Tasks Details
easy
Maximize A[P] * A[Q] * A[R] for any triplet (P, Q, R).
Task Score
100%
Correctness
100%
Performance
100%
A non-empty array A consisting of N integers is given. The product of triplet (P, Q, R) equates to A[P] * A[Q] * A[R] (0 ≤ P < Q < R < N).
For example, array A such that:
A[0] = -3 A[1] = 1 A[2] = 2 A[3] = -2 A[4] = 5 A[5] = 6contains the following example triplets:
- (0, 1, 2), product is −3 * 1 * 2 = −6
- (1, 2, 4), product is 1 * 2 * 5 = 10
- (2, 4, 5), product is 2 * 5 * 6 = 60
Your goal is to find the maximal product of any triplet.
Write a function:
class Solution { public int solution(int[] A); }
that, given a non-empty array A, returns the value of the maximal product of any triplet.
For example, given array A such that:
A[0] = -3 A[1] = 1 A[2] = 2 A[3] = -2 A[4] = 5 A[5] = 6the function should return 60, as the product of triplet (2, 4, 5) is maximal.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [3..100,000];
- each element of array A is an integer within the range [−1,000..1,000].
Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Java 8
Time spent on task 11 minutes
Notes
not defined yet
Task timeline
Code: 07:49:46 UTC,
java,
verify,
result: Failed
// you can also use imports, for example:
// import java.util.*;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = new int[3]; // maxes[0] <= maxes[1] <= maxes[2]
int[] mins = new int[2]; // mins [0] <= mins [1]
boolean foundZero = false;
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
Analysis
Compile error
Solution.java:20: error: cannot find symbol
System.out.println(Arrays.toString(maxes));
^
symbol: variable Arrays
location: class Solution
Solution.java:21: error: cannot find symbol
System.out.println(Arrays.toString(mins));
^
symbol: variable Arrays
location: class Solution
2 errors
Code: 07:50:05 UTC,
java,
verify,
result: Passed
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = new int[3]; // maxes[0] <= maxes[1] <= maxes[2]
int[] mins = new int[2]; // mins [0] <= mins [1]
boolean foundZero = false;
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
Analysis
expand all
Example tests
1.
1.504 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-3, -2]
Code: 07:53:12 UTC,
java,
verify,
result: Passed
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = new int[3]; // maxes[0] <= maxes[1] <= maxes[2]
int[] mins = new int[2]; // mins [0] <= mins [1]
boolean foundZero = false;
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
User test case 1:
None
User test case 2:
None
User test case 3:
None
User test case 4:
None
Analysis
expand all
Example tests
1.
1.076 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-3, -2]
expand all
User tests
1.
0.940 s
OK
function result: 180
function result: 180
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-6, -5]
1.
0.904 s
OK
function result: 36
function result: 36
stdout:
WARNING: producing output may seriously slow down your code! [0, 1, 6] [-3, -2]
1.
0.912 s
OK
function result: 6
function result: 6
stdout:
WARNING: producing output may seriously slow down your code! [0, 0, 1] [-3, -2]
1.
0.916 s
OK
function result: 0
function result: 0
stdout:
WARNING: producing output may seriously slow down your code! [0, 0, 1] [-2, 0]
Code: 07:57:44 UTC,
java,
verify,
result: Failed
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = {Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE};
// Invariant: maxes[0] <= maxes[1] <= maxes[2]
int[] mins = {Integer.MAX_VALUE, Integer.MAX_VALUE}
// Invariant: mins[0] <= mins[1]
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
Analysis
Compile error
Solution.java:13: error: ';' expected
int[] mins = {Integer.MAX_VALUE, Integer.MAX_VALUE}
^
1 error
Code: 07:57:56 UTC,
java,
verify,
result: Passed
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = {Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE};
// Invariant: maxes[0] <= maxes[1] <= maxes[2]
int[] mins = {Integer.MAX_VALUE, Integer.MAX_VALUE};
// Invariant: mins[0] <= mins[1]
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
User test case 1:
None
User test case 2:
None
User test case 3:
None
User test case 4:
None
Analysis
expand all
Example tests
1.
