数据结构基础 算法复杂度分析（二） 典例篇

标签：算法复杂度   时间复杂度   空间复杂度   渐进复杂度   渐近符   

decimal Factorial(int n)
    {
      if (n == 0)
        return 1;
      else
        return n * Factorial(n - 1);
    }

int FindMaxElement(int[] array)
    {
      int max = array[0];
      for (int i = 0; i < array.Length; i++)
      {
        if (array[i] > max)
        {
          max = array[i];
        }
      }
      return max;
    }

long FindInversions(int[] array)
    {
      long inversions = 0;
      for (int i = 0; i < array.Length; i++)
        for (int j = i + 1; j < array.Length; j++)
          if (array[i] > array[j])
            inversions++;
      return inversions;
    }

long SumMN(int n, int m)
    {
      long sum = 0;
      for (int x = 0; x < n; x++)
        for (int y = 0; y < m; y++)
          sum += x * y;
      return sum;
    }

decimal Sum3(int n)
    {
      decimal sum = 0;
      for (int a = 0; a < n; a++)
        for (int b = 0; b < n; b++)
          for (int c = 0; c < n; c++)
            sum += a * b * c;
      return sum;
    }

decimal Calculation(int n)
    {
      decimal result = 0;
      for (int i = 0; i < (1 << n); i++)
        result += i;
      return result;
    }

int Fibonacci(int n)
    {
      if (n <= 1)
        return n;
      else
        return Fibonacci(n - 1) + Fibonacci(n - 2);
    }

int Fibonacci(int n)
    {
      if (n <= 1)
        return n;
      else
      {
        int[] f = new int[n + 1];
        f[0] = 0;
        f[1] = 1;

        for (int i = 2; i <= n; i++)
        {
          f[i] = f[i - 1] + f[i - 2];
        }

        return f[n];
      }
    }

int Fibonacci(int n)
    {
      if (n <= 1)
        return n;
      else
      {
        int iter1 = 0;
        int iter2 = 1;
        int f = 0;

        for (int i = 2; i <= n; i++)
        {
          f = iter1 + iter2;
          iter1 = iter2;
          iter2 = f;
        }

        return f;
      }
    }

示例代码（10）

static int Fibonacci(int n)
    {
      if (n <= 1)
        return n;

      int[,] f = { { 1, 1 }, { 1, 0 } };
      Power(f, n - 1);

      return f[0, 0];
    }

    static void Power(int[,] f, int n)
    {
      if (n <= 1)
        return;

      int[,] m = { { 1, 1 }, { 1, 0 } };

      Power(f, n / 2);
      Multiply(f, f);

      if (n % 2 != 0)
        Multiply(f, m);
    }

    static void Multiply(int[,] f, int[,] m)
    {
      int x = f[0, 0] * m[0, 0] + f[0, 1] * m[1, 0];
      int y = f[0, 0] * m[0, 1] + f[0, 1] * m[1, 1];
      int z = f[1, 0] * m[0, 0] + f[1, 1] * m[1, 0];
      int w = f[1, 0] * m[0, 1] + f[1, 1] * m[1, 1];

      f[0, 0] = x;
      f[0, 1] = y;
      f[1, 0] = z;
      f[1, 1] = w;
    }

static double Fibonacci(int n)
    {
      double sqrt5 = Math.Sqrt(5);
      double phi = (1 + sqrt5) / 2.0;
      double fn = (Math.Pow(phi, n) - Math.Pow(1 - phi, n)) / sqrt5;
      return fn;
    }

private static void InsertionSortInPlace(int[] unsorted)
    {
      for (int i = 1; i < unsorted.Length; i++)
      {
        if (unsorted[i - 1] > unsorted[i])
        {
          int key = unsorted[i];
          int j = i;
          while (j > 0 && unsorted[j - 1] > key)
          {
            unsorted[j] = unsorted[j - 1];
            j--;
          }
          unsorted[j] = key;
        }
      }
    }

数据结构基础 算法复杂度分析（二） 典例篇

标签：算法复杂度   时间复杂度   空间复杂度   渐进复杂度   渐近符   

原文地址：http://blog.csdn.net/u013630349/article/details/47210431