剑指offer - 二维数组中的查找

Posted 2021-03-23 darkchii

　　这题我总觉得 oj 有问题。。。就算真的复杂度很高，也不可能通不过一个样例吧。。。

　　第一眼没注意到每一列都从上到下递增，写出来的算法平均时间复杂度为 O(lgn * lgm)，最坏为O(nlgm)，思路就是对第一列做二分查找得到一个行区间，然后遍历行区间，对每一行做二分查找，但提交后有段错误（本地 MSVC 编译、运行没问题）。。。

　　然后又认真看一遍题之后，经过思考各种边界情况，优化了很多小地方的查找步数，时间复杂度肯定比第一个小很多，所以有点不敢相信居然超时？

class Solution {
public:
    bool Find(int target, std::vector<std::vector<int>> array) {
        if (array.empty()) return false;
        if (array[0][0] > target) return false;
        if (array[array.size() - 1][array[0].size() - 1] < target) return false;
        int start_col = 0,
            end_col = array.size() - 1,
            mid_col = (start_col + end_col) / 2;
        while (array[start_col][0] < target
            && target < array[end_col][0])
        {
            if (array[start_col][0] < target
                && target < array[mid_col][0])
                start_col = (start_col + mid_col) / 2,
                end_col = mid_col,
                mid_col = (start_col + end_col) / 2;
            else if (array[mid_col][0] < target
                && target < array[end_col][0])
                end_col = (mid_col + end_col) / 2,
                start_col = mid_col,
                mid_col = (start_col + end_col) / 2;
            else break;
        }

        for (int i = start_col; i <= end_col; i++)
        {
            int start_row = 0,
                end_row = array[0].size() - 1,
                mid_row = (start_row + end_row) / 2;
            if (array[i][start_row] == target) return true;
            if (array[i][end_row] == target) return true;
            while (start_row < end_row)
            {
                if (target == array[i][mid_row]) return true;
                else if (array[i][start_row] <= target
                    && target <= array[i][mid_row])
                    start_row = (start_row + mid_row) / 2,
                    end_row = mid_row,
                    mid_row = (start_row + end_row) / 2;
                else if (array[i][mid_row] <= target
                    && target <= array[i][end_row])
                    end_row = (mid_row + end_row) / 2,
                    start_row = mid_row,
                    mid_row = (start_row + end_row) / 2;
                else break;
            }
        }
        return false;
    } 

    bool Find2(int target, std::vector<std::vector<int>> array)
    {
        int row = 0, col = 0;
        int row_siz = array.size(), col_siz = array[0].size();
        while (row < row_siz && col < col_siz)
        {
            if (target == array[row][col]) return true;
            else if (col + 1 < col_siz && row + 1 < row_siz
                && target < array[row + 1][col + 1]
                && target > array[row + 1][col]
                && target > array[row][col + 1]) return false;
            else if (target < array[row][col]) {
                row--;
                if (row <= 0) return false;
            }
            
            if (col + 1 < col_siz
                && row + 1 < row_siz
                && target >= array[row + 1][col + 1]) col++, row++;
            else if (col + 1 < col_siz
                && target >= array[row][col + 1]) col++;
            else if (row + 1 < row_siz
                && target >= array[row + 1][col]) row++;
            else if (col + 1 < col_siz
                && target <= array[row][col + 1]) row--;
            else break;
        }
        return false;
    }
};