

 

參考：http://blog.csdn.net/nciaebupt/article/details/8466049

可是，他的程序有問題，我作了修改。