一、题目说明
题目240. Search a 2D Matrix II，从一个m*n的二维矩阵查找一个整数，每一行从左到右递增，每一列从上到下递增。
二、我的解答
先计算矩阵中点matrix[row_mid][col_mid]，然后将矩阵分成4个区间：
class Solution{
public:
bool dfs(vector<vector<int> >& matrix,int target,int start_x, int end_x, int start_y, int end_y){
if(start_x > end_x || start_y > end_y)
return false;
if(start_x == end_x && start_y == end_y)
return matrix[start_x][start_y] == target;
if(target < matrix[start_x][start_y] || target > matrix[end_x][end_y])
return false;
int mid_x = start_x + (end_x - start_x) / 2;
int mid_y = start_y + (end_y - start_y) / 2;
if(matrix[mid_x][mid_y] == target) {
return true;
} else if(matrix[mid_x][mid_y] > target) {
//在1,2,3区域找
return dfs(matrix, target, start_x, mid_x - 1, start_y, mid_y - 1)
|| dfs(matrix, target, mid_x, end_x, start_y, mid_y - 1)
|| dfs(matrix, target, start_x, mid_x - 1, mid_y, end_y);
} else {
//在2,3,4区域找
return dfs(matrix, target, mid_x + 1, end_x, mid_y + 1, end_y)
|| dfs(matrix, target, start_x, mid_x, mid_y + 1, end_y)
|| dfs(matrix, target, start_x + 1, end_x, start_y, mid_y);
}
}
bool searchMatrix(vector<vector<int> >& matrix,int target){
if(matrix.size()<1){
return false;
}
row = matrix.size();
col = matrix[0].size();
bool result = dfs(matrix,target,0,row-1,0,col-1);
if(result) return true;
else return false;
}
private:
int row,col;
};
性能如下：
Runtime: 148 ms, faster than 24.09% of C++ online submissions for Search a 2D Matrix II.
Memory Usage: 13.1 MB, less than 6.67% of C++ online submissions for Search a 2D Matrix II.
三、优化措施
从左下角（右上角也行）出发，比较绝妙的解答：
class Solution{
public:
//从左下角（或者 右上角）出发，判断
bool searchMatrix(vector<vector<int> >& matrix,int target){
if(matrix.size()<1){
return false;
}
row = matrix.size();
col = matrix[0].size();
int curRow = row-1;
int curCol = 0;
while(curRow<row && curCol<col){
if(matrix[curRow][curCol] == target) return true;
else if(matrix[curRow][curCol] < target){
curCol ++;
}else if(matrix[curRow][curCol] > target){
curRow--;
}
}
return false;
}
private:
int row,col;
};
性能如下：
Runtime: 72 ms, faster than 61.20% of C++ online submissions for Search a 2D Matrix II.
Memory Usage: 13 MB, less than 55.56% of C++ online submissions for Search a 2D Matrix II.