74. Search a 2D Matrix(剑指offer 1)

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.

Example 1:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true

Example 2:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false

class Solution:
    def searchMatrix(self, num: List[List[int]], target: int) -> bool:
        n1 = len(num)
        n2 = len(num[0])
        lo = 0
        hi = n1*n2 -1 
        while lo <=hi:
            mid = lo +(hi-lo)//2
            i = mid //n2
            j = mid % n2
            if num[i][j] < target:
                lo = mid + 1
            elif target  < num[i][j]:
                hi = mid - 1
            else:
                return True
        return False
                

 

 

class Solution:
    def searchMatrix(self, matrix: List[List[int]], target: int) -> bool:
        n1 = len(matrix)
        n2 = len(matrix[0])

        l = 0
        r = n1*n2 - 1
       
        while l <=r :
            mid = l + (r-l)//2
            cur = matrix[mid//n2][mid%n2]
            if cur == target:
                return True
            elif cur > target:
                r = mid - 1
            else:
                l = mid + 1
        return False

 

 

 

 

 

class Solution {
public:
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        // 先根据最后一列二分查找，确定 target 在哪一行。
        int n = matrix.size(); //3
        int m = matrix[0].size();//4
        int low = 0;
        int high = n -1 ;
        while(low < high) {
            int mid = low + (high - low) / 2;
            if (matrix[mid][m-1] < target) {
                low = mid + 1;
            } else if(matrix[mid][m-1] > target) {
                high = mid ;
            } else {
                return true;
            }
        }
        // low is the target 行
        int wanted_row = low;
        low = 0;
        high = m - 1 ;

        while(low < high) {
            int mid = low + (high - low) /2;
            if(matrix[wanted_row][mid] < target) {
                low = mid + 1;
            } else if (matrix[wanted_row][mid] > target) {
                high = mid ;
            } else {
                return true;
            }
        }
        return matrix[wanted_row][low] == target;
    }
};

 

　

class Solution {
    public boolean searchMatrix(int[][] a, int target) {
        if (a.length<1)
            return false;
        int i = 0;
        int j = a[0].length-1;
        while(i<a.length && j>=0){
            if(target==a[i][j])
                return true;
            else if(target>a[i][j])
                i++;
            else
                j--;
        }
        return false;
    }
}