Leetcode 312. Burst Balloons

Given n Balloons, indexed from 0 to n-1 . Each balloon are painted with a number on the IT represented by array nums . You is asked to burst all the balloons. If The burst balloon you'll i get nums[left] * nums[i] * nums[right] coins. Here and is left right adjacent indices of i . After the burst, the and then left right becomes adjacent.

Find The maximum coins you can collect by bursting the balloons wisely.

Note:
(1) May imagine nums[-1] = nums[n] = 1 . They is not real therefore you can not burst them.
(2) 0≤ n ≤ 500, 0≤ nums[i] ≤100

Example:

Given[3, 1, 5, 8]

Return167

    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

Parsing: Typical DP problem, from DP[1][1] iteration of the dp[1][n],n represents the subscript of the last number of arrays, the recurrence relationship is: dp[i][j] = max (Dp[i][k-1] + nums[i-1]*nums[k]*nums[j+1]+dp[k+ 1][J]), here the K range is "I,j", here is the more difficult point is nums[i-1]*nums[k]*nums[j+1] The meaning of this item, why this, if we burst to the last balloon, The last available score is nums[-1]*nums[k]*nums[n], assuming two balloons (if 1 is the optimal K value), dp[1][2] = dp[1][1] + dp[2][2] + nums[1]*nums[2]*1, and so on, The above iteration formula can be summed up. (There is no clear proof of the process, if the great God can give a complete deduction, but also hope to guide the maze)

Code:

classSolution { Public:    intMaxcoins (vector<int>&nums) {         for(intI=0; I<nums.size (); i++){            if(Nums[i] = =0) {nums.erase (Nums.begin ()+H); --i; }        }                Const intn =nums.size (); if(n = =0)return 0; Nums.insert (Nums.begin (),1); Nums.insert (Nums.end (),1); intm =nums.size (); Vector<vector<int>> DP (m,vector<int> (M,0));  for(intk=1; K <= N; k++){             for(ints =1; s+k-1<= N; s++){                intBest =0;  for(intb=0; b<k; b++) { best= Max (best,dp[s][s+b-1]+nums[s-1]*nums[s+b]*nums[s+k]+dp[s+b+1][s+k-1]); } dp[s][s+k-1] =Best ; }        }        returndp[1][n]; }};

Leetcode 312. Burst Balloons