算法实践--最长递增子序列(Longest Increasing Subsquence)

for (i=N; i>0; --i) {1. 找到所有长度为i的子序列;   //复杂度为(N!)/(i!)(N-i)!    O(exp(N))
   2. 判断是否其中有一个为递增子序列
}

对于矢量D = {3, 2, 6, 4, 5, 1}；

LIS[0]:  3
LIS[1]:  2
LIS[2]:  2,6
LIS[3]:  2,4
LIS[4]:  2,4,5
LIS[5]:  1

using namespace std;

void prt(vector<int>& arr, string msg = "") {
    cout << msg << " ";
    for  (auto i: arr) {
        cout << i << " ";
    }
    cout << endl;
}


void calc_LIS(vector<int>& D) {
    vector< vector<int> > L(D.size());  // The longest increasing subsequence ends with D[i]

   L[0].push_back(D[0]);

    for (int i=1; i<D.size(); i++) {
        for(int j=0; j<i; j++) {
            if ( (D[j] < D[i]) && ( L[i].size() < L[j].size() ) ) {
                L[i] = L[j];                  
            }         
        }
      L[i].push_back(D[i]);
    }

    for (auto x: L) {
        prt(x);
    }
}

int main() {
    int a[] = {3, 2, 6, 4, 5, 1};
    vector<int> arr(a, a + sizeof(a)/sizeof(a[0]));

    prt(arr, "Data In:");
    calc_LIS(arr);

    return 0;
}