题目原文: Decimal dominants. Given an array with n keys, design an algorithm to find all values that occur more than  n/10 times. The expected running time of your algorithm should be linear. 分析: 直观上将n个元素遍历一遍,并记录每个元素出现的次数就可以实现,虽然时间复杂度是O(n),但是空间复杂度却高达n,这肯…

题目原文: Nuts and bolts. A disorganized carpenter has a mixed pile of n nuts and n bolts. The goal is to find the corresponding pairs of nuts and bolts. Each nut fits exactly one bolt and each bolt fits exactly one nut. By fitting a nut and a bolt toget…

题目原文 Selection in two sorted arrays. Given two sorted arrays a[] and b[], of sizes n1 and n2, respectively, design an algorithm to find the kth largest key. The order  of growth of the worst case running time of your algorithm should be logn, where n…

题目原文: Shuffling a linked list. Given a singly-linked list containing n items, rearrange the items uniformly at random. Your algorithm should consume a logarithmic (or constant) amount of extra memory and run in time proportional to nlogn in the worst…

题目原文: An inversion in an array a[] is a pair of entries a[i] and a[j] such that i<j but a[i]>a[j]. Given an array, design a linearithmic algorithm to count the number of inversions. 分析: 如果没有性能限制,用插入排序算法可以实现.题目性能被限制在nlogn,又是归并排序的练习题,很显然要实现个归并排序,并在里面计…

题目原文: Suppose that the subarray a[0] to a[n-1] is sorted and the subarray a[n] to a[2*n-1] is sorted. How can you merge the two subarrays so that a[0] to a[2*n-1] is sorted using an auxiliary array of length n (instead of 2n) 分析: 对两个大小分别为n的有序子数组进行归并,…

题目原文: Suppose that you have an n-story building (with floors 1 through n) and plenty of eggs. An egg breaks if it is dropped from floor T or higher and does not break otherwise. Your goal is to devise a strategy to determine the value of T given the…

题目要求: Design an algorithm for the 3-SUM problem that takes time proportional to n2 in the worst case. You may assume that you can sort the n integers in time proportional to n2 or better. 分析: <算法4>这本书提供的TwoSumFast解法为NlogN,ThreeSumFast解法为N2logN,根据课后练…

第二周课程的Elementray Sorts部分练习测验Interview Questions的第3题荷兰国旗问题很有意思.题目的原文描述如下: Dutch national flag. Given an array of n buckets, each containing a red, white, or blue pebble, sort them by color. The allowed operations are: swap(i,j): swap the pebble in buc…

题目原文: Design an algorithm to perform an inorder traversal of a binary search tree using only a constant amount of extra space. public void traverse(BST<Key,Value> bst) { traverse(bst.root.left, bst.root); } private void traverse(Node current, Node p…