search/search-a-2d-matrix-ii

Search a 2D Matrix II

描述

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:

[
  [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.

分析

从右上角开始, 比较target 和 matrix[i][j]的值。如果小于target, 则该行不可能有此数, 所以i++; 如果大于target, 则该列不可能有此数, 所以j--。遇到边界则表明该矩阵不含target.

代码

// Search a 2D Matrix II
// 时间复杂度O(m + n)，空间复杂度O(1)
public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if(matrix.length==0 || matrix[0].length==0) return false;

        int i = 0;
        int j = matrix[0].length-1;
        while(i < matrix.length && j >= 0) {
            final int x = matrix[i][j];
            if(target == x) {
                return true;
            } else if (x < target) {
                ++i;
            } else {
                --j;
            }
        }
        return false;
    }
}

相关题目

• Search a 2D Matrix