LeetCode 304. Range Sum Query 2D - Immutable

最新推荐文章于 2025-02-03 15:37:10 发布

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最新推荐文章于 2025-02-03 15:37:10 发布

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本文介绍了一种预先计算二维矩阵的方法，使得后续对该矩阵任意指定区域的元素求和操作能在常数时间内完成。通过实现一个名为NumMatrix的类，我们可以高效地获取由其左上角(row1, col1)和右下角(row2, col2)定义的矩形内所有元素之和。

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#include <vector>
#include <iostream>
using namespace std;

/*
  Given a 2D matrix, find the sum of the elements inside the rectangle defined by
  its upper left corner (row1, col1) and lower right corner(row2, col2).
  For example:
  Given 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]]

  sumRegion(2, 1, 4, 3) -> 8
  sumRegion(1, 1, 2, 2) -> 11
  sumRegion(1, 2, 2, 4) -> 12
*/
// to preCompute the matrix, the time complexity for queries can be lowered down to O(1).
class NumMatrix {
private:
  vector< vector<int> > sumMatrix;
private:
  void preComputeMatrix(vector< vector<int> >& matrix) {
    int m = matrix.size(), n = matrix[0].size();
    for(int k = 1; k < m; ++k) {
      matrix[k][0] += matrix[k-1][0];
    }
    for(int k = 1; k < n; ++k) {
      matrix[0][k] += matrix[0][k-1];
    }
    for(int i = 1; i < m; ++i) {
      for(int j = 1; j < n; ++j) {
        matrix[i][j] += matrix[i-1][j] + matrix[i][j-1] - matrix[i-1][j-1];
      }
    }
  }
public:
  NumMatrix(vector< vector<int> >& matrix) {
    sumMatrix = matrix;
    preComputeMatrix(sumMatrix);
  }
  int sumRegion(int row1, int col1, int row2, int col2) {
    return sumMatrix[row2][col2] - sumMatrix[row1 - 1][col2] - sumMatrix[row2][col1 - 1] + sumMatrix[row1-1][col1-1];
  }
};

int main(void) {
  vector< vector<int> > 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}};
  NumMatrix sumMatrix(matrix);
  int tmp = sumMatrix.sumRegion(2, 1, 4, 3);
  int tmp_2 = sumMatrix.sumRegion(1, 1, 2, 2);
  int tmp_3 = sumMatrix.sumRegion(1, 2, 2, 4);
  cout << tmp << endl;
  cout << tmp_2 << endl;
  cout << tmp_3 << endl;
}