LeetCode 304. 二维区域和检索 - 矩阵不可变（DP）

1. 题目

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2. 解题

类似题目：LeetCode 308. 二维区域和检索 - 可变（前缀和）

dp[i][j]数组表示从左上角到i,j位置的所有和
$s u m [i + 1] [j + 1] = s u m [i + 1] [j] + s u m [i] [j + 1] + m a t r i x [i] [j] - s u m [i] [j]$

class NumMatrix {vector<vector<int>> sum;
public:NumMatrix(vector<vector<int>>& matrix) {if(matrix.empty())return;int r = matrix.size(), c = matrix[0].size(), i, j;sum = vector<vector<int>> (r+1, vector<int>(c+1, 0));for(i = 0; i < r; i++){for(j = 0; j < c; j++){sum[i+1][j+1] = sum[i+1][j]+sum[i][j+1]+matrix[i][j]-sum[i][j];}}}int sumRegion(int row1, int col1, int row2, int col2) {if(sum.empty())return 0;return sum[row2+1][col2+1] - sum[row1][col2+1] - sum[row2+1][col1] + sum[row1][col1];}
};

or
按行dp

class NumMatrix {vector<vector<int>> sumofrows;
public:NumMatrix(vector<vector<int>>& matrix) {if(matrix.empty())return;int r = matrix.size(), c = matrix[0].size(), i, j, sum = 0;vector<int> temp(c,0);for(i = 0; i < r; i++){sum = 0;for(j = 0; j < c; j++){sum += matrix[i][j];temp[j] = sum;}sumofrows.push_back(temp);}}int sumRegion(int row1, int col1, int row2, int col2) {if(sumofrows.empty())return 0;int i, j, sum = 0;if(col1 != 0)for(i = row1; i <= row2; i++){sum += sumofrows[i][col2]-sumofrows[i][col1-1];}elsefor(i = row1; i <= row2; i++){sum += sumofrows[i][col2];}return sum;}
};/*** Your NumMatrix object will be instantiated and called as such:* NumMatrix* obj = new NumMatrix(matrix);* int param_1 = obj->sumRegion(row1,col1,row2,col2);*/