**Problem Links**

**Difficulty**

Easy DP

**PREREQUISITES**

Ad hoc

**Problem**

Given a grid of 2 × 1 tiles. We have to find the maximum sum of the absolute difference of the number in two consecutive tiles , such as that arrangement covers the entire grid.

**EXPLANATION**

The problem can be easily be solved using DP.

The tiles are 2X1 rectangular ones. Now let the grid be a[2][N] , where N is the length of matrix.

let dp[i] denote the maximum sum of the arrangement till length i.

Therefore

dp[i+1]=max(dp[i]+abs(a[0][i+1]-abs[1][i+1]), dp[i-2]+abs(a[0][i]-a[0][i+1])+abs(a[1][i])-a[1][i]))

We can either add a single vertical brick to the grid of length i or we can add two horizontal bricks to the grid. We just have to see which one gives the maximum answer

**Editorialist’s Solution**