Problem

In MATLAB, there is a very useful function called ‘reshape’, which can reshape a matrix into a new one with different size but keep its original data.

You’re given a matrix represented by a two-dimensional array, and twoĀ positiveĀ integersĀ rĀ andĀ cĀ representing theĀ rowĀ number andĀ columnĀ number of the wanted reshaped matrix, respectively.

The reshaped matrix need to be filled with all the elements of the original matrix in the sameĀ row-traversingĀ order as they were.

If the ‘reshape’ operation with given parameters is possible and legal, output the new reshaped matrix; Otherwise, output the original matrix.

Example 1:

Input:
nums =
[[1,2],
[3,4]]
r = 1, c = 4
Output:
[[1,2,3,4]]
Explanation:
The row-traversing of nums is [1,2,3,4]. The new reshaped matrix is a 1 * 4 matrix, fill it row by row by using the previous list.


Example 2:

Input:
nums =
[[1,2],
[3,4]]
r = 2, c = 4
Output:
[[1,2],
[3,4]]
Explanation:
There is no way to reshape a 2 * 2 matrix to a 2 * 4 matrix. So output the original matrix.


Note:

1. The height and width of the given matrix is in range [1, 100].
2. The given r and c are all positive.

Solution1: Brute Force

Time complexity: O(mn)

Space complexity: O(mn)

Problem

The demons had captured the princess (P) and imprisoned her in the bottom-right corner of a dungeon. The dungeon consists of M x N rooms laid out in a 2D grid. Our valiant knight (K) was initially positioned in the top-left room and must fight his way through the dungeon to rescue the princess.

The knight has an initial health point represented by a positive integer. If at any point his health point drops to 0 or below, he dies immediately.

Some of the rooms are guarded by demons, so the knight loses health (negativeĀ integers) upon entering these rooms; other rooms are either empty (0’s) or contain magic orbs that increase the knight’s health (positiveĀ integers).

In order to reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.

Write a function to determine the knight’s minimum initial health so that he is able to rescue the princess.

For example, given the dungeon below, the initial health of the knight must be at leastĀ 7Ā if he follows the optimal pathĀ RIGHT-> RIGHT -> DOWN -> DOWN.

 -2 (K) -3 3 -5 -10 1 10 30 -5 (P)

Note:

• The knight’s health has no upper bound.
• Any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.

Solution: DP

Time complexity: O(mn)

Space complexity: O(mn) -> O(n)

C++

O(n) space

Problem

GivenĀ s1,Ā s2,Ā s3, find whetherĀ s3Ā is formed by the interleaving ofĀ s1Ā andĀ s2.

Example 1:

Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
Output: true


Example 2:

Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
Output: false


Solution: DP

Subproblems : whether s3[0:i+j] can be formed by interleaving s1[0:i] and s2[0:j].

Time complexity: O(mn)

Space complexity: O(mn)

Recursion + Memorization