**Task Score**

**Correctness**

**Performance**

A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P < Q < N, is called a *slice* of array A (notice that the slice contains at least two elements). The *average* of a slice (P, Q) is the sum of A[P] + A[P + 1] + ... + A[Q] divided by the length of the slice. To be precise, the average equals (A[P] + A[P + 1] + ... + A[Q]) / (Q − P + 1).

For example, array A such that:

`A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8`

contains the following example slices:

- slice (1, 2), whose average is (2 + 2) / 2 = 2;
- slice (3, 4), whose average is (5 + 1) / 2 = 3;
- slice (1, 4), whose average is (2 + 2 + 5 + 1) / 4 = 2.5.

The goal is to find the starting position of a slice whose average is minimal.

Write a function:

function solution($A);

that, given a non-empty array A consisting of N integers, returns the starting position of the slice with the minimal average. If there is more than one slice with a minimal average, you should return the smallest starting position of such a slice.

For example, given array A such that:

`A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8`

the function should return 1, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [2..100,000];
- each element of array A is an integer within the range [−10,000..10,000].

*not defined yet*

**Passed**

```
// you can write to stdout for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
// write your code in PHP5.5
$min_avg = ( $A[0] + $A[1] ) / 2;
$index = 0;
$n = count( $A );
$nm = $n - 1;
for( $k = 0; $k < $nm; $k++) {
$a = ( $A[$k] + $A[$k+1] ) / 2;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
if( isset( $A[k+3] ) ) {
$a = ( $A[$k] + $A[$k+1] + $A[$k+2] ) / 3;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
}
}
$last = ( $A[$n-1] + $A[$n-2] ) / 2;
if( $last < $min_avg ) {
$index = $nm-1;
}
return $index;
}
```

**Example tests**

**OK**

PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Undefined offset: 7 in /tmp/user.php on line 21 Notice: Undefined offset: 7 in /tmp/user.php on line 21

**Passed**

```
// you can write to stdout for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
// write your code in PHP5.5
$min_avg = ( $A[0] + $A[1] ) / 2;
$index = 0;
$n = count( $A );
$nm = $n - 1;
for( $k = 0; $k < $nm; $k++) {
$a = ( $A[$k] + $A[$k+1] ) / 2;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
if( isset( $A[k+2] ) ) {
$a = ( $A[$k] + $A[$k+1] + $A[$k+2] ) / 3;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
}
}
$last = ( $A[$n-1] + $A[$n-2] ) / 2;
if( $last < $min_avg ) {
$index = $nm-1;
}
return $index;
}
```

**Example tests**

**OK**

PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 Notice: Use of undefined constant k - assumed 'k' in /tmp/user.php on line 20 PHP Notice: Undefined offset: 7 in /tmp/user.php on line 21 Notice: Undefined offset: 7 in /tmp/user.php on line 21

**Passed**

```
// you can write to stdout for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
// write your code in PHP5.5
$min_avg = ( $A[0] + $A[1] ) / 2;
$index = 0;
$n = count( $A );
$nm = $n - 1;
for( $k = 0; $k < $nm; $k++) {
$a = ( $A[$k] + $A[$k+1] ) / 2;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
if( isset( $A[$k+2] ) ) {
$a = ( $A[$k] + $A[$k+1] + $A[$k+2] ) / 3;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
}
}
$last = ( $A[$n-1] + $A[$n-2] ) / 2;
if( $last < $min_avg ) {
$index = $nm-1;
}
return $index;
}
```

**Passed**

```
// you can write to stdout for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
// write your code in PHP5.5
$min_avg = ( $A[0] + $A[1] ) / 2;
$index = 0;
$n = count( $A );
$nm = $n - 1;
for( $k = 0; $k < $nm; $k++) {
$a = ( $A[$k] + $A[$k+1] ) / 2;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
if( isset( $A[$k+2] ) ) {
$a = ( $A[$k] + $A[$k+1] + $A[$k+2] ) / 3;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
}
}
$last = ( $A[$n-1] + $A[$n-2] ) / 2;
if( $last < $min_avg ) {
$index = $nm-1;
}
return $index;
}
```

**100**

```
// you can write to stdout for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
// write your code in PHP5.5
$min_avg = ( $A[0] + $A[1] ) / 2;
$index = 0;
$n = count( $A );
$nm = $n - 1;
for( $k = 0; $k < $nm; $k++) {
$a = ( $A[$k] + $A[$k+1] ) / 2;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
if( isset( $A[$k+2] ) ) {
$a = ( $A[$k] + $A[$k+1] + $A[$k+2] ) / 3;
if( $a < $min_avg ) {
$index = $k;
$min_avg = $a;
}
}
}
$last = ( $A[$n-1] + $A[$n-2] ) / 2;
if( $last < $min_avg ) {
$index = $nm-1;
}
return $index;
}
```

The solution obtained perfect score.

**O(N)**

**Correctness tests**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**Performance tests**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**

**OK**