#### Binary

F
```package search

// Binary search for target within a sorted array by repeatedly dividing the array in half and comparing the midpoint with the target.
// This function uses recursive call to itself.
// If a target is found, the index of the target is returned. Else the function return -1 and ErrNotFound.
func Binary(array []int, target int, lowIndex int, highIndex int) (int, error) {
if highIndex < lowIndex || len(array) == 0 {
return -1, ErrNotFound
}
mid := int(lowIndex + (highIndex-lowIndex)/2)
if array[mid] > target {
return Binary(array, target, lowIndex, mid-1)
} else if array[mid] < target {
return Binary(array, target, mid+1, highIndex)
} else {
return mid, nil
}
}

// BinaryIterative search for target within a sorted array by repeatedly dividing the array in half and comparing the midpoint with the target.
// Unlike Binary, this function uses iterative method and not recursive.
// If a target is found, the index of the target is returned. Else the function return -1 and ErrNotFound.
func BinaryIterative(array []int, target int) (int, error) {
startIndex := 0
endIndex := len(array) - 1
var mid int
for startIndex <= endIndex {
mid = int(startIndex + (endIndex-startIndex)/2)
if array[mid] > target {
endIndex = mid - 1
} else if array[mid] < target {
startIndex = mid + 1
} else {
return mid, nil
}
}
return -1, ErrNotFound
}

// Returns index to the first element in the range [0, len(array)-1] that is not less than (i.e. greater or equal to) target.
// return -1 and ErrNotFound if no such element is found.
func LowerBound(array []int, target int) (int, error) {
startIndex := 0
endIndex := len(array) - 1
var mid int
for startIndex <= endIndex {
mid = int(startIndex + (endIndex-startIndex)/2)
if array[mid] < target {
startIndex = mid + 1
} else {
endIndex = mid - 1
}
}

//when target greater than every element in array, startIndex will out of bounds
if startIndex >= len(array) {
return -1, ErrNotFound
}
return startIndex, nil
}

// Returns index to the first element in the range [lowIndex, len(array)-1] that is greater than target.
// return -1 and ErrNotFound if no such element is found.
func UpperBound(array []int, target int) (int, error) {
startIndex := 0
endIndex := len(array) - 1
var mid int
for startIndex <= endIndex {
mid = int(startIndex + (endIndex-startIndex)/2)
if array[mid] > target {
endIndex = mid - 1
} else {
startIndex = mid + 1
}
}

//when target greater or equal than every element in array, startIndex will out of bounds
if startIndex >= len(array) {
return -1, ErrNotFound
}
return startIndex, nil
}
```