240 Search a 2D Matrix II

240. Search a 2D Matrix II​
1. 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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[
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  [1,   4,  7, 11, 15],
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  [2,   5,  8, 12, 19],
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  [3,   6,  9, 16, 22],
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  [10, 13, 14, 17, 24],
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  [18, 21, 23, 26, 30]
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]
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Given target=5, returntrue.
Given target=20, returnfalse.
2. Implementation
(1) Binary Search
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class Solution {
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    public boolean searchMatrix(int[][] matrix, int target) {
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        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
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            return false;
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        }
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​
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        int m = matrix.length, n = matrix[0].length;
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​
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        int rowStart = 0, rowEnd = m - 1, rowMid = 0;
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​
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        while (rowStart + 1 < rowEnd) {
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            rowMid = rowStart + (rowEnd - rowStart) / 2;
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​
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            if (matrix[rowMid][0] < target) {
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                rowStart = rowMid + 1;
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            }
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            else {
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                rowEnd = rowMid;
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            }
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        }
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​
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        rowStart = matrix[rowStart][0] >= target ? rowStart : rowEnd;
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​
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        for (int i = 0; i <= rowStart; i++) {
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            int colStart = 0, colEnd = n - 1, colMid = 0;
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​
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            while (colStart <= colEnd) {
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                colMid = colStart + (colEnd - colStart) / 2;
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​
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                if (matrix[i][colMid] == target) {
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                    return true;
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                }
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                else if (matrix[i][colMid] < target) {
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                    colStart = colMid + 1;
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                }
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                else {
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                    colEnd = colMid - 1;
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                }
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            }
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        }
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        return false;
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    }
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}
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3. Time & Space Complexity
Binary Search: 时间复杂度O(logm + mlogn), 空间复杂度O(1)

162 Find Peak Element

275 H-Index II

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Contents

240. Search a 2D Matrix II

1. Question

2. Implementation

3. Time & Space Complexity

240. Search a 2D Matrix II​

1. Question

2. Implementation

3. Time & Space Complexity

240. Search a 2D Matrix II