Doubt in comparison logic

#1

Sir, in money change problem, even after defining our comparator function, why we still need to subtract 1 in line number 17.
Here is the link of solution- https://ide.codingblocks.com/s/648734

#2

Hi @singhkaranpreet710_f5e2ca6a9e8e0721,
if we dont use comparator, then the lower bound function gives the first value in the sorted array that is greater than or equal to the value to be found i.e it will ignore all values smaller than the value to be found. But, when we define a comparator same as defined in the lecture, the lower bound function ignores all the value smaller than or equal to the value to be found and hence will always return the index of key which has value greater than the value to be found. Hence we will have to subtract 1 from index in order to get the index of key which has value smaller than or equal to the required value.

For eg. arr=[1,2,3,5,7,9,13]
and we need to find lower bound of 5 and 6.
so if we use lower_bound without comparator, we will get ans as value=5 -> index=3 and value=6 -> index=4.
but if we use the comparator as discussed in lecture, we will get ans as value=5 -> index=4 and value=6 -> index=4.
So we will have to subtract 1 in latter case to get index of value smaller than or equal to the value to be found

using a<=b, comparator function returns true for all elements <= value to be found. When the comparator function returns false at that time we see that the current index might be the answer. If we dont use comparator function, it returns true only for elements < value to be found.
Since lower bound uses binary search approach internally, it use comparator <= condition in order to search for element greater than value to be found. In the later case lower bound use < condition to find the required index.

Hope this helps

#3

Thank you so much sir @Vaibhav277 for clearing my doubt.

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#4

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