# Determinig Array index when given arrayan Element without using loops; array elements follow a set pattern where next element is twice the current element

Suppose the length of array is dynamic and the elements follow the same pattern where by the next element is half the previous element. For example
``````1024, 512, 256, 128...
``````

I would like to directly determine the index of an element. For example if I have
``````512
``````
I would output index
``````1
``````
without looping through the elements and comparing them with 512 then output 1. i.e not like this:

``````for (int i = 0;  i < length;  ++i) {
if (array[i] == 512) {
printf("%d\n", i);
break;
}
}
``````

I have been thinking of using modulus or bit manipulation like shifts but I can't get it to work. How can this be achieved?
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Commented:
If your pattern really always consists of base2 exponentials (2,4,8 ...) you could use the logarithm
`````` log(number)/log(2)
``````
In C the log is natural so you need to convert it to base 2. Then you substract the log result from the current array length, since you store them in descending order. This however depends on the value your array ends on and you might need to adjust to get the correct index. But may I ask why you need this array? Couldn't a function of n that returns the power 2^n achieve what you want to do?
0
Commented:
if your pattern really always consists of base2 exponentials (2,4,8 ...)

that doesn't matter. the only important thing is that the next item is the half of the previous item.

then (array[0] / number) necessarily is a multiple of 2's only.

``````int bitpos(unsigned char b)
{
int bit = 0;
if (b != 0)
{
switch(b)
{
case 1<<0: bit = 1;  break;
case 1<<1: bit = 2;  break;
case 1<<2: bit = 3;  break;
case 1<<3: bit = 4;  break;
case 1<<4: bit = 5;  break;
case 1<<5: bit = 6;  break;
case 1<<6: bit = 7;  break;
case 1<<7: bit = 8;  break;
}
}
return bit;
}

int index_in_half_series(int start, int find)
{
unsigned int n = start/find;

unsigned char b0 = bitpos((unsigned char)(n & 0xff));
unsigned char b1 = bitpos((unsigned char)((n>>8) & 0xff));
unsigned char b2 = bitpos((unsigned char)((n>>16) & 0xff));
unsigned char b3 = bitpos((unsigned char)((n>>24) & 0xff));
int index = b0? (b0 - 1) : b1? (7+b1) : b2?(15+b2) : (23+b3);
return index;
}

int main()
{
int array1[] = {1024,512,256,128,64,32,16,8,4,2,1};
int number1  = 16;
int index1   = index_in_half_series(array1[0], number1);

int array2[] = { 737, 368, 184, 92 };
int number2  = 92;
int index2   = index_in_half_series(array2[0], number2);
return 0;
}
``````

Sara
1

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Software EngineerAuthor Commented:
The solution works well and I have a shortcut:
index=logb2((array[0])/size);
where logb2() is a function to find log to base 2, array[0] is the first element in the array and it is the largest value in the array (the array is arranged in descending order), and size is the value which it's index in the array is being determined.
0
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