# NAG CL Interfacem01nbc (intvec_​search)

## 1Purpose

m01nbc searches an ordered vector of integer numbers and returns the index of the first value equal to the sought-after item.

## 2Specification

 #include
 Integer m01nbc (Nag_Boolean validate, const Integer iv[], Integer m1, Integer m2, Integer item, NagError *fail)
The function may be called by the names: m01nbc, nag_sort_intvec_search or nag_search_int.

## 3Description

m01nbc is based on Professor Niklaus Wirth's implementation of the Binary Search algorithm (see Wirth (2004)), but with two modifications. First, if the sought-after item is less than the value of the first element of the array to be searched, $-1$ is returned. Second, if a value equal to the sought-after item is not found, the index of the immediate lower value is returned.

## 4References

Wirth N (2004) Algorithms and Data Structures 35–36 Prentice Hall

## 5Arguments

1: $\mathbf{validate}$Nag_Boolean Input
On entry: if validate is set to Nag_TRUE argument checking will be performed. If validate is set to Nag_FALSE m01nbc will be called without argument checking (which includes checking that array iv is sorted in ascending order) and the function will return with ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_NOERROR. See Section 9 for further details.
2: $\mathbf{iv}\left[{\mathbf{m2}}+1\right]$const Integer Input
On entry: elements m1 to m2 contain integer values to be searched.
Constraint: elements m1 to m2 of iv must be sorted in ascending order.
3: $\mathbf{m1}$Integer Input
On entry: the index of the first element of iv to be searched.
Constraint: ${\mathbf{m1}}\ge 0$.
4: $\mathbf{m2}$Integer Input
On entry: the index of the last element of iv to be searched.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
5: $\mathbf{item}$Integer Input
On entry: the sought-after item.
6: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

Note: these errors will only be returned if ${\mathbf{validate}}=\mathrm{Nag_TRUE}$.).
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\ge 1-1$.
NE_INT_2
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$, ${\mathbf{m2}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\le {\mathbf{m2}}$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_NOT_INCREASING
On entry, iv must be sorted in ascending order: ${\mathbf{iv}}\text{​ element ​}〈\mathit{\text{value}}〉>\text{​ element ​}〈\mathit{\text{value}}〉$.

Not applicable.

## 8Parallelism and Performance

m01nbc is not threaded in any implementation.

The argument validate should be used with caution. Set it to Nag_FALSE only if you are confident that the other arguments are correct, in particular that array iv is in fact arranged in ascending order. If you wish to search the same array iv many times, you are recommended to set validate to Nag_TRUE on first call of m01nbc and to Nag_FALSE on subsequent calls, in order to minimize the amount of time spent checking iv, which may be significant if iv is large.
The time taken by m01nbc is $\mathit{O}\left(\mathrm{log}\left(n\right)\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$, when ${\mathbf{validate}}=\mathrm{Nag_FALSE}$.

## 10Example

This example reads a list of integer numbers and sought-after items and performs the search for these items.

### 10.1Program Text

Program Text (m01nbce.c)

### 10.2Program Data

Program Data (m01nbce.d)

### 10.3Program Results

Program Results (m01nbce.r)