# Find element in 4d array with special properties

If N is less than 10000, then you can't see why you can't use unordered_set. Then do one search. If there can be the same values for each dimension, then you will need to track this somehow. But I don't know of any code that implements unordered_set for C. So you probably have to use C ++ for this.

If you cannot use unordered_set, then since the data is in sorted order for each dimension, you can also use binary search for each dimension. This would mean looking for no more than 15 values for each dimension on average - assuming the total number of items in each dimension is less than 16K. 15 searches * 4 dimensions = 60 searches. Is it too slow?

Another improvement could be to create one large sorted and unique array of 4 dimensions and search for it instead. This would give a total of about 17 searches (assuming <= 64K items) .vs. 60, which is 3.5 times faster. However, it will also depend on how often values are added to or removed from dimensions to determine if this is actually faster or not - since you will have to add and remove them from the same table. Also, remember to use a table to track duplicate values - if applicable.

If the values are relatively small integers - such as a billion or less, then you can use a bitmap scheme. The bitmap schema will be faster than using unordered_set for each dimension. An array of bytes can be used as a bitmap. The value set in the bitmap means that this value is present. For example, if the value is zero, then bit 0 will be set. If the value is 3, then bit 2 will be set. If the value is 5, then bit 4 will be set, and so on. So 100MB would need to be used to display all values for 1 billion (2 ^ 30). If there can be duplicate values in each dimension, then you will need to keep track of this,so that when a value is removed from a dimension, it is not removed from the bitmap if it does not exist in any other dimensions. If your values are floating point numbers, you can convert them to ints if the total significant digits are <= 9. If the values are strings or structures, then the bitmap schema might still work if you could figure out a way to translate it into a unique integer.if you could figure out a way to translate it into a unique integer.if you could figure out a way to translate it into a unique integer.

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