LintCode 1138: Can Place Flowers (数学规律+双指针)

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分类专栏： algorithm-design 文章标签： LintCode

于 2018-12-27 16:17:01 首次发布

本文链接：https://blog.youkuaiyun.com/roufoo/article/details/85288576

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本文探讨了在遵循不相邻种植规则的情况下，在花坛中能否种植指定数量的新花的问题。通过分析不同场景下花坛的状态，提出了三种有效的算法解决方案：双指针法、逐个检查法和边界填充法，帮助理解并解决此类问题。

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Can Place Flowers
Suppose you have a long flowerbed in which some of the pots are planted and some are not. However, flowers cannot be planted in adjacent plots - they would compete for water and both would die.

Given a flowerbed (represented as an array containing 0 and 1, where 0 means empty and 1 means not empty), and a number n, return if n new flowers can be planted in it without violating the no-adjacent-flowers rule.

Example
Example 1:
Input: flowerbed = [1,0,0,0,1], n = 1
Output: True
Example 2:
Input: flowerbed = [1,0,0,0,1], n = 2
Output: False
Notice
1.The input array won’t violate no-adjacent-flowers rule.
2.The input array size is in the range of [1, 20000].
3.n is a non-negative integer which won’t exceed the input array size.

解法：
我的解法是分析1和0的规律。
101 gap = 1 -> 0 tree
1001 gap = 2 -> 0 tree
10001 gap = 3 -> 1 tree
100001 gap = 4 -> 1 tree
1000001 gap = 5 -> 2 trees
10000001 gap = 6 -> 2 trees
100000001 gap = 7 -> 3 trees
1000000001 gap = 8 - 3 trees
可知两个1中间可种的树数目为 (gap + 1) / 2 - 1。
而gap = p2 - p1 -1。
用双指针p1, p2遍历vector。p2和p1分别记录下新旧1的位置（p2前，p1后）。p2初始化为0，p1初始化为-1。

class Solution {
public:
    /**
     * @param flowerbed: an array
     * @param n: an Integer
     * @return: if n new flowers can be planted in it without violating the no-adjacent-flowers rule
     */
    bool canPlaceFlowers(vector<int> &flowerbed, int n) {
        int len = flowerbed.size();
        if ((len == 0) || (len < n)) return false;
        
        int p1 = -1, p2 = 0;  //p2 is ahead of p1
        while (p2 < len) {
            while(flowerbed[p2] == 0) p2++;
            if (p2 > 0) {
                int gap = p2 - p1 - 1; //gap is the available slots between 1s, such as 1---1
                n -= (gap + 1) / 2 - 1;
                p1 = p2;
            }
            p2++;
        }
        if (n == 0) return true;
        else return false;
    }
};

解法2：九章的解法，不用双指针，直接遍历，但逻辑较复杂。

public class Solution {
    public boolean canPlaceFlowers(int[] flowerbed, int n) {
        int count = 0;
        for (int i = 0; i < flowerbed.length; i++) {
            if (flowerbed[i] == 0 && (i == 0 || flowerbed[i - 1] == 0)
            && (i == flowerbed.length - 1 || flowerbed[i + 1] == 0)) {
                flowerbed[i] = 1;
                count++;
            }
            if (count >= n) {
                return true;
            }
        }
        return false;
    }
}

解法2：
在原vector的前后各加一个0，就可以利用公式flowerCount += (zeroCount - 1) >> 1;

class Solution {
public:
    bool canPlaceFlowers(vector<int>& flowerbed, int n) {
        flowerbed.insert(flowerbed.begin(), 0);
        flowerbed.push_back(0);
        int bedSize = flowerbed.size();
        int zeroCount = 0, flowerCount = 0;
        for (int i = 0; i < bedSize; i++) {
            if (flowerbed[i] == 1) {
                flowerCount += (zeroCount - 1) >> 1;
                zeroCount = 0;
            } else {
                zeroCount++;
           }
        }
        flowerCount += (zeroCount - 1) >> 1;
        return flowerCount >= n;
    }
};