岛屿的最大面积-蒲公英云

一、前言

问题来源LeetCode

问题链接：https://leetcode-cn.com/explore/interview/card/bytedance/243/array-and-sorting/1034/

二、题目

给定一个包含了一些 0 和 1 的非空二维数组 grid 。一个岛屿是由一些相邻的 1 (代表土地) 构成的组合，这里的「相邻」要求两个 1 必须在水平或者竖直方向上相邻。你可以假设 grid 的四个边缘都被 0（代表水）包围着。找到给定的二维数组中最大的岛屿面积。(如果没有岛屿，则返回面积为 0 。)

示例 1:

[[0,0,1,0,0,0,0,1,0,0,0,0,0],
 [0,0,0,0,0,0,0,1,1,1,0,0,0],
 [0,1,1,0,1,0,0,0,0,0,0,0,0],
 [0,1,0,0,1,1,0,0,1,0,1,0,0],
 [0,1,0,0,1,1,0,0,1,1,1,0,0],
 [0,0,0,0,0,0,0,0,0,0,1,0,0],
 [0,0,0,0,0,0,0,1,1,1,0,0,0],
 [0,0,0,0,0,0,0,1,1,0,0,0,0]]

对于上面这个给定矩阵应返回 6。注意答案不应该是 11 ，因为岛屿只能包含水平或垂直的四个方向的 1 。

示例 2:

[[0,0,0,0,0,0,0,0]]

对于上面这个给定的矩阵, 返回 0。

注意: 给定的矩阵grid 的长度和宽度都不超过 50。

三、思路

用回溯法，简单直接

四、编码实现

//==========================================================================
/**
* @file    : 02_MaxAreaOfIsland.h
* @blogs   : https://blog.csdn.net/nie2314550441/article/details/106863629
* @author  : niebingyu
* @title   : 岛屿的最大面积
* @purpose : 给定一个包含了一些 0 和 1 的非空二维数组 grid 。
* 一个 岛屿 是由一些相邻的 1 (代表土地) 构成的组合，这里的「相邻」要求两个 1 必须在水平或者竖直方向上相邻。你可以假设 grid 的四个边缘都被 0（代表水）包围着。
* 找到给定的二维数组中最大的岛屿面积。(如果没有岛屿，则返回面积为 0 。)
*
* 示例 1:
* [[0,0,1,0,0,0,0,1,0,0,0,0,0],
*  [0,0,0,0,0,0,0,1,1,1,0,0,0],
*  [0,1,1,0,1,0,0,0,0,0,0,0,0],
*  [0,1,0,0,1,1,0,0,1,0,1,0,0],
*  [0,1,0,0,1,1,0,0,1,1,1,0,0],
*  [0,0,0,0,0,0,0,0,0,0,1,0,0],
*  [0,0,0,0,0,0,0,1,1,1,0,0,0],
*  [0,0,0,0,0,0,0,1,1,0,0,0,0]]
* 对于上面这个给定矩阵应返回 6。注意答案不应该是 11 ，因为岛屿只能包含水平或垂直的四个方向的 1 。
*
* 示例 2:
* [[0,0,0,0,0,0,0,0]]
* 对于上面这个给定的矩阵, 返回 0。
* 注意: 给定的矩阵grid 的长度和宽度都不超过 50。
*
* 来源：力扣（LeetCode）
* 链接：https://leetcode-cn.com/explore/interview/card/bytedance/243/array-and-sorting/1034/
*/
//==========================================================================
#pragma once
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
#define NAMESPACE_MAXAREAOFISLAND namespace NAME_MAXAREAOFISLAND {
#define NAMESPACE_MAXAREAOFISLANDEND }
NAMESPACE_MAXAREAOFISLAND
class Solution
{
public:
    int maxAreaOfIsland(vector<vector<int>>& grid)
    {
        if (grid.empty() || grid[0].empty())
            return 0;
        // 这里按照题意给定的是矩形，不做校验
        int maxRet = 0;
        for (int i = 0; i < grid.size(); ++i)
        {
            for (int j = 0; j< grid[0].size(); ++j)
            {
                if (grid[i][j] == 1)
                {
                    maxRet = max(maxRet, maxAreaOfIsland(grid, i, j));
                }
            }
        }
        return maxRet;
    }
private:
    int maxAreaOfIsland(vector<vector<int>>& grid, int i, int j)
    {
        if (i < 0 || i >= grid.size() || j < 0 || j >= grid[0].size() || grid[i][j] != 1)
            return 0;
        // 这里按照题意给定的是矩形，不做校验
        int ret = 1;
        grid[i][j] = 2;     //2 标记为已经访问
        static int dir[4][2] = { {0,1}, {1,0}, {0,-1}, {-1,0} };
        for (int k = 0; k < 4; ++k)
        {
            int ix = i + dir[k][0];
            int jx = j + dir[k][1];
            if (ix >= 0 && ix < grid.size() && jx >= 0 && jx < grid[0].size())
            {
                ret += maxAreaOfIsland(grid, ix, jx);
            }
        }
        return ret;
    }
};
//
// 测试 用例 START
void test(const char* testName, vector<vector<int>>& grid, int expect)
{
    Solution S;
    int result = S.maxAreaOfIsland(grid);
    // 粗略校验
    if (result == expect)
        cout << testName << ", solution passed." << endl;
    else
        cout << testName << ", solution failed. result:" << result << " ,expect:" << expect << endl;
}
// 测试用例
void Test1()
{
    vector<vector<int>> grid =
    {
        {0,0,0,0,0,0,0,0}
    };
    int expect = 0;
    test("Test1()", grid, expect);
}
void Test2()
{
    vector<vector<int>> grid =
    {
        {0,1},
        {1,1},
    };
    int expect = 3;
    test("Test2()", grid, expect);
}
void Test3()
{
    vector<vector<int>> grid =
    {
        {1,1,1},
        {1,0,1},
    };
    int expect = 5;
    test("Test3()", grid, expect);
}
void Test4()
{
    vector<vector<int>> grid =
    {
        {0,0,0},
        {0,1,1},
    };
    int expect = 2;
    test("Test4()", grid, expect);
}
void Test5()
{
    vector<vector<int>> grid =
    {
        {0,0,1,0,0,0,0,1,0,0,0,0,0},
        {0,0,0,0,0,0,0,1,1,1,0,0,0},
        {0,1,1,0,1,0,0,0,0,0,0,0,0},
        {0,1,0,0,1,1,0,0,1,0,1,0,0},
        {0,1,0,0,1,1,0,0,1,1,1,0,0},
        {0,0,0,0,0,0,0,0,0,0,1,0,0},
        {0,0,0,0,0,0,0,1,1,1,0,0,0},
        {0,0,0,0,0,0,0,1,1,0,0,0,0}
    };
    int expect = 6;
    test("Test5()", grid, expect);
}
NAMESPACE_MAXAREAOFISLANDEND
// 测试 用例 END
//
void MaxAreaOfIsland_Test()
{
    NAME_MAXAREAOFISLAND::Test1();
    NAME_MAXAREAOFISLAND::Test2();
    NAME_MAXAREAOFISLAND::Test3();
    NAME_MAXAREAOFISLAND::Test4();
    NAME_MAXAREAOFISLAND::Test5();
}