Tasks Details
hard
1.
Clocks
Find the maximal number of clocks with hands that look identical when rotated.
Task Score
42%
Correctness
Not assessed
Performance
Not assessed
You are given N round clocks.
Every clock has M hands, and these hands can point to positions 1, 2, 3, ..., P (yes, these represent numbers around each face). The clocks are represented by the matrix A consisting of N rows and M columns of integers. The first row represents the hands of the first clock, and so on.
For example, you are given matrix A consisting of five rows and two columns, and P = 4:
A[0][0] = 1 A[0][1] = 2 A[1][0] = 2 A[1][1] = 4 A[2][0] = 4 A[2][1] = 3 A[3][0] = 2 A[3][1] = 3 A[4][0] = 1 A[4][1] = 3
You can rotate the clocks to obtain several clocks that look identical. For example, if you rotate the third, fourth and fifth clocks you can obtain the following clocks:
After rotation, the first, third and fourth clocks look the same, and the second clock looks the same as the fifth one. That means there are four pairs of clocks that look the same: (1, 3), (1, 4), (2, 5) and (3, 4).
Write a function:
function solution(A, P);
that, given a zero-indexed matrix A consisting of N rows and M columns of integers and integer P, returns the maximal number of pairs of clocks that can look the same after rotation.
For example, given the following array A and P = 4:
A[0][0] = 1 A[0][1] = 2 A[1][0] = 2 A[1][1] = 4 A[2][0] = 4 A[2][1] = 3 A[3][0] = 2 A[3][1] = 3 A[4][0] = 1 A[4][1] = 3the function should return 4, as explained above.
Write an efficient algorithm for the following assumptions:
- N and M are integers within the range [1..500];
- P is an integer within the range [1..1,000,000,000];
- each element of matrix A is an integer within the range [1..P];
- the elements of each row of matrix A are all distinct.
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used JavaScript
Time spent on task 11 minutes
Notes
not defined yet
Code: 12:42:18 UTC,
js,
verify,
result: Passed
function rotate(arr) {
var min = arr.reduce(function(a,b) { return a > b ? b : a });
while (arr[0] != min) {
var first = arr.shift();
arr.push(first);
}
}
function solution(A, P) {
var positions = [];
A.forEach(function(clock) {
var position = [];
clock.sort(function(a, b) { return a - b });
clock.push(clock[0] + P);
clock.forEach(function(hand, idx) {
if (idx == 0) return;
position.push(clock[idx] - clock[idx - 1]);
});
rotate(position);
positions.push(position);
});
positions.sort();
var sum = 0;
var type = positions[0].join(",");
var n = 0;
positions.forEach(function(position, idx) {
if (type == position.join(",")) {
n++;
} else {
type = position.join(",");
sum += (n * (n-1)) / 2;
n = 1;
}
});
sum += (n * (n-1)) / 2;
return sum;
}
Analysis
Code: 12:44:04 UTC,
js,
verify,
result: Passed
function rotate(arr) {
var min = arr.reduce(function(a,b) { return a > b ? b : a });
while (arr[0] != min) {
var first = arr.shift();
arr.push(first);
}
}
function solution(A, P) {
var positions = [];
A.forEach(function(clock) {
var position = [];
clock.sort(function(a, b) { return a - b });
clock.push(clock[0] + P);
clock.forEach(function(hand, idx) {
if (idx == 0) return;
position.push(clock[idx] - clock[idx - 1]);
});
rotate(position);
positions.push(position);
});
positions.sort();
var sum = 0;
var type = positions[0].join(",");
var n = 0;
positions.forEach(function(position, idx) {
if (type == position.join(",")) {
n++;
} else {
type = position.join(",");
sum += (n * (n-1)) / 2;
n = 1;
}
});
sum += (n * (n-1)) / 2;
return sum;
}
Analysis
Code: 12:52:04 UTC,
js,
verify,
result: Passed
function rotate(arr) {
var min = arr.reduce(function(a,b) { return a > b ? b : a });
while (arr[0] != min) {
var first = arr.shift();
arr.push(first);
}
}
function solution(A, P) {
var positions = [];
A.forEach(function(clock) {
var position = [];
clock.sort(function(a, b) { return a - b });
clock.push(clock[0] + P);
clock.forEach(function(hand, idx) {
