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] = 8contains 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($A);
that, given a non-empty array A consisting of N integers, returns the starting position of the slice with the minimal average. If there is more than one slice with a minimal average, you should return the smallest starting position of such a slice.
For example, given array A such that:
A[0] = 4 A[1] = 2 A[2] = 2 A[3] = 5 A[4] = 1 A[5] = 5 A[6] = 8the function should return 1, as explained above.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [2..100,000];
- each element of array A is an integer within the range [−10,000..10,000].
array(4) { [0]=> int(0) [1]=> int(4) [2]=> int(6) [3]=> int(8) } Invalid result type, int expected.
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
var_dump ($min_avg);
}
int(3) Invalid result type, int expected.
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i] - $P[$i-1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i] - $P[$i-1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg_idx;
}
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
if (($P[$i] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i] - $P[$i-1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i] - $P[$i-1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
array_push($P, $A[$i] + $P[$i]);
}
return $min_avg_idx;
}
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1] - $P[$i])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1] - $P[$i])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg_idx;
}
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1] - $P[$i])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1] - $P[$i])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg;
}
Invalid result type, int expected.
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1] - $P[$i])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1] - $P[$i])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($min_avg);
return $min_avg_idx;
}
float(-2.6666666666667)
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1] - $P[$i])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1] - $P[$i])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($P);
return $min_avg_idx;
}
array(8) { [0]=> int(0) [1]=> int(4) [2]=> int(6) [3]=> int(8) [4]=> int(13) [5]=> int(14) [6]=> int(19) [7]=> int(27) }
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($P);
return $min_avg_idx;
}
array(8) { [0]=> int(0) [1]=> int(4) [2]=> int(6) [3]=> int(8) [4]=> int(13) [5]=> int(14) [6]=> int(19) [7]=> int(27) }
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($min_avg);
return $min_avg_idx;
}
float(0.5)
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-1])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($min_avg);
var_dump ($P);
return $min_avg_idx;
}
float(0.5) array(8) { [0]=> int(0) [1]=> int(4) [2]=> int(6) [3]=> int(8) [4]=> int(13) [5]=> int(14) [6]=> int(19) [7]=> int(27) }
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
}
var_dump ($min_avg);
var_dump ($P);
return $min_avg_idx;
}
WARNING: producing output may seriously slow down your code! int(2) array(8) { [0]=> int(0) [1]=> int(4) [2]=> int(6) [3]=> int(8) [4]=> int(13) [5]=> int(14) [6]=> int(19) [7]=> int(27) }
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg_idx;
}
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg_idx;
}
// you can use print for debugging purposes, e.g.
// print "this is a debug message\n";
function solution($A) {
$n = count($A);
$P = array(0);
array_push($P, $A[0]);
array_push($P, $A[1] + $P[1]);
//array_push($P, $A[2] + $P[2]);
$min_avg_idx = 0;
$min_avg = $P[2]/2;
for ($i = 2; $i<$n; $i++) {
array_push($P, $A[$i] + $P[$i]);
if (($P[$i+1] - $P[$i-1])/2<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-1])/2;
$min_avg_idx = $i-1;
}
if (($P[$i+1] - $P[$i-2])/3<$min_avg) {
$min_avg = ($P[$i+1] - $P[$i-2])/3;
$min_avg_idx = $i-2;
}
}
return $min_avg_idx;
}
The solution obtained perfect score.