数据结构时间复杂度

问题引出:

编程找出指定数列的所有子列和的最大值;

假定数列:

int arry[16] = {5, -6, 4, -5, 3, 1, 2, -4, 8, -9, 3, 1, -7, 6, 4, -1};

 

算法一:

#include <iostream>
using namespace std;
int main()
{
    const int N = 16;
    int arry[N] = {5, -6, 4, -5, 3, 1, 2, -4, 8, -9, 3, 1, -7, 6, 4, -1};
    int maxsum = 0;
    
    for (int k = 0; k < N; k++)
    {
        for (int j = k; j < N; j++)
        {
            int tempsum = 0;
            for (int i = k; i <= j; i++)
            {
                tempsum += arry[i];  
            }
            maxsum = tempsum > maxsum ? tempsum : maxsum;
        }
    }
    cout << maxsum << endl;
    return 0;
}

例用三个循环:其时间复杂度T(N) = O(N³);

算法二:

#include <iostream>
using namespace std;
int main()
{
    const int N = 16;
    int arry[N] = {5, -6, 4, -5, 3, 1, 2, -4, 8, -9, 3, 1, -7, 6, 4, -1};
    int maxsum = 0;
    
    for (int k = 0; k < N; k++)
    {
        int tempsum = 0;
        for (int j = k; j < N; j++)
        {
            tempsum += arry[j];    
            maxsum = tempsum > maxsum ? tempsum : maxsum;
        }
    }
    cout << maxsum << endl;
    return 0;
}

例用两个循环:其时间复杂度T(N) = O(N²);

算法三:

#include <iostream>
using namespace std;
int main()
{
    const int N = 15;
    int arry[N] = {5, -6, 4, 5, 3, 1, 2, -4, 8, -9, 3, 1, -7, 6, -4};
    int maxsum = 0;
    int tempsum = 0;
    for (int k = 0; k < N; k++)
    {
        tempsum += arry[k];
        if (tempsum < 0)
        {
            tempsum = 0;
        }
        else
        {
            maxsum = maxsum > tempsum ? maxsum : tempsum;
        }
        
    }
    cout << maxsum << endl;
    return 0;
}

例用一个循环:其时间复杂度T(N) = O(N);