Leetcode算法Java全解答--74. 搜索二维矩阵.md

Posted by lizhao on 07-09,2019

Leetcode算法Java全解答--74. 搜索二维矩阵

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题目

编写一个高效的算法来判断 m x n 矩阵中,是否存在一个目标值。该矩阵具有如下特性:

每行中的整数从左到右按升序排列。 每行的第一个整数大于前一行的最后一个整数。 示例:

示例 1:

输入:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
输出: true
示例 2:

输入:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
输出: false

想法

  1. 先编历第一列的数据,找到那个比target大的数据,那么target在这一项的前一行(遍历1/10/23)

在关键行使用二分查找

2.陈独秀方法(better),把二维数组转换成一个一维数组,直接上二分查找

坐标转换:matrix[i][j] <=> matrix[a] 其中a=i*n+j, i=a/n, j=a%n;

结果

超过98%的测试案例

时间复杂度/空间复杂度:n/1

总结

代码

我的答案


public boolean searchMatrix(int[][] matrix, int target) {
    if (matrix.length == 0 || matrix[0].length == 0 || matrix[0][0] > target) {
        return false;
    }
    int muchTargetIndex = -1;
    for (int i = 0; i < matrix.length; i++) {
        if (matrix[i][0] == target) {
            return true;
        } else if (matrix[i][0] > target) {
            muchTargetIndex = i - 1;
            break;
        } else {
            muchTargetIndex++;
        }
    }

    int left = 0;
    int right = matrix[muchTargetIndex].length - 1;
    int center = 0;
    while (left <= right) {
        center = left + (right - left) / 2;
        if (matrix[muchTargetIndex][center] == target) {
            return true;
        } else if (matrix[muchTargetIndex][center] > target) {
            right = center - 1;
        } else {
            left = center + 1;
        }
    }

    return false;
}

大佬们的答案

public boolean better(int[][] matrix, int target) {
    if(matrix.length == 0) {
        return false;
    }
    int m = matrix.length;
    int n = matrix[0].length;
    int low = 0, high = m * n;
    while(low < high){
        int mid = (low + high) / 2;
        if(matrix[mid / n][mid % n] == target){
            return true;
        }else if(matrix[mid / n][mid % n] < target){
            low = mid + 1;
        }else{
            high = mid;
        }
    }
    return false;
}

测试用例


    @Test
    public void test074() {
        // 创建测试案例
        int[][] arr1 = new int[3][4];
        arr1[0][0] = 1;
        arr1[0][1] = 3;
        arr1[0][2] = 5;
        arr1[0][3] = 7;
        arr1[1][0] = 10;
        arr1[1][1] = 11;
        arr1[1][2] = 16;
        arr1[1][3] = 20;
        arr1[2][0] = 23;
        arr1[2][1] = 30;
        arr1[2][2] = 34;
        arr1[2][3] = 50;
        int target1 = 16;
        int target2 = 13;


        int[][] arr2 = new int[1][2];
        arr2[0][0] = 1;
        arr2[0][1] = 3;
        int target3 = 3;

        // 测试案例期望值
        boolean expResult1 = true;
        boolean expResult2 = false;
        boolean expResult3 = true;

        // 执行方法
        Solution074 solution074 = new Solution074();
        boolean result1 = solution074.searchMatrix(arr1, target1);
        boolean result2 = solution074.searchMatrix(arr1, target2);
        boolean result3 = solution074.searchMatrix(arr2, target3);

        // 判断期望值与实际值
        Assert.assertEquals(expResult1, result1);
        Assert.assertEquals(expResult2, result2);
        Assert.assertEquals(expResult3, result3);

    }

其他

代码托管码云地址:https://gitee.com/lizhaoandroid/LeetCodeAll.git

查看其他内容可以点击专栏或者我的博客哈:https://blog.csdn.net/cmqwan

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