[leetcode] Search a 2D Matrix

Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

For example,

Consider the following matrix:

```[
[1,   3,  5,  7],
[10, 11, 16, 20],
[23, 30, 34, 50]
]
```

Given target = `3`, return `true`.

10/3/2015 update

```//[start, end] inclusive, it may stop at 1 element left or 2,
class Solution {
public:
bool searchMatrix(vector<vector<int>>& matrix, int target) {
int start = 0;
int end = matrix.size() - 1;
while(end - start > 1){
int mid = (start + end) / 2;
if(matrix[mid][0] > target){
end = mid - 1;
}
else{
start = mid;
}
}
if(end - start == 1){
start = matrix[end][0] <= target?end:start;//BUG HERE, <= not <
}
int row = start;
start = 0;
end = matrix[0].size() - 1;
while(end >= start){
int mid = (start + end) / 2;
if(matrix[row][mid] == target){
return true;
}
else if(matrix[row][mid] > target){
end = mid - 1;
}
else{
start = mid + 1;
}
}
return false;

}
};```

```class Solution {
public:
//apply two binary search process
//first search the possible row
//second search the exact column
bool searchMatrix(vector<vector<int> > &matrix, int target) {
if(matrix.empty()) return false;
size_t height = matrix.size();
size_t width = matrix.front().size();
int row = findRow(matrix, 0, height, target);
if(row == -1) return false;
int column = findColumn(matrix[row], 0, width, target);
return column != -1;
}
int findRow(vector<vector<int>> &matrix, int start, int end, int target){
//base case
if(end - start == 1){
if(matrix[start][0] <= target){
return start;
}
else{
return -1;
}
}
int mid = (start + end) / 2;
if(matrix[mid][0] <= target){
return findRow(matrix, mid, end, target);
}
else{
return findRow(matrix, start, mid, target);
}
}
int findColumn(vector<int> &row, int start, int end, int target){
//base case
if(end - start == 1){
if(row[start] == target){
return start;
}
else{
return -1;
}
}
int mid = (start + end) / 2;
if(row[mid] <= target){
return findColumn(row, mid, end, target);
}
else{
return findColumn(row, start, mid, target);
}
}
};```

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