1.136 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-3, -2]
expand all
User tests
1.
1.060 s
OK
function result: 180
function result: 180
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-6, -5]
1.
0.960 s
OK
function result: 36
function result: 36
stdout:
WARNING: producing output may seriously slow down your code! [0, 1, 6] [-3, -2]
1.
0.968 s
OK
function result: 6
function result: 6
stdout:
WARNING: producing output may seriously slow down your code! [-3, -2, 1] [-3, -2]
1.
0.952 s
OK
function result: 0
function result: 0
stdout:
WARNING: producing output may seriously slow down your code! [-2, 0, 1] [-2, 0]
Code: 07:58:51 UTC,
java,
verify,
result: Passed
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = {Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE};
// Invariant: maxes[0] <= maxes[1] <= maxes[2]
int[] mins = {Integer.MAX_VALUE, Integer.MAX_VALUE};
// Invariant: mins[0] <= mins[1]
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}
User test case 1:
None
User test case 2:
None
User test case 3:
None
User test case 4:
None
Analysis
expand all
Example tests
1.
1.528 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-3, -2]
expand all
User tests
1.
1.488 s
OK
function result: 180
function result: 180
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-6, -5]
1.
1.496 s
OK
function result: 36
function result: 36
stdout:
WARNING: producing output may seriously slow down your code! [0, 1, 6] [-3, -2]
1.
1.472 s
OK
function result: 6
function result: 6
stdout:
WARNING: producing output may seriously slow down your code! [-3, -2, 1] [-3, -2]
1.
1.480 s
OK
function result: 0
function result: 0
stdout:
WARNING: producing output may seriously slow down your code! [-2, 0, 1] [-2, 0]
Code: 07:59:09 UTC,
java,
final,
score:
100
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556
// you can also use imports, for example:
import java.util.Arrays;
// you can use System.out.println for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A) {
int[] maxes = {Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE};
// Invariant: maxes[0] <= maxes[1] <= maxes[2]
int[] mins = {Integer.MAX_VALUE, Integer.MAX_VALUE};
// Invariant: mins[0] <= mins[1]
// O(n)
for( int a : A )
{
updateMaxes( a, maxes );
updateMins( a, mins );
}
System.out.println(Arrays.toString(maxes));
System.out.println(Arrays.toString(mins));
int obvious = maxes[0] * maxes[1] * maxes[2];
int twoBigNegs = mins[0] * mins[1] * maxes[2];
return Math.max( obvious, twoBigNegs );
}
private static void updateMaxes( int a, int[] maxes )
{
if( a >= maxes[2] ) {
// Found new max, shift down
maxes[0] = maxes[1];
maxes[1] = maxes[2];
maxes[2] = a;
} else if( a >= maxes[1] ) {
maxes[0] = maxes[1];
maxes[1] = a;
} else if( a > maxes[0] ) {
maxes[0] = a;
}
}
private static void updateMins( int a, int[] mins )
{
if( a <= mins[0] ) {
// Found new min, shift down
mins[1] = mins[0];
mins[0] = a;
} else if( a < mins[1] ) {
mins[1] = a;
}
}
}Analysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N * log(N))
expand all
Example tests
1.
1.512 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 5, 6] [-3, -2]
expand all
Correctness tests
1.
1.424 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [1000, 1000, 1000] [1000, 1000]
1.
1.456 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [1, 4, 5] [0, 1]
1.
1.468 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [2, 3, 100] [-1000, 2]
1.
1.464 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [974, 993, 997] [-981, -965]
expand all
Performance tests
1.
1.500 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [998, 999, 1000] [-1000, -999]
1.
1.504 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [1000, 1000, 1000] [-1000, -1000]
1.
1.680 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [1000, 1000, 1000] [-1000, -1000]
1.
1.448 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [10, 10, 500] [-1000, -10]
1.
1.748 s
OK
stdout:
WARNING: producing output may seriously slow down your code! [-1000, -1000, -1000] [-1000, -1000]