You are climbing a stair case.

It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps.

In how many distinct ways can you climb to the top?

EASY

Recursion

DP

Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) which sum to n.

NORMAL

Input: 12
Output: 3 (4+4+4)

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Now consider if some obstacles are added to the grids. How many unique paths would there be?

NORMAL

1. define the state dp[i][j] to be the minimum number of operations to convert word1[0..i) to word2[0..j)

2. For the base case, dp[i][0] = i and dp[0][j] = j

3. if word1[i - 1] == word2[j - 1], then no more operation is needed and dp[i][j] = dp[i - 1][j - 1]

4. If word1[i - 1] != word2[j - 1], we need to consider three cases.

Replace word1[i - 1] by word2[j - 1] (dp[i][j] = dp[i - 1][j - 1] + 1);

If word1[0..i - 1) = word2[0..j) then delete word1[i - 1] (dp[i][j] = dp[i - 1][j] + 1);

If word1[0..i) + word2[j - 1] = word2[0..j) then insert word2[j - 1] to word1[0..i) (dp[i][j] = dp[i][j - 1] + 1).

So dp[i][j] will just be the minimum of the above three cases.