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

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

  1. // Search a 2D Matrix II
  2. // 时间复杂度O(m + n)，空间复杂度O(1)
  3. public class Solution {
  4.     public boolean searchMatrix(int[][] matrix, int target) {
  5.         if(matrix.length==0 || matrix[0].length==0) return false;
  7.         int i = 0;
  8.         int j = matrix[0].length-1;
  9.         while(i < matrix.length && j >= 0) {
  10.             final int x = matrix[i][j];
  11.             if(target == x) {
  12.                 return true;
  13.             } else if (x < target) {
  14.                 ++i;
  15.             } else {
  16.                 --j;
  17.             }
  18.         }
  19.         return false;
  20.     }
  21. }

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原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/search/search-a-2d-matrix-ii.html