[leetcode] Search a 2D Matrix II

Cabinathor

于 2015-07-28 20:45:32 发布

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本文链接：https://blog.youkuaiyun.com/lmxmimihuhu/article/details/47111061

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本文介绍了一种高效的算法，用于在一个m x n的矩阵中搜索特定值。该矩阵每一行及每一列都按升序排列。文章提供了一个具体的实现示例，并解释了从右上角开始搜索的策略。

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From : https://leetcode.com/problems/search-a-2d-matrix-ii/

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.

思路：从右上角或者左下角开始，偏大向左上走，偏小往右下走。证明方法是假设法。

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