1. Design a randomized algorithm to find the i-th smallest element in a given array of length n. The expected running time of your algorithm should be O(n). (15分)

7. 使用 linked list 實作 stack，運用以下 C 語言程式：typedef struct node { int value; node *next;}void push (node **top, int new_value) { // assume top is not nullnode new_node = (node ) malloc (sizeof (node));// (A) 實作以下敘述 (5 分)// add new_node to stack by top}int pop (node **top) { // assume top is not nullint value;node deleting_node = top;// (B) 實作以下敘述(5 分)// remove the deleting node from stack, get the value of deleting nodefree(deleting_node);return value;}

1. Design a randomized algorithm to find the i-th smallest element in a given array of length \( n \). The expected running time of your algorithm should be \( O(n) \). (15分)

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