Leetcode Burst Balloons

The original title link is here: https://leetcode.com/problems/burst-balloons/

Topic:

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

Exercises

DP title, Dp[l][r] indicates the maximum number of coins obtained by all balloons in the range of Pierce (L, R), without Borders.

We can imagine: when the last remaining balloon is m, you can get a score of nums[-1]*nums[m]*nums[n].

Then M between L, R, with dp[l][r] = max (Dp[l][r], dp[l][m] + nums[l] * nums[m] * Nums[r] + dp[m][r]).

The span K of L and R increases gradually from 2 onwards;

The triple loop enumerates in sequence the span K, left boundary L, Midpoint m, right boundary R = L + K

Time Complexity:o (n^3). Space:o (n^2).

AC Java:

1  Public classSolution {2      Public intMaxcoins (int[] nums) {3         if(Nums = =NULL|| Nums.length = = 0){4             return0;5         }6         intLen = nums.length+2;7         int[] Newnums =New int[Len];8          for(inti = 1; i<len-1; i++){9Newnums[i] = nums[i-1];Ten         } OneNewnums[0] = 1; ANewnums[len-1] = 1; -          -         int[] DP =New int[Len][len]; the          for(intK = 2; k<len; k++){ -              for(intL = 0; l<len-k; l++){ -                 intR = L +K; -                  for(intm = l+1; m<r; m++){ +Dp[l][r] = Math.max (Dp[l][r], dp[l][m] + newnums[l]*newnums[m]*newnums[r] +dp[m][r]); -                 } +             } A         } at         returnDp[0][len-1]; -     } -}

Leetcode Burst Balloons