304. Range Sum Query 2D - Immutable(动态规划)
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:
- You may assume that the matrix does not change.
- There are many calls to sumRegion function.
- You may assume that row1 ≤ row2 and col1 ≤ col2.
Sum(ABCD)=Sum(OD)−Sum(OB)−Sum(OC)+Sum(OA)
ps: 注意dp的递推公式
class NumMatrix {
public:
vector<vector<int>> dp; NumMatrix(vector<vector<int>> matrix) {
int n =matrix.size();
int m = n==?:matrix[].size(); dp = vector<vector<int>>(n+,vector<int>(m+,));
for(int i = ;i<n;i++)
for(int j = ;j<m;j++){
dp[i+][j+] = dp[i][j+]+dp[i+][j]-dp[i][j]+matrix[i][j];
}
} int sumRegion(int rows1, int cols1, int rows2, int cols2) {
return dp[rows2+][cols2+] - dp[rows1][cols2+] - dp[rows2+][cols1] +dp[rows1][cols1];
}
}; /**
* Your NumMatrix object will be instantiated and called as such:
* NumMatrix obj = new NumMatrix(matrix);
* int param_1 = obj.sumRegion(row1,col1,row2,col2);
*/
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