Minimum of a List

The minimum is the name given to the smallest value among a list of numbers (the greatest value is called the maximum).

To find the smallest value (the minimum) among a list of numbers, it is necessary to go through the whole list of numbers and compare their values one after the other. The minimum in the list is the smallest value found when all values have been compared.

Example: The list of 4 values: 8,2,4,6 has for minimum 2

For positive values, the minimum is the value closest to $ 0 $ and for negative values the minimum is the value that is closest to $ -\infty $ (minus infinity).

A naive algorithm for calculating a minimum of a list A of $ n $ integers is:function min(list) {
min = list[0]
for i = 1 , i < n {
if list[i] < min {
min = list[i]
}
}
return min
}

The complexity is of order $ n $, as there are $ n - 1 $ comparisons and in the worst case, $ n $ assignments (if the table is sorted by descending order) and in the best case only 1 assignment (if the minimum is the first value in the list).