Tasks Details
hard
Count the minimum number of moves required to rearrange sprinklers so as to maximize the number of farmland fields that get watered.
Task Score
100%
Correctness
100%
Performance
100%
Joe the Farmer owns a square plot of farmland whose sides are of length N. The land is split into N rows and N columns of equal size, so that there are N2 identical square fields within the farmland. Thanks to the abundant crops that Joe harvested last year, he could afford to buy N sprinklers. They significantly reduce the amount of time that Joe spends watering his plants.
Every sprinkler can be placed in any field of the farmland, but no two sprinklers can occupy the same field. Upon activation, each sprinkler irrigates every field within the same column and row in which it appears.
After delivery, the sprinklers were placed in a batch, so the K-th sprinkler is positioned in field (XK, YK). Joe knows that this arrangement is not optimal, as some fields may not be watered by any sprinkler. Moreover, no column or row should be watered by more than one sprinkler, as it may cause over-hydration of the crops.
In one move, the farmer can move a single sprinkler to an adjacent unoccupied field. Two fields are adjacent to one another if they have a common side.
What is the minimum number of moves required to rearrange the sprinklers so that all fields will be irrigated by sprinklers, and no two sprinklers will water the same column or row? Since the answer can be very large, provide it modulo 1,000,000,007 (109 + 7).
Write a function:
int solution(vector<int> &X, vector<int> &Y);
that, given arrays X and Y, both consisting of N integers and representing the coordinates of consecutive sprinklers, returns a minimal number of moves modulo 1,000,000,007, required to irrigate all fields.
For example, given array X = [1, 2, 2, 3, 4] and array Y = [1, 1, 4, 5, 4] the function should return 5, as we can make following moves:
For another example, given array X = [1, 1, 1, 1] and array Y = [1, 2, 3, 4] the function should return 6:
Given array X = [1, 1, 2] and array Y = [1, 2, 1] the function should return 4:
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [2..100,000];
- each element of arrays X and Y is an integer within the range [1..N];
- each sprinkler appears in a distinct field (no field may contain more than one sprinkler).
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used C++
Time spent on task 18 minutes
Notes
not defined yet
Code: 16:00:26 UTC,
java,
autosave
Code: 16:01:46 UTC,
cpp,
autosave
Code: 16:03:07 UTC,
cpp,
autosave
Code: 16:03:18 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
}
Code: 16:09:08 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
ve
}
Code: 16:09:18 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
vector<int>
}
Code: 16:09:48 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n =
}
Code: 16:10:19 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> count()
}
Code: 16:10:42 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> count(n + 1, 0);
for (int i = 0; i < n; i++) {
count[x[i]]++;
}
}
Code: 16:11:03 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> count(n + 1, 0);
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
}
Code: 16:11:34 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
for (int i = 1; i <= n; i++) {
}
}
Code: 16:12:04 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for ()
}
}
Code: 16:12:35 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 0; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
a
}
}
}
Code: 16:13:05 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 1; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
ans += abs(i - r);
order.push_back({})
}
}
}
Code: 16:13:18 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 1; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
ans += abs(i - r);
order.push_back({r, y});
r++;
}
}
}
Code: 16:13:33 UTC,
cpp,
autosave
// you can use includes, for example:
// #include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 1; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
ans += abs(i - r);
ans %= mod;
order.push_back({r, y});
r++;
}
}
}
Code: 16:13:49 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 1; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
ans += abs(i - r);
ans %= mod;
order.push_back({r, y});
r++;
}
}
}
Code: 16:14:00 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]].push_back(Y[i]);
}
vector<pair<int, int> > order;
int r = 1; // current row to be filled.
int ans = 0;
for (int i = 1; i <= n; i++) {
if (count[i].size() == 0) continue;
for (auto y: count[i]) {
ans += abs(i - r);
ans %= mod;
order.push_back({r, y});
r++;
}
}
}
Code: 16:14:30 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]]++;
}
int ans = 0;
for (int i = 1; i <= n; i++) {
for
}
}
Code: 16:15:00 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]]++;
}
int ans = 0;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < count[i]; sprinkle++) {
ans += abs(i - r);
ans %
}
}
}
Code: 16:15:19 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> count(n + 1, vector<int>());
for (int i = 0; i < n; i++) {
count[x[i]]++;
}
int ans = 0;
int r = 0;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < count[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
}
}
Code: 16:15:44 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<vector<int>> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[x[i]]++;
cols[y[i]]++;
}
int ans = 0;
int r = 0;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < count[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
}
}
Code: 16:16:12 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[x[i]]++;
cols[y[i]]++;
}
int ans = 0;
int r = 0;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}
Code: 16:16:22 UTC,
cpp,
autosave
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[x[i]]++;
cols[y[i]]++;
}
int ans = 0;
int r = 1, c = 1;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}
Code: 16:16:41 UTC,
cpp,
verify,
result: Failed
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[x[i]]++;
cols[y[i]]++;
}
int ans = 0;
int r = 1, c = 1;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}
Analysis
Compile error
func.cpp: In function 'int solution(std::vector<int>&, std::vector<int>&)':
func.cpp:16:14: error: 'x' was not declared in this scope
rows[x[i]]++;
^
func.cpp:17:14: error: 'y' was not declared in this scope
cols[y[i]]++;
^
Code: 16:16:51 UTC,
cpp,
verify,
result: Passed
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[X[i]]++;
cols[Y[i]]++;
}
int ans = 0;
int r = 1, c = 1;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}
Analysis
Code: 16:17:26 UTC,
cpp,
verify,
result: Passed
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[X[i]]++;
cols[Y[i]]++;
}
int ans = 0;
int r = 1, c = 1;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}
Analysis
Code: 16:17:29 UTC,
cpp,
final,
score:
100
// you can use includes, for example:
#include <vector>
#include <algorithm>
// you can write to stdout for debugging purposes, e.g.
// cout << "this is a debug message" << endl;
const int mod = (int) 1e9 + 7;
int solution(vector<int> &X, vector<int> &Y) {
// write your code in C++14 (g++ 6.2.0)
int n = X.size();
vector<int> rows(n + 1, 0), cols(n + 1, 0);
for (int i = 0; i < n; i++) {
rows[X[i]]++;
cols[Y[i]]++;
}
int ans = 0;
int r = 1, c = 1;
for (int i = 1; i <= n; i++) {
for (int sprinkle = 0; sprinkle < rows[i]; sprinkle++) {
ans += abs(i - r);
ans %= mod;
r++;
}
for (int sprinkle = 0; sprinkle < cols[i]; sprinkle++) {
ans += abs(i - c);
ans %= mod;
c++;
}
}
return ans;
}Analysis summary
The solution obtained perfect score.
Analysis
Detected time complexity:
O(N) or O(N*log(N))
expand all
Correctness tests
1.
0.001 s
OK
2.
0.001 s
OK
3.
0.001 s
OK
1.
0.001 s
OK
1.
0.001 s
OK
small_offset_from_diagonal
Test with one sprinkler in the corner and all the others very close to diagonal
Test with one sprinkler in the corner and all the others very close to diagonal
✔
OK
1.
0.001 s
OK
1.
0.001 s
OK
1.
0.001 s
OK
1.
0.001 s
OK
expand all
Correctness/performance tests
1.
0.001 s
OK
2.
0.001 s
OK
all_sprinklers_in_a_square_area
All sprinklers are gathered in left upper corner / right lower corner
All sprinklers are gathered in left upper corner / right lower corner
✔
OK
1.
0.008 s
OK
2.
0.012 s
OK
1.
0.016 s
OK