[CareerCup] 17.6 Sort Array 排列数组

17.6 Given an array of integers, write a method to find indices m and n such that if you sorted elements m through n, the entire array would be sorted. Minimize n - m (that is, find the smallest such sequence). 

为了更好的理解题意，我们通过一个例子来分析，比如我们有如下的数组：

1, 2, 4, 7, 10, 11, 7, 12, 6, 7, 16, 18, 19

那么我们可以按照递增顺序将其分为三个部分：

left:         1, 2, 4, 7, 10, 11

middle:    7, 12

right:       6, 7, 16, 18, 19

只要从左右两端开始往中间搜索即可，遇到不是递增的数字就停止，然后我们要给中间的部分排序，排完序我们看left的最右边的数字是否比middle的最左边的数字小，right的最左边的数字是否比middle的最右边的数字大，如果不是，我们要shift_left和shift_right，向左边，我们再来验证整个数列是否是有序的，如果不是有序的，则说明不存在这样的index，参见代码如下：

int find_end_of_left_subsequence(vector<int> array) {
    for (int i = 1; i < array.size(); ++i) {
        if (array[i] < array[i - 1]) {
            return i - 1;
        }
    }
    return array.size() - 1;
}

int find_start_of_right_subsequence(vector<int> array) {
    for (int i = array.size() - 2; i >= 0; --i) {
        if (array[i] > array[i + 1]) {
            return i + 1;
        }
    }
    return 0;
}

int shrink_left(vector<int> array, int min_idx, int start) {
    int cmp = array[min_idx];
    for (int i = start - 1; i >= 0; --i) {
        if (array[i] <= cmp) {
            return i + 1;
        }
    }
    return 0;
}

int shrink_right(vector<int> array, int max_idx, int start) {
    int cmp = array[max_idx];
    for (int i = start; i < array.size(); ++i) {
        if (array[i] >= cmp) {
            return i - 1;
        }
    }
    return array.size() - 1;
}

bool validate(vector<int> array, int left_idx, int right_idx) {
    vector<int> middle(right_idx - left_idx + 1);
    for (int i = left_idx; i <= right_idx; ++i) {
        middle[i - left_idx] = array[i];
    }
    sort(middle.begin(), middle.end());
    for (int i = left_idx; i <= right_idx; ++i) {
        array[i] = middle[i - left_idx];
    }
    for (int i = 1; i < array.size(); ++i) {
        if (array[i - 1] > array[i]) {
            return false;
        }
    }
    return true;
}

void find_unsorted_sequence(vector<int> array) {
    int end_left = find_end_of_left_subsequence(array);
    if (end_left >= array.size() - 1) return;
    int start_right = find_start_of_right_subsequence(array);
    int max_idx = end_left;
    int min_idx = start_right;
    for (int i = end_left + 1; i < start_right; ++i) {
        if (array[i] < array[min_idx]) {
            min_idx = i;
        }
        if (array[i] > array[max_idx]) {
            max_idx = i;
        }
    }
    int left_idx = shrink_left(array, min_idx, end_left);
    int right_idx = shrink_right(array, max_idx, start_right);
    if (validate(array, left_idx, right_idx)) {
        cout << "True: " << left_idx << " " << right_idx << endl;
    } else {
        cout << "False: " << left_idx << " " << right_idx << endl;
    }
}

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