Search a 2D Matrix || Search a 2D Matrix II

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Search a 2D Matrix

Question

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:

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

Given target = 3, return true.

Analysis

Don’t treat it as a 2D matrix, just treat it as a sorted list

Code
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public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if(matrix==null||matrix.length==0) 
            return false;
        int row=matrix.length;
        int col=matrix[0].length;
        int left=0;
        int right=row*col-1;
        while(left<=right){
            int mid=(left+right)/2;
            int i=mid/col;
            int j=mid%col;
            if(target==matrix[i][j])    return true;
            else if(target>matrix[i][j])    left=mid+1;
            else right=mid-1;
        }
        return false;
    }
}

Search a 2D Matrix II

Question

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 in ascending from left to right.
  • Integers in each column are sorted in ascending from top to bottom.

For example,

Consider the following matrix:

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[
  [1,   4,  7, 11, 15],
  [2,   5,  8, 12, 19],
  [3,   6,  9, 16, 22],
  [10, 13, 14, 17, 24],
  [18, 21, 23, 26, 30]
]

Given target = 5, return true.

Given target = 20, return false.

Analysis

My concise O(m+n) Java solution

从右上角的元素开始扫描，若当前元素小于target，说明整行元素都小于target，向下移动col；若大于target，则向左移动row，无嵌套循环

Code
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public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if(matrix==null||matrix.length==0)
            return false;
        int row=0;
        int col=matrix[0].length-1;
        while(row<=matrix.length-1&&col>=0){
            if(matrix[row][col]==target)
                return true;
            else if(matrix[row][col]>target)
                col--;
            else 
                row++;
        }
        return false;
    }
}