问题描述:
Shuffle a set of numbers without duplicates.
示例:
// Init an array with set 1, 2, and 3. int[] nums = {1,2,3}; Solution solution = new Solution(nums); // Shuffle the array [1,2,3] and return its result. Any permutation of [1,2,3] must equally likely to be returned. solution.shuffle(); // Resets the array back to its original configuration [1,2,3]. solution.reset(); // Returns the random shuffling of array [1,2,3]. solution.shuffle();问题分析:
本题主要考察经典的洗牌算法Fisher Yates 洗牌算法。
算法过程 :数组中随机抽一个元素与最后一个进行交换,下次在前n-1个元素中随机抽,依次类推直到最后一个。
该算法同样可以理解成为这样的过程:从1到n个数字中依次随机抽取一个数字,并放到一个新序列的尾端(该算法通过互换数字实现),逐渐形成一个新的 序列。计算一下概率:如果某个元素被放入第i(1≤i≤n)个位置,就必须是在前 i-1 次选取中都没有选到它,并且第 i 次恰好选中它。其概率为:
过程详见代码:
class Solution { public: vector<int> arr, idx; Solution(vector<int> nums) { srand(time(NULL)); arr.resize(nums.size()); idx.resize(nums.size()); for (int i = 0; i < nums.size(); i++) { arr[i] = nums[i]; idx[i] = nums[i]; } } /** Resets the array to its original configuration and return it. */ vector<int> reset() { for (int i = 0; i < arr.size(); i++) idx[i] = arr[i]; return idx; } /** Returns a random shuffling of the array. */ vector<int> shuffle() { for (int i = idx.size() - 1; i > 0; i--) { int j = rand() % (i + 1); swap(idx[i], idx[j]); } return idx; } }; /** * Your Solution object will be instantiated and called as such: * Solution obj = new Solution(nums); * vector<int> param_1 = obj.reset(); * vector<int> param_2 = obj.shuffle(); */