if (idx == 0) return;
position.push(clock[idx] - clock[idx - 1]);
});
rotate(position);
positions.push(position);
});
positions.sort();
var sum = 0;
var type = positions[0].join(",");
var n = 0;
positions.forEach(function(position, idx) {
if (type == position.join(",")) {
n++;
} else {
type = position.join(",");
sum += (n * (n-1)) / 2;
n = 1;
}
});
sum += (n * (n-1)) / 2;
return sum;
}
Analysis
Code: 12:52:11 UTC,
js,
final,
score:
42
function rotate(arr) {
var min = arr.reduce(function(a,b) { return a > b ? b : a });
while (arr[0] != min) {
var first = arr.shift();
arr.push(first);
}
}
function solution(A, P) {
var positions = [];
A.forEach(function(clock) {
var position = [];
clock.sort(function(a, b) { return a - b });
clock.push(clock[0] + P);
clock.forEach(function(hand, idx) {
if (idx == 0) return;
position.push(clock[idx] - clock[idx - 1]);
});
rotate(position);
positions.push(position);
});
positions.sort();
var sum = 0;
var type = positions[0].join(",");
var n = 0;
positions.forEach(function(position, idx) {
if (type == position.join(",")) {
n++;
} else {
type = position.join(",");
sum += (n * (n-1)) / 2;
n = 1;
}
});
sum += (n * (n-1)) / 2;
return sum;
}Analysis summary
The following issues have been detected: wrong answers.
Analysis
expand all
Assessment tests
1.
0.080 s
OK
1.
0.080 s
OK
1.
0.080 s
OK
1.
0.080 s
OK
small_random
small random test, number of clocks = 10 (different = 3)
small random test, number of clocks = 10 (different = 3)
✘
WRONG ANSWER
got 6 expected 13
got 6 expected 13
1.
0.080 s
WRONG ANSWER,
got 6 expected 13
small_constantSpace
all the same space except two, number of clocks = 15
all the same space except two, number of clocks = 15
✘
WRONG ANSWER
got 8 expected 14
got 8 expected 14
1.
0.080 s
WRONG ANSWER,
got 8 expected 14
small_rangeSpace
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 20
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 20
✘
WRONG ANSWER
got 63 expected 190
got 63 expected 190
1.
0.100 s
WRONG ANSWER,
got 63 expected 190
1.
0.080 s
WRONG ANSWER,
got 30 expected 34
medium_random_smallDifferent
medium random test, number of clocks = 100 (different = 7)
medium random test, number of clocks = 100 (different = 7)
✘
WRONG ANSWER
got 573 expected 701
got 573 expected 701
1.
0.120 s
WRONG ANSWER,
got 573 expected 701
1.
0.130 s
OK
medium_constantSpace
all the same space except two, number of clocks = 115
all the same space except two, number of clocks = 115
✘
WRONG ANSWER
got 20 expected 124
got 20 expected 124
1.
0.120 s
WRONG ANSWER,
got 20 expected 124
medium_rangeSpace
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 113
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 113
✘
WRONG ANSWER
got 925 expected 6328
got 925 expected 6328
1.
0.120 s
WRONG ANSWER,
got 925 expected 6328
1.
0.100 s
OK
large_random_tinyDifferent
large random tests, number of clocks = 500 (different = 2)
large random tests, number of clocks = 500 (different = 2)
✘
WRONG ANSWER
got 3204 expected 62251
got 3204 expected 62251
1.
0.490 s
WRONG ANSWER,
got 3204 expected 62251
1.
0.430 s
OK
large_random_bigDifferent
large random test, number of clocks = 487 (different = 99)
large random test, number of clocks = 487 (different = 99)
✘
WRONG ANSWER
got 541 expected 1187
got 541 expected 1187
1.
0.500 s
WRONG ANSWER,
got 541 expected 1187
1.
0.590 s
OK
large_rangeSpace1
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 500
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 500
✘
WRONG ANSWER
got 41434 expected 124750
got 41434 expected 124750
1.
0.430 s
WRONG ANSWER,
got 41434 expected 124750
large_rangeSpace2
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 496
spaces are 1, 2, ... x, 1, 2, ... (x-1) ..., clocks = 496
✘
WRONG ANSWER
got 9485 expected 122760
got 9485 expected 122760
1.
0.340 s
WRONG ANSWER,
got 9485 expected 122760
1.
0.110 s
WRONG ANSWER,
got 29042 expected 34487
1.
0.390 s
OK