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LeetCode 304. Range Sum Query 2D - Immutable

2024-08-19 14:40:12   219人阅读

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).

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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
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12

 

Note:

  1. You may assume that the matrix does not change.
  2. There are many calls to sumRegion function.
  3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Solution: can be simplified to add one column and one row to dp(dp[row+1][column+1] )

 1 public class NumMatrix {
 2     private int[,] dp {get;set;}
 3     public NumMatrix(int[,] matrix) {
 4         int r = matrix.GetLength(0);
 5         int c = matrix.GetLength(1);
 6         if(r>0&&c>0)
 7         {
 8             dp = new int[r, c];
 9             for(int i=0; i<r;i++)
10             {
11                 for(int j=0;j<c; j++)
12                 {
13                     if(i==0&&j==0)
14                     {
15                         dp[0,0]=matrix[0,0];
16                     }
17                     else if(i==0)
18                     {
19                         dp[0,j]=dp[0,j-1]+matrix[0,j];
20                     }
21                     else if(j==0)
22                     {
23                         dp[i,0] = dp[i-1,0]+matrix[i,0];
24                     }
25                     else
26                     {
27                         dp[i,j] = dp[i-1,j]+dp[i, j-1]-dp[i-1,j-1]+matrix[i,j];
28                     }
29                 }
30             }
31         }
32         
33     }
34 
35     public int SumRegion(int row1, int col1, int row2, int col2) {
36         if(row1==0 && col1==0)
37         {
38             return dp[row2,col2];
39         }
40         else if(col1==0)
41         {
42             return dp[row2, col2]-dp[row1-1, col2];
43         }
44         else if(row1==0)
45         {
46             return dp[row2, col2]-dp[row2, col1-1];
47         }
48         else
49         {
50             return dp[row2, col2]-dp[row1-1, col2]-dp[row2, col1-1]+dp[row1-1, col1-1];
51         }
52     }
53 }

 

 

 

LeetCode 304. Range Sum Query 2D - Immutable


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