312. poke the balloon

Preface

C++ It's a high-level programming language , from C Language expansion and upgrading , As early as 1979 By Benjani · Strauss LUP is AT&T Developed by Bell studio .
C++ Both can be carried out C Process programming of language , It can also be used for object-based programming characterized by abstract data types , It can also carry out object-oriented programming characterized by inheritance and polymorphism .C++ Good at object-oriented programming at the same time , You can also do process based programming .
C++ Have the practical characteristics of computer operation , At the same time, it is also committed to improving the programming quality of large-scale programs and the problem description ability of programming languages .

Java Is an object-oriented programming language , Not only absorbed C++ The advantages of language , It's abandoned C++ The incomprehensible inheritance in 、 Concepts such as pointer , therefore Java Language has two characteristics: powerful and easy to use .Java As the representative of static object-oriented programming language , Excellent implementation of object-oriented theory , Allow programmers to do complex programming in an elegant way of thinking .
Java It's simple 、 object-oriented 、 Distributed 、 Robustness, 、 Security 、 Platform independence and portability 、 Multithreading 、 Dynamic and so on .Java Can write desktop applications 、Web Applications 、 Distributed system and embedded system applications, etc .

Python By Guido of the Dutch Society for mathematical and computer science research · Van rosum On 1990 It was designed in the early 's , As a course called ABC A substitute for language .Python Provides efficient advanced data structure , It's also a simple and effective way of object-oriented programming .Python Syntax and dynamic types , And the nature of interpretative language , Make it a programming language for scripting and rapid application development on most platforms , With the continuous update of the version and the addition of new language features , Gradually used for independent 、 Development of large projects .
Python The interpreter is easy to extend , have access to C Language or C++（ Or something else can be done through C Calling language ） Expand new functions and data types .Python It can also be used as an extensible programming language in customizable software .Python Rich library of standards , Provides source code or machine code for each major system platform .
2021 year 10 month , Compiler for language popularity index Tiobe take Python Crowned the most popular programming language ,20 Put it in... For the first time in years Java、C and JavaScript above .

describe

Yes n A balloon , The number is 0 To n - 1, Each balloon is marked with a number , There are arrays of these numbers nums in .

Now I ask you to prick all the balloons . Pierce the second i A balloon , You can get nums[i - 1] * nums[i] * nums[i + 1] Coin . there i - 1 and i + 1 For and on behalf of i The serial number of the two adjacent balloons . If i - 1 or i + 1 Beyond the bounds of the array , Then think of it as a number for 1 The balloon .

Find the maximum number of coins you can get .

 
Example 1：

Input ：nums = [3,1,5,8]
Output ：167
explain ：
nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []
coins =  3*1*5    +   3*5*8   +  1*3*8  + 1*8*1 = 167

Example 2：

Input ：nums = [1,5]
Output ：10

class Solution {
    public int[][] rec;
    public int[] val;

    public int maxCoins(int[] nums) {
        int n = nums.length;
        val = new int[n + 2];
        for (int i = 1; i <= n; i++) {
            val[i] = nums[i - 1];
        }
        val[0] = val[n + 1] = 1;
        rec = new int[n + 2][n + 2];
        for (int i = 0; i <= n + 1; i++) {
            Arrays.fill(rec[i], -1);
        }
        return solve(0, n + 1);
    }

    public int solve(int left, int right) {
        if (left >= right - 1) {
            return 0;
        }
        if (rec[left][right] != -1) {
            return rec[left][right];
        }
        for (int i = left + 1; i < right; i++) {
            int sum = val[left] * val[i] * val[right];
            sum += solve(left, i) + solve(i, right);
            rec[left][right] = Math.max(rec[left][right], sum);
        }
        return rec[left][right];
    }
}