Is the height of binary tree [log2n]+1 equal to log2 (n+1)

  and      Whether it is equal or not ？

  For integers , The two are equal ; For floating point numbers , The two are not necessarily equal .

  Test code ：

#include <stdio.h>
#include <math.h>
int main()
{
    long int maxnum = 100000;
    // Integer test 
    for(int n = 1; n<maxnum; n++)
    {
        int down = floor(log(n)/log(2)) + 1;
        int up = ceil(log(n+1)/log(2));
        if(down != up)
            printf("down = %d,up = %d,n = %f\n",down,up,n);
    }
    printf("1 To %lu All integers between satisfy the equality of two formulas \n",maxnum);

    // Floating point test 
    for(double n = 1; n<maxnum; n+=0.11)
    {
        int down = floor(log(n)/log(2)) + 1;
        int up = ceil(log(n+1)/log(2));
        if(down != up)
            printf("down = %d,up = %d,n = %f\n",down,up,n);
    }

    double d = 3.0;
    int b = floor(log(3.0)/log(2.0)) + 1;
    int e = ceil(log(3.0+1)/log(2.0));
    printf("\nb = %d,e = %d",b,e);

    double p = log(3.000001+1);
    double q = log(2);
    int out = ceil(p/q);
    printf("\np = %f,q = %f,out = %d",p,q,out);

    return 0;
}

For the convenience of screenshots , Set the maximum value of the test to 30, Readers can set a larger value to test , The result should be the same  

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