Coursera - Algorithm (Princeton) - 习题与解答 - Week 12

Week 12

Longest path and longest cycle

问题

Consider the following two problems

• LongestPath: Given an undirected graph GG and two distinct vertices $s$ and $t$, find a simple path (no repeated vertices) between $s$ and $t$ with the most edges.
• LongestCycle: Given an undirected graph G’, find a simple cycle (no repeated vertices or edges except the first and last vertex) with the most edges.

Show that LongestPath linear-time reduces to LongestCycle.

分析

从路径到环，可以说是在环路是路径的完备情况（两条最长路径构成一个长环），也就是说后者是前者多找一条最长路径（环路问题一次调用，线性时间归约到路径问题）

3Sum and 4Sum

问题

Consider the following two problems:

• 3Sum: Given an integer array $a$, are there three distinct indices $i$, $j$, and $k$ such that $a_i+a_j+a_k=0$?
• 4Sum: Given an integer array $b$, are there four distinct integers i i