Vernacular time complexity and space complexity

time complexity

Used to represent, the time it takes for an algorithm to solve a problem of size n.
Comprehension: Measured by the number of times the same code block is executed

sum = n*(n+1)/2; //顺序执行时，此代码块只会运行一次因此时间复杂度为 O(1)

for(int i = 0; i < n; i++){
    printf("%d ",i);     //根据上面的理解它的时间复杂度O(n)
}                       

Sometimes approximate values ​​are taken for convenience, such as:

for(int i = 0; i < n; i++){
    for(int j = 0; j < n; j++){
        printf("%d ",i);       //准确的时间复杂度为O(n^2)
    }
}               

but

for(int i = 0; i < n; i++){
    for(int j = i; j < n; j++){
        printf("%d ",i);//此代码块运行次数为 (1+n)*n/2 
//由高数中的极限可推n无限大时，(1+n)*n/2极限为n^2，因此时间复杂度O(n^2)
    }
}   

How does log ₂ n appear?

int i = 1, n = 100;
while(i < n){
    i = i * 2;   //设执行次数为x。 2^x = n 即x = log_2 n，时间复杂度O(log2n)
//当循环步数不为1跳跃时，便会产生多种答案
}

Reference Time Complexity and Space Complexity

space complexity

Used to represent, the space consumed by an algorithm to solve a problem of size n.
Comprehension: amount of extra space to generate (temporary variables included)

    public static void swap(int a, int b) {
        int temp = a;
        a = b;
        b =temp;
    }

A simple exchange is completed with the help of a temporary variable temp, so the space complexity is O(1)

    public static void swap(int a, int b) {
        a = a+b;
        b = a-b;
        a = a-b;
    }

And using addition and subtraction swap will not generate temporary variables so the space complexity is O(0)