Given a 2D matrix matrix, handle multiple queries of the following types:
Update the value of a cell in matrix.
Calculate the sum of the elements of matrix inside the rectangle defined by its upper left corner(row1, col1) and lower right corner(row2, col2).
Implement the NumMatrix class:
NumMatrix(int[][] matrix) Initializes the object with the integer matrix matrix.
void update(int row, int col, int val)Updates the value of matrix[row][col] to be val.
int sumRegion(int row1, int col1, int row2, int col2) Returns the sum of the elements of matrix inside the rectangle defined by its upper left corner(row1, col1) and lower right corner(row2, col2).
Example 1:
**Input**
["NumMatrix", "sumRegion", "update", "sumRegion"]
[[[[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], [3, 2, 2], [2, 1, 4, 3]]
**Output**
[null, 8, null, 10]
**Explanation**
NumMatrix numMatrix = new NumMatrix([[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.sumRegion(2, 1, 4, 3); // return 8 (i.e. sum of the left red rectangle)
numMatrix.update(3, 2, 2); // matrix changes from left image to right image
numMatrix.sumRegion(2, 1, 4, 3); // return 10 (i.e. sum of the right red rectangle)
Constraints:
m == matrix.length
n == matrix[i].length
1 <= m, n <= 200
-105 <= matrix[i][j] <= 105
0 <= row < m
0 <= col < n
-105 <= val <= 105
0 <= row1 <= row2 < m
0 <= col1 <= col2 < n
At most 104 calls will be made to sumRegion and update.
ac1: plain pre-sum
Notice:
matrix cannot use clone(), the array is Object, so it's shallow copy
be careful handling first row, out of boundary exception.
class NumMatrix {
int[][] matrix, sumMatrix;
public NumMatrix(int[][] matrix) {
if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return;
this.matrix = matrix;
int row = matrix.length;
int col = matrix[0].length;
this.sumMatrix = new int[row][col];
for(int c = 0; c < col; c++) {
sumMatrix[0][c] = matrix[0][c];
}
for (int r = 1; r < row; r++) {
for (int c = 0; c < col; c++) {
sumMatrix[r][c] = sumMatrix[r-1][c] + matrix[r][c];
}
}
}
public void update(int row, int col, int val) {
int diff = val - matrix[row][col];
matrix[row][col] = val;
for (int r = row; r < sumMatrix.length; r++) {
sumMatrix[r][col] += diff;
}
}
public int sumRegion(int row1, int col1, int row2, int col2) {
int sum = 0;
for (int c = col1; c <= col2; c++) {
if (row1 == 0) {
sum += sumMatrix[row2][c];
} else {
sum += sumMatrix[row2][c] - sumMatrix[row1-1][c];
}
}
return sum;
}
}
/**
* 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);
*/
ac2: Binary Indexed Tree
class NumMatrix {
int[][] matrix, bit;
public NumMatrix(int[][] matrix) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return;
this.matrix = matrix;
int row = matrix.length;
int col = matrix[0].length;
bit = new int[row+1][col+1];
for (int r = 0; r < row; r++) {
for (int c = 0; c < col; c++) {
int val = matrix[r][c];
matrix[r][c] = 0;
update(r, c, val);
}
}
}
public void update(int row, int col, int val) {
int diff = val - matrix[row][col];
matrix[row][col] = val;
for (int r = row+1; r < bit.length; r += r & -r) {
for (int c = col+1; c < bit[0].length; c += c & -c) {
bit[r][c] += diff;
}
}
}
public int sumRegion(int row1, int col1, int row2, int col2) {
return getSum(row2, col2) - getSum(row1-1, col2) - getSum(row2, col1-1) + getSum(row1-1, col1-1);
}
private int getSum(int row, int col) {
int sum = 0;
for (int r = row+1; r > 0; r -= r & -r) {
for (int c = col+1; c > 0; c -= c & -c) {
sum += bit[r][c];
}
}
return sum;
}
}
/**
* 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);
*/
