package _interview_question

/**
 * You are given a list of non-negative integers.
 * Find the largest value of the expression you can get by using +, * and ( ) operators.
Example:
Input: [1, 2, 1, 2]
Output: 9
Explanation: (1 + 2) * (1 + 2) = 9
Follow-up:
Negative values are allowed.
 * */
class Solution17 {
    
 
/*
    * solution: DP, Top-Down, Time:O(n^2), Space:O(n^2)
    * */
    fun largestValue(nums: IntArray): Int {
        if (nums == null || nums.isEmpty()) {
            return 0
        }
        val n = nums.size
        val dp = Array(n) { IntArray(n) { Int.MIN_VALUE } }
        return help(nums, 0, n - 1, dp)
    }

    
 
private fun help(nums: IntArray, l: Int, r: Int, dp: Array<IntArray>): Int {
        if (l == r) {
            return nums[l]
        }
        if (dp[l][r] != Int.MIN_VALUE) {
            return dp[l][r]
        }
        var result = 0
        for (i in 0 until r - l) {
            /*
            * sum up and multiply each number one by one then find out the maximum value, for example:1,2,3,4:
            * 1+2,1+3,1+4,2+3,2+4...
            * 
 
*/
            result = Math.max(result, help(nums, l, l + i, dp) + help(nums, l + i + 1, r, dp))
            result = Math.max(result, help(nums, l, l + i, dp) * help(nums, l + i + 1, r, dp))
        }
        dp[l][r] = result
        return result
    }
}