Codility-Dominator

Task description

A zero-indexed array A consisting of N integers is given. The dominatorof array A is the value that occurs in more than half of the elements of A.

For example, consider array A such that

A[0] = 3    A[1] = 4    A[2] =  3A[3] = 2    A[4] = 3    A[5] = -1A[6] = 3    A[7] = 3

The dominator of A is 3 because it occurs in 5 out of 8 elements of A (namely in those with indices 0, 2, 4, 6 and 7) and 5 is more than a half of 8.

Write a function

int solution(const vector<int> &A);

that, given a zero-indexed array A consisting of N integers, returns index of any element of array A in which the dominator of A occurs. The function should return −1 if array A does not have a dominator.

Assume that:

• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].

For example, given array A such that

A[0] = 3    A[1] = 4    A[2] =  3A[3] = 2    A[4] = 3    A[5] = -1A[6] = 3    A[7] = 3

the function may return 0, 2, 4, 6 or 7, as explained above.

Complexity:

• expected worst-case time complexity is O(N);
• expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

此题放在lesson 6--leader，在其阅读材料中讲了选取leader的方法，我们只要在选取leader的同时记录下该元素下标即可。

选取leader的思路如下：

注意到如果序列a1~~an中含有leader，那么在移除两个不相等的元素后，剩余序列与原序列有相同的leader。

建立一个空栈，将a1~~an依次压入，每次压入新元素后检查栈顶的两个元素是否相等，如不等，则将这两个元素移除。最后，如果该序列中确实含有leader，则栈中剩下的元素就是leader。

事实上该序列中可能不含leader，故最后要检验一下栈中剩余元素是否为leader。

代码如下：