#130 Heapify

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题目描述：

Given an integer array, heapify it into a min-heap array.

For a heap array A, A[0] is the root of heap, and for each A[i], A[i * 2 + 1] is the left child of A[i] and A[i * 2 + 2] is the right child of A[i].

Have you met this question in a real interview?

Yes

Clarification

What is heap?

Heap is a data structure, which usually have three methods: push, pop and top. where "push" add a new element the heap, "pop" delete the minimum/maximum element in the heap, "top" return the minimum/maximum element.

What is heapify?

Convert an unordered integer array into a heap array. If it is min-heap, for each element A[i], we will get A[i * 2 + 1] >= A[i] and A[i * 2 + 2] >= A[i].

What if there is a lot of solutions?

Return any of them.

Example

Given [3,2,1,4,5], return [1,2,3,4,5] or any legal heap array.

题目思路：

这题给了提示说是A满足：A[i * 2 + 1] >= A[i] and A[i * 2 + 2] >= A[i]。这样，我们就可以把A的前半部分的每个i遍历一遍，对于每个i来说，如果不满足这样的关系式，就在它的子heap中找出最小值，然后将i和最小值对应的坐标smallest互换。然后check i在它的新位置是不是满足heap的关系，不行再互换，一直把i换到它应该在的位置为止。

同时，我们要注意遍历i的时候要从A.size() / 2往前遍历，否则，后面的互换操作会打乱前面已经换好的那些。

Mycode（AC = 238ms）：

class Solution {public:    /**     * @param A: Given an integer array     * @return: void     */    void heapify(vector<int> &A) {        // write your code here        for (int i = A.size() / 2; i >= 0; i--) {            sift_down(A, i);        }    }        void sift_down(vector<int> &A, int k) {        int idx = k;                while (idx < A.size()) {            int smallest = idx;            // find the smallest number among its subheap            if (idx * 2 + 1 < A.size() && A[idx * 2 + 1] < A[smallest]) {                smallest = idx * 2 + 1;            }                        if (idx * 2 + 2 < A.size() && A[idx * 2 + 2] < A[smallest]) {                smallest = idx * 2 + 2;            }                        if (smallest != idx) {                swap(A, smallest, idx);            }            else {                break;            }                        idx = smallest;        }    }        void swap(vector<int> &A, int i, int j) {        int tmp = A[i];        A[i] = A[j];        A[j] = tmp;    }};

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