104 lines
4.1 KiB
C++
104 lines
4.1 KiB
C++
// Source : https://leetcode.com/problems/range-sum-query-2d-immutable/
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// Author : Hao Chen
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// Date : 2015-11-14
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/***************************************************************************************
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*
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* Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined
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* by its upper left corner (row1, col1) and lower right corner (row2, col2).
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*
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* The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and
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* (row2, col2) = (4, 3), which contains sum = 8.
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*
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* Example:
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*
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* Given matrix = [
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* [3, 0, 1, 4, 2],
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* [5, 6, 3, 2, 1],
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* [1, 2, 0, 1, 5],
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* [4, 1, 0, 1, 7],
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* [1, 0, 3, 0, 5]
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* ]
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*
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* sumRegion(2, 1, 4, 3) -> 8
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* sumRegion(1, 1, 2, 2) -> 11
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* sumRegion(1, 2, 2, 4) -> 12
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*
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* Note:
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*
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* You may assume that the matrix does not change.
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* There are many calls to sumRegion function.
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* You may assume that row1 ≤ row2 and col1 ≤ col2.
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*
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***************************************************************************************/
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/*
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*
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* Construct a 2D array `sums[row+1][col+1]`
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*
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* (**notice**: we add additional blank row `sums[0][col+1]={0}` and blank column `sums[row+1][0]={0}`
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* to remove the edge case checking), so, we can have the following definition
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*
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* `sums[i+1][j+1]` represents the sum of area from `matrix[0][0]` to `matrix[i][j]`
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*
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* To calculate sums, the ideas as below
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*
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* +-----+-+-------+ +--------+-----+ +-----+---------+ +-----+--------+
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* | | | | | | | | | | | | |
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* | | | | | | | | | | | | |
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* +-----+-+ | +--------+ | | | | +-----+ |
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* | | | | = | | + | | | - | |
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* +-----+-+ | | | +-----+ | | |
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* | | | | | | | |
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* | | | | | | | |
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* +---------------+ +--------------+ +---------------+ +--------------+
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*
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* sums[i][j] = sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1] +
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*
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* matrix[i-1][j-1]
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*
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* So, we use the same idea to find the specific area's sum.
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*
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*
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*
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* +---------------+ +--------------+ +---------------+ +--------------+ +--------------+
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* | | | | | | | | | | | | | |
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* | (r1,c1) | | | | | | | | | | | | |
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* | +------+ | | | | | | | +---------+ | +---+ |
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* | | | | = | | | - | | | - | (r1,c2) | + | (r1,c1) |
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* | | | | | | | | | | | | | |
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* | +------+ | +---------+ | +---+ | | | | |
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* | (r2,c2)| | (r2,c2)| | (r2,c1) | | | | |
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* +---------------+ +--------------+ +---------------+ +--------------+ +--------------+
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*
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*
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*/
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class NumMatrix {
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private:
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int row, col;
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vector<vector<int>> sums;
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public:
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NumMatrix(vector<vector<int>> &matrix) {
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row = matrix.size();
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col = row>0 ? matrix[0].size() : 0;
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sums = vector<vector<int>>(row+1, vector<int>(col+1, 0));
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for(int i=1; i<=row; i++) {
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for(int j=1; j<=col; j++) {
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sums[i][j] = sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1] + matrix[i-1][j-1];
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}
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}
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}
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int sumRegion(int row1, int col1, int row2, int col2) {
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return sums[row2+1][col2+1] - sums[row2+1][col1] - sums[row1][col2+1] + sums[row1][col1];
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}
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};
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// Your NumMatrix object will be instantiated and called as such:
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// NumMatrix numMatrix(matrix);
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// numMatrix.sumRegion(0, 1, 2, 3);
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// numMatrix.sumRegion(1, 2, 3, 4);
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