Tasks Details
hard
1.
MinAbsSum
Given array of integers, find the lowest absolute sum of elements.
Task Score
100%
Correctness
100%
Performance
100%
For a given array A of N integers and a sequence S of N integers from the set {−1, 1}, we define val(A, S) as follows:
val(A, S) = |sum{ A[i]*S[i] for i = 0..N−1 }|
(Assume that the sum of zero elements equals zero.)
For a given array A, we are looking for such a sequence S that minimizes val(A,S).
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A of N integers, computes the minimum value of val(A,S) from all possible values of val(A,S) for all possible sequences S of N integers from the set {−1, 1}.
For example, given array:
A[0] = 1 A[1] = 5 A[2] = 2 A[3] = -2your function should return 0, since for S = [−1, 1, −1, 1], val(A, S) = 0, which is the minimum possible value.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [0..20,000];
- each element of array A is an integer within the range [−100..100].
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Java 21
Time spent on task 27 minutes
Notes
not defined yet
Code: 13:38:19 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=-1;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<max; i++){
if(hash[j]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-can<<1);
}
}
Analysis
Compile error
Solution.java:31: error: cannot find symbol
if(hash[j]>0){
^
symbol: variable j
location: class Solution
1 error
Code: 13:39:01 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=-1;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-can<<1);
}
}
Analysis
expand all
Example tests
1.
0.983 s
WRONG ANSWER,
got 10 expected 0
Code: 13:39:35 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-can<<1);
}
}
Analysis
expand all
Example tests
1.
1.315 s
WRONG ANSWER,
got 10 expected 0
Code: 13:39:49 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
//if(can>=half) break;
}
return Math.abs(sum-can<<1);
}
}
Analysis
expand all
Example tests
1.
1.325 s
WRONG ANSWER,
got 10 expected 0
Code: 13:40:01 UTC,
java,
verify,
result: Passed
// 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
//if(can>=half) break;
}
return Math.abs(sum-(can<<1));
}
}
Analysis
Code: 13:41:11 UTC,
java,
verify,
result: Passed
// 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<=max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-(can<<1));
}
}
Analysis
Code: 13:41:33 UTC,
java,
verify,
result: Passed
// 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<=max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-(can<<1));
}
}
Analysis
Code: 13:41:38 UTC,
java,
final,
score:
100
// 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) {
// write your code in Java SE 8
int[] hash = new int[101];
int max = 0;
int sum = 0;
for(int i=0; i<A.length; i++){
int a=Math.abs(A[i]);
hash[a]++;
sum+=a;
max = Math.max(max,a);
}
//
int half = sum/2+1;
int[] dp = new int[half];
for(int i=0; i<dp.length; i++){
dp[i]=-1;
}
dp[0]=0;
int can=0;
// dp save the left number of item i to achive the sum j
// -1 means sum 0-i < j
for(int i=1; i<=max; i++){
if(hash[i]>0){
for(int j=0; j<dp.length; j++){
if(dp[j]>=0){
dp[j]=hash[i];
if(j>can){
can = j;
}
}
else{
if(j-i>=0 && dp[j-i]>0){
dp[j] = dp[j-i]-1;
if(j>can){
can = j;
}
}
}
}
}
if(can>=half) break;
}
return Math.abs(sum-(can<<1));
}
}
Analysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N * max(abs(A))**2)
expand all
Correctness tests
1.
1.325 s
OK
2.
1.312 s
OK
3.
1.317 s
OK
1.
1.327 s
OK
2.
1.314 s
OK
1.
1.321 s
OK
2.
1.329 s
OK
3.
1.322 s
OK
1.
1.310 s
OK
2.
1.321 s
OK
1.
1.324 s
OK
2.
1.320 s
OK
1.
1.304 s
OK
2.
1.319 s
OK
expand all
Performance tests
1.
1.032 s
OK
2.
0.991 s
OK
1.
1.325 s
OK
2.
1.315 s
OK
1.
1.379 s
OK
2.
1.319 s
OK
1.
1.344 s
OK
1.
1.433 s
OK
2.
1.328 s
OK