Round C APAC Test 2017 Problem B. Monster Path
2016-10-04 16:13
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Problem B. Safe Squares
Codejamon trainers are actively looking for monsters, but if you are not a trainer, these monsters could be really dangerous for you. You might want to find safe places that do not have any monsters!Consider our world as a grid, and some of the cells have been occupied by monsters. We define a safe square as
a grid-aligned D × D square
of grid cells (with D ≥ 1) that does not contain any monsters. Your task is to find out how many safe squares (of any size)
we have in the entire world.
Input
The first line of the input gives the number of test cases, T. T testcases follow. Each test case starts with a line with three integers, R, C,
and K. The grid has R rows
and Ccolumns, and contains K monsters. K more
lines follow; each contains two integers Ri andCi,
indicating the row and column that the i-th monster is in. (Rows are numbered from top to bottom, starting from 0; columns are numbered from left to right, starting from 0.)
Output
For each test case, output one line containingCase #x: y,
where
xis the test case number (starting from 1) and
yis
the the total number of safe zones for this test case.
Limits
1 ≤ T ≤ 20.(Ri, Ci) ≠ (Rj, Cj) for i ≠ j. (No two monsters are in the same grid cell.)
0 ≤ Ri < R, i from 1 to K
0 ≤ Ci < C, i from 1 to K
Small dataset
1 ≤ R ≤ 10.1 ≤ C ≤ 10.
0 ≤ K ≤ 10.
Large dataset
1 ≤ R ≤ 3000.1 ≤ C ≤ 3000.
0 ≤ K ≤ 3000.
Sample
Input | Output |
2 3 3 1 2 1 4 11 12 0 1 0 3 0 4 0 10 1 0 1 9 2 0 2 4 2 9 2 10 3 4 3 10 | Case #1: 10 Case #2: 51 |
0 0 0 0 0 0 0 1 0
Here, 0 represents a cell with no monster, and 1 represents a cell with a monster. It has 10 safe squares: 8 1x1 and 2 2x2.
The grid of sample case #2 is:
0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1
Note that sample case #2 will only appear in the Large dataset. It has 51 safe squares: 32 1x1, 13 2x2, 5 3x3, and 1 4x4.
S[i][j] represents size of the square sub-matrix with all 1s including M[i][j] where M[i][j] is the rightmost and bottommost entry in sub-matrix.
Solution
#include <iostream> #include <cstdio> #include <cstring> using namespace std; typedef long long ll; const int MAXN = 3000; bool grid[MAXN][MAXN]; ll dp[MAXN][MAXN]; ll get_res(int R, int C) { ll res = 0; for (int i = 0; i < R; i++) { dp[i][0] = !grid[i][0]; res += dp[i][0]; } for (int j = 1; j < C; j++) { dp[0][j] = !grid[0][j]; res += dp[0][j]; } for (int i = 1; i < R; i++) for (int j = 1; j < C; j++) { if (!grid[i][j]) { dp[i][j] = min(dp[i-1][j], min(dp[i][j-1], dp[i-1][j-1])) + 1; res += dp[i][j]; } else dp[i][j] = 0; } return res; } int main(int argc, char* argv[]) { #ifndef TEST if (argc != 2) { cout << "Invalid input" << endl; return 1; } string input = argv[1]; string output = input.substr(0, input.length() - 2) + "out"; freopen(input.c_str(), "r", stdin); freopen(output.c_str(), "w", stdout); #endif int T, R, C, K, Ri, Ci; cin >> T; for (int i = 1; i <= T; i++) { memset(grid, 0, MAXN * MAXN * sizeof(bool)); memset(dp, 0, MAXN * MAXN * sizeof(ll)); cin >> R >> C >> K; for (int j = 0; j < K; j++) { cin >> Ri >> Ci; grid[Ri][Ci] = 1; } ll res = get_res(R, C); cout << "Case #" << i << ": " << res << endl; } fclose(stdin); fclose(stdout); return 0; }
Note
dp[i][j] represents width of the maximum square sub-matrix with all 0s including grid[i][j] where grid[i][j] is the rightmost and bottommost entry in sub-matrix.Reference
https://code.google.com/codejam/contest/6274486/dashboard#s=p1http://codeforces.com/blog/entry/47185
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