LeetCode [304] Range Sum Query 2D - Immutable

 304. Range Sum Query 2D - Immutable

Medium

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
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.

//C++: 
class NumMatrix {
    vector<vector<int>> mt;
public:
    NumMatrix(vector<vector<int>> &matrix) {
        int m = matrix.size();
        if(m==0) return;
        int n = matrix[0].size();
        if(n==0) return;
        mt.resize(m+1, vector<int>(n+1, 0));
        for(int i=1; i<=m; ++i){
            for(int j=1; j<=n; ++j){
                mt[i][j] += matrix[i-1][j-1] + mt[i-1][j] + mt[i][j-1] - mt[i-1][j-1];
            }
        }
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        return mt[row2+1][col2+1] - mt[row2+1][col1] - mt[row1][col2+1] + mt[row1][col1];
    }
};

//Java
class NumMatrix {
    int[][] extMatrix;
    public NumMatrix(int[][] matrix) {
        int m = matrix.length;
        if(m==0) return;
        int n = matrix[0].length;
        if(n==0) return;
        extMatrix = new int[m+1][n+1];
        for(int i=1; i<=m; ++i){
            for(int j=1; j<=n; ++j){
                extMatrix[i][j] = extMatrix[i-1][j]+extMatrix[i][j-1]+matrix[i-1][j-1]-extMatrix[i-1][j-1];
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        int r = extMatrix[row2+1][col2+1]-extMatrix[row2+1][col1]-extMatrix[row1][col2+1]+extMatrix[row1][col1];
        return r;
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * int param_1 = obj.sumRegion(row1,col1,row2,col2);
 */

//Java, BIT
class NumArray {
    int[] arr;
    int[] tree;
    int m;
    public NumArray(int[] nums) {
        m = nums.length;
        arr = new int[m];
        tree = new int[m+1];
        for(int i=0; i<m; ++i){
            update(i, nums[i]);
        }
    }
    
    //index for arr
    public void update(int k, int val) {
        int d = val-arr[k];
        arr[k] = val;
        for(int i=k+1; i<=m; i+=i&(-i)){
            tree[i]+=d;
        }
    }
    
    //index for tree
    public int sum(int k){
        int s = 0;
        for(int i=k; i>0; i-=i&(-i)){
            s += tree[i];
        }
        return s;
    }
    public int sumRange(int i, int j) {
        return sum(j+1)-sum(i);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */