文章目录
🎨1.算法的复杂度介绍
🎨2.时间复杂度的概念
📝代码样例
// 请计算一下Func1中++count语句总共执行了多少次？
void Func1(int N)
{
int count = 0;
for (int i = 0; i < N ; ++ i)
{
for (int j = 0; j < N ; ++ j)
{
++count;
}
}
for (int k = 0; k < 2 * N ; ++ k)
{
++count;
}
int M = 10;
while (M--)
{
++count;
}
}
🎨3.大O的渐进表示法
📝实例1
void Func3(int N, int M)
{
int count = 0;
for (int k = 0; k < M; ++k)
{
++count;
}
for (int k = 0; k < N; ++k)
{
++count;
}
printf("%d\n", count);
}
📝实例2
void Func4(int N)
{
int count = 0;
for (int k = 0; k < 100; ++k)
{
++count;
}
printf("%d\n", count);
}
📝实例3
void Func2(int N)
{
int count = 0;
for (int k = 0; k < 2 * N; ++k)
{
++count;
}
int M = 10;
while (M--)
{
++count;
}
printf("%d\n", count);
}
📝实例4
📝实例5
// 计算BubbleSort的时间复杂度？
void BubbleSort(int* a, int n)
{
assert(a);
for (size_t end = n; end > 0; --end)
{
int exchange = 0;
for (size_t i = 1; i < end; ++i)
{
if (a[i - 1] > a[i])
{
Swap(&a[i - 1], &a[i]);
exchange = 1;
}
}
if (exchange == 0)
break;
}
}
📝实例6
// 计算BinarySearch的时间复杂度
int BinarySearch(int* a, int n, int x)
{
assert(a);
int begin = 0;
int end = n - 1;
while (begin <= end)
{
int mid = begin + ((end - begin) >> 1);
if (a[mid] < x)
begin = mid + 1;
else if (a[mid] > x)
end = mid - 1;
else
return mid;
}
return -1;
}
📝实例7(⭐两种递归的区别）
1.递归里没有循环
long long Fac(size_t N)
{
if (0 == N)
return 1;
return Fac(N - 1) * N;
}
2.递归里有循环
long long Fac(size_t N)
{
if (0 == N)
return 1;
for (size_t i; i < N; ++i)
{
//...
}
return Fac(N - 1) * N;
}
🌟误区
📝实例8
// 计算斐波那契递归Fib的时间复杂度
long long Fib(size_t N)
{
if (N < 3)
return 1;
return Fib(N - 1) + Fib(N - 2);
}
🎨4.空间复杂度的概念
📝实例1
void BubbleSort(int* a, int n)
{
assert(a);
for (size_t end = n; end > 0; --end)
{
int exchange = 0;
for (size_t i = 1; i < end; ++i)
{
if (a[i - 1] > a[i])
{
Swap(&a[i - 1], &a[i]);
exchange = 1;
}
}
if (exchange == 0)
break;
}
}
🌟误区
📝实例2
long long* Fibonacci(size_t n)
{
if (n == 0)
return NULL;
long long* fibArray = (long long*)malloc((n + 1) * sizeof(long long));
fibArray[0] = 0;
fibArray[1] = 1;
for (int i = 2; i <= n; ++i)
{
fibArray[i] = fibArray[i - 1] + fibArray[i - 2];
}
return fibArray;
}
📝实例3
long long Fac(size_t N)
{
if (0 == N)
return 1;
return Fac(N - 1) * N;
}
📝实例4(🎃斐波那契递归Fib的空间复杂度）
long long Fib(size_t N)
{
if (N < 3)
return 1;
return Fib(N - 1) + Fib(N - 2);
}
🖊代码证明
void Func1()
{
int a = 0;
printf("%p\n", &a);
}
void Func2()
{
int b = 0;
printf("%p\n", &b);
}
int main()
{
Func1();
Func2();
return 0;
}
