leetcode 308. Range Sum Query 2D - Mutable

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

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

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
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

 

Note:

1. The matrix is only modifiable by the update function.
2. You may assume the number of calls to update and sumRegion function is distributed evenly.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

解題思路：

定義一個sum的二維向量 ， sum[i][j]爲 i 行[0 , j]的和 ；

update函數：

      更新矩陣matrix中的值 ， 然後更新相應行(row)的sum值 ， 從col開始更新 ；

      時間複雜度爲o(n) ;

sumRegion:

for(int i = row1 ; i <= row2 ; ++i)
{
   if(col1 == 0) res += sum[i][col2] ;
   else res += (sum[i][col2] - sum[i][col1 - 1]) ;
}

時間複雜度爲o(n) ;

class NumMatrix {
public:
    NumMatrix(vector<vector<int>>& matrix) : matrix(matrix)
    {
        rows = matrix.size() ;
        if(rows > 0) cols = matrix[0].size() ;
        if(rows && cols) sum = vector<vector<int>>(rows , vector<int>(cols , 0)) ;
        
        //初始化sum
        for(int i = 0 ; i < rows ; ++i)
        {
            for(int j = 0 ; j < cols ; ++j)
            {
                if(j == 0) 
                {
                    sum[i][0] = matrix[i][0] ;
                    continue ;
                }
                sum[i][j] = sum[i][j - 1] + matrix[i][j] ;
            }
        }
    }
    
    void update(int row, int col, int val) 
    {
        if(row < 0 || row >= rows || col < 0 || col >= cols) return ;
        matrix[row][col] = val ;
        
        for(int i = col ; i < cols ; ++i)
        {
            if(i == 0) sum[row][0] = matrix[row][0] ;
            else sum[row][i] = sum[row][i - 1] + matrix[row][i] ;
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) 
    {
        
        int res = 0 ;
        for(int i = row1 ; i <= row2 ; ++i)
        {
            if(col1 == 0) res += sum[i][col2] ;
            else res += (sum[i][col2] - sum[i][col1 - 1]) ;
        }
        
        return res ;
    }
    
private :
    
    vector<vector<int>> sum , matrix;
    int rows , cols ;
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * obj->update(row,col,val);
 * int param_2 = obj->sumRegion(row1,col1,row2,col2);
 */