[OJ] Find Minimum in Rotated Sorted Array II

LintCode 160. Find Minimum in Rotated Sorted Array II (Medium)
LeetCode 154. Find Minimum in Rotated Sorted Array II (Hard)

解法1

自己做了半个小时, 想分情况判断num[mid]与num[start], num[mid]与num[end]的大小关系, 每个关系分>, =, <的情况, 于是就是9种情况...

>, >, L = M + 1
>, =, 选L
>, <, 选L
=, >, L = M + 1
=, =, 二分递归
=, <, 选L
<, >, 不可能
<, =, R = M
<, <, R = M

然后就是下面这蛋疼的代码...

class Solution {
private:
    int rec(vector<int> &num, int start, int end) {
        if (start == end) return num[start];
        while (start + 1 < end) {
            int mid = start + (end - start) / 2;
            if (num[mid] > num[start]) {
                if (num[mid] > num[end]) {
                    start = mid + 1;
                } else {
                    return num[start];
                }
            } else if (num[mid] == num[start]) {
                if (num[mid] > num[end]) {
                    start = mid + 1;
                } else if (num[mid] == num[mid]) {
                    return min(rec(num, start, mid), rec(num, mid + 1, end));
                } else {
                    return num[start];
                }
            } else {
                end = mid;
            }
        }
        return min(num[start], num[end]);
    }
public:
    int findMin(vector<int> &num) {
        return rec(num, 0, num.size() - 1);
    }
};

解法1.1

观察9种情况发现有些情况可以合并.

x, >, L = M + 1
<, x, R = M
x, =, --R
else 选L

class Solution {
public:
    int findMin(vector<int> &num) {
        if (num.empty()) return 0;
        int start = 0, end = num.size() - 1;
        while (start < end) {
            int mid = start + (end - start) / 2;
            if (num[mid] > num[end]) {
                start = mid + 1;
            } else if (num[mid] < num[start]) {
                end = mid;
            } else if (num[mid] == num[end]) {
                --end;
            } else {
                return num[start];
            }
        }
        return num[start];
    }
};

解法2

参考这篇博文, 在Find Minimum in Rotated Sorted Array代码的基础上稍事修改就可以得到下面的代码. 当num[M] == num[R]时, 将R左移一位即可.

class Solution {
public:
    int findMin(vector<int> &num) {
        int n = num.size();
        int L = 0, R = n - 1;
        while (L < R && num[L] >= num[R]) {
            int M = (R - L) / 2 + L;
            if (num[M] > num[R]) {
                L = M + 1;
            } else if (num[M] < num[R]) {
                R = M;
            } else {
                --R;
            }
        }
        return num[L];
    }
};

时间复杂度: O(logn) (在数组恒值的最差情况下退化到O(n))
空间复杂度: O(1)