Introduction

This program includes a simple 2048 game and a AI solver written in JavaScript.

Strategy Explanation

This solver deploys a DFS method with below heuristic metrics construction.

metrics = $\theta_1E_1 + \theta_2E_2 + \theta_3E_3 + \theta_4E_4$, where $a_{ij} = \log m_{ij}, m_{ij}$ is the element in the matrix of the board $M$.
$E_1$ is the Smoothness of the matrix. Define gradient $\nabla$ of an element on the board as below. $$\nabla a_{ij} = ( a_{ij} - a_{i+1,j} ,a_{ij} - a_{i,j+1})$$

for any $a_{pq} \neq 0$, $p\in[0, 3]$, $q\in[0, 3]$, when p or q exceed index boundaries, assign 0 for that deduction. e.g. $$\nabla a_{0,3} = ( a_{0, 3} - a_{1,3} ,0)$$ Then we have below expression for Smoothness of the matrix $$E_1 = \displaystyle\sum_{i=0}^3\displaystyle\sum_{j=0}^3|\nabla a_{ij}|_\infty$$ $E_2$ is the Monotonicity of the matrix,
$E_3$ is the empty cells on the board,
$E_4$ is the maximum value.

Given board $A=[a_{i_j}]$, where $a_{ij} = [0, 2^k, \dots, 2^11]$, $k = 1, 2, \dots 11$, $i\in[0, 3]$, $j\in[0, 3]$.

$E_1$ can be obtained by looping each element and calculating the differences comparing with the four edging points.
$E_2$ can be obtained by comparing each element and its neighbor in row or in column and choosing the max in either of the two directions. $E_3$ is the quantity when $a_{ij} = 0$.
$E_4 = \displaystyle\max_{i,j}a_{ij} $

Solver Autorun

Example of the Autorun.