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Leetcode Range Sum Query 2D - Immutable

2015-12-15 11:30 381 查看
Leetcode Range Sum Query 2D - Immutable, 本题主要利用每个区域都可以用为0,0有原点的四个区域,通过加减而快速算出,本题是动态规划的一个经典使用,在图像处理方面使用得相当多,相关算法如下:

using namespace std;
class NumMatrix {
public:
vector<vector<int > > recoder;
NumMatrix(vector<vector<int> > &matrix) {
int len_row = matrix.size();
int len_col = 0;
if (len_row > 0) {
len_col = matrix[0].size();
}
int sum1 = 0;
vector<int> sum2(len_col, 0);
recoder = vector<vector<int> >(len_row + 1, vector<int>(len_col + 1, 0));
// we calculate all matrix[0...row][0...col]
for (int i = 1; i <= len_row; i ++) {
sum1 = 0;
for (int col = 0; col < len_col; col ++) {
sum2[col] += matrix[i - 1][col];
}
for (int j = 1; j <= len_col; j ++) {
sum1 += matrix[i - 1][j - 1];
recoder[i][j] = recoder[i - 1][j - 1] + sum1 + sum2[j - 1] - \
matrix[i - 1][j - 1];
}
}
}

int sumRegion(int row1, int col1, int row2, int col2) {
// Apply the formula given above.
int re = recoder[row2 + 1][col2 + 1];
re -= recoder[row2 + 1][col1];
re -= recoder[row1][col2 + 1];
re += recoder[row1][col1];
return re;
}
};

// Sample input: ./a.out row col matrix_element_split_by_space calculate_-
// regions_four_element_in_a_groupt...
int main(int argc, char* argv[]) {
int row = atoi(argv[1]);
int col = atoi(argv[2]);
vector<vector<int> > matrix(row, vector<int>(col, 0));
cout<<"matrix: "<<endl;
for (int i = 0; i < row; i ++) {
for (int j = 0; j < col; j ++) {
matrix[i][j] = atoi(argv[row * i + j + 3]);
cout<<matrix[i][j]<<" ";
}
cout<<endl;
}
cout<<endl;
NumMatrix m(matrix);
cout<<"results: "<<endl;
for (int i = row * col + 3; i < argc; i += 4) {
int row1 = atoi(argv[i]);
int col1 = atoi(argv[i + 1]);
int row2 = atoi(argv[i + 2]);
int col2 = atoi(argv[i + 3]);
int re = m.sumRegion(row1, col1, row2, col2);
cout<<"sumRegion("<<row1<<", "<<col1<<", "<<row2<<", "<<col2<<"): "<<re<<endl;
}
return 0;
}


测试用例:

input:
./a.out 5 5 3 0 1 4 2 5 6 3 2 1 1 2 0 1 5 4 1 0 1 7 1 0 3 0 5 2 1 4 3 1 1 2 2 1 2 2 4
output:
matrix:
3 0 1 4 2
5 6 3 2 1
1 2 0 1 5
4 1 0 1 7
1 0 3 0 5

results:
sumRegion(2, 1, 4, 3): 8
sumRegion(1, 1, 2, 2): 11
sumRegion(1, 2, 2, 4): 12
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