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Range Sum Query 2D - Mutable in C++
Suppose we have a 2D matrix called matrix, we have to calculate the sum of the elements inside the rectangle defined by its upper left corner and lower right corner.
So, if the input is like
| 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 |
So will be methods to find sum, update value, if we call them like
sumRegion(2, 1, 4, 3)
update(3, 2, 2)
sumRegion(2, 1, 4, 3) ,
then the output will be 8 and 10, as the above rectangle (with the green color) is defined by (2,1) and (4, 3), which contains sum = 8.
To solve this, we will follow these steps −
Define one 2D array tree
Define one 2D array value
Define initializer that takes matrix as input
n := row size of matrix
m := (if not n is non-zero, then 0, otherwise col size of matrix)
value := Define one 2D array of size n x m
tree := Define one 2D array of order (n + 1) x (m + 1)
for initialize i := 0, when i − n, update (increase i by 1), do −
for initialize j := 0, when j < m, update (increase j by 1), do −
update(i, j, matrix[i, j])
Define a function update(), this will take row, col, val,
if n is same as 0 or m is same as 0, then −
return
delta := val - value[row, col]
value[row, col] := val
for initialize i := row + 1, when i <= n, update i := i + i & (-i), do −
for initialize j := col + 1, when j <= m, update j := j + j & (-j), do −
tree[i, j] := tree[i, j] + delta
Define a function sum(), this will take row, col,
ret := 0
for initialize i := row, when i > 0, update i := i - i & (-i), do −
for initialize j := col, when j > 0, update j := j - j & (-j), do −
ret := ret + tree[i, j]
return ret
Define a function sumRegion(), this will take row1, col1, row2, col2,
if m is same as 0 or n is same as 0, then −
return 0
(increase row2 by 1)
(increase row1 by 1)
(increase col1 by 1)
(increase col2 by 1)
return sum(row2, col2) + sum(row1 - 1, col1 - 1) - sum(row1 - 1, col2) - sum(row2, col1 - 1)
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
class NumMatrix {
public:
int n, m;
vector<vector<int>> tree;
vector<vector<int>> value;
NumMatrix(vector<vector<int>> &matrix) {
n = matrix.size();
m = !n ? 0 : matrix[0].size();
value = vector<vector<int>>(n, vector<int>(m));
tree = vector<vector<int>>(n + 1, vector<int>(m + 1));
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
update(i, j, matrix[i][j]);
}
}
}
void update(int row, int col, int val) {
if (n == 0 || m == 0)
return;
int delta = val - value[row][col];
value[row][col] = val;
for (int i = row + 1; i <= n; i += i & (-i)) {
for (int j = col + 1; j <= m; j += j & (-j)) {
tree[i][j] += delta;
}
}
}
int sum(int row, int col) {
int ret = 0;
for (int i = row; i > 0; i -= i & (-i)) {
for (int j = col; j > 0; j -= j & (-j)) {
ret += tree[i][j];
}
}
return ret;
}
int sumRegion(int row1, int col1, int row2, int col2) {
if (m == 0 || n == 0)
return 0;
row2++;
row1++;
col1++;
col2++;
return sum(row2, col2) + sum(row1 - 1, col1 - 1) - sum(row1 - 1, col2) - sum(row2, col1 - 1);
}
};
main() {
vector<vector<int>> v = {
{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 ob(v);
cout << (ob.sumRegion(2, 1, 4, 3)) << endl;
ob.update(3, 2, 2);
cout << (ob.sumRegion(2, 1, 4, 3)) << endl;
}Input
vector<vector<int>> v = {
{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 ob(v);
cout << (ob.sumRegion(2, 1, 4, 3)) << endl;
ob.update(3, 2, 2);
cout << (ob.sumRegion(2, 1, 4, 3)) << endl;Output
8 10
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