在数组中删除尽可能少的数,使得数组满足“先由小到大,再由大到小”

void MyDelete(int* a, int n)
{ 
    int* asc = new int[n];    // asc[i]表示以a[i]结尾的最长升序数的个数
    int* desc = new int[n];   // desc[i]表示从a[i]开始的最长降序数的个数
    int* inc = new int[n];    // 亮点,用辅助数组的巧妙之处
    const int max_int = numeric_limits<int>::max();
    
    //求解asc[];
    for(int i=0; i<n; ++i) 
        inc[i] = max_int;
    for(int i=0; i<n; ++i)
    {
        int low = 0, high = i;
        while(low <= high)
        {
            int mid = (low+high)/2;
            if(inc[mid] <= a[i])
                low = mid + 1;
            else
                high = mid - 1;
        }
        asc[i] = high+2;
        inc[high+1] = a[i];  
    }
    //求解desc[];
    for(int i=0; i<n; ++i)
        inc[i] = max_int;
    for(int i=n-1; i>=0; --i)
    {
        int low = 0, high = n-1-i;
        while(low <= high)
        {
            int mid = (low+high)/2;
            if(inc[mid] <= a[i])
                low = mid + 1;
            else
                high = mid - 1;
        }
        desc[i] = high + 2;
        inc[high+1] = a[i];
    }
    // const int max_len = max(asc[i]+desc[i]-1);     0<= i < n
}

此题的巧妙之处在于,用辅助数据inc[]求解最长升序 数的个数。 

题目变型:  求数组最长升序

    int len = asc[0];
    int index = 0;
    for(int j=1; j<n; ++j)
        if(len < asc[j])
    {
        len = asc[j];
        index = j;
    }
    vector<int> vect;
    for(int j=index; j>=0; --j)
    {
        if(len == asc[j])
        {
            vect.push_back(a[j]);
            len--;
        }
    }
    copy(vect.rbegin(),vect.rend(), ostream_iterator<int>(cout,"  "));
    cout << endl;
点赞