# 312.Burst Balloons

Source: Internet
Author: User

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]`

Return`167`

`    Nums = [3,1,5,8]--[3,5,8]--[   3,8]--  --  []   coins =  3*1*5      +  * 5*8    +  1*3*8      + 1*8*1   = 167`

Exercises

Balloon game, hit the balloon after the score is nums[i] * nums[i-1] * nums[i-2], after the left and right side of the balloon connected. The idea of this problem is also very around, see the dietpepsi solution is also very vague, with the sale of stocks with cooldown the same. The method should be with DP or divide and conquer, presumably the idea is that every burst drop a balloon, we do it again 2d DP. The code is not long, so I memorized the answer ... Wipe. Understand to give the two brushes.

Time Complexity-o (n3), Space Complexity-o (n2)

` Public classSolution { Public intMaxcoins (int[] orgnums) {        if(Orgnums = =NULL|| Orgnums.length = = 0) {            return0; }        intLen = orgnums.length + 2; int[] Nums =New int[Len]; nums = nums[len-1] = 1;//Boundary         for(inti = 0; i < orgnums.length; i++) {nums[i+ 1] =Orgnums[i]; }        int[] DP =New int[Len][len];  for(inti = 1; i < Len; i++) {//First balloon             for(intLo = 0; Lo < len-i; lo++) {// Left part                inthi = Lo + i;//Right part Boundary                 for(intK = lo + 1; K < hi; k++) {Dp[lo][hi]= Math.max (Dp[lo][hi], Nums[lo] * nums[k] * Nums[hi] + dp[lo][k] +Dp[k][hi]); }            }          }                returnDp[len-1]; }}`

Reference:

Https://leetcode.com/discuss/72216/share-some-analysis-and-explanations

Https://leetcode.com/discuss/72215/java-dp-solution-with-detailed-explanation-o-n-3

Https://leetcode.com/discuss/72683/my-c-code-dp-o-n-3-20ms

Https://leetcode.com/discuss/73288/python-dp-n-3-solutions

Https://leetcode.com/discuss/72802/share-my-both-dp-and-divide-conquer-solutions

Https://leetcode.com/discuss/73924/my-36ms-c-solution

312.Burst Balloons

Related Keywords:
Related Article ## Cloud Intelligence Leading the Digital Future

Alibaba Cloud ACtivate Online Conference, Nov. 20th & 21st, 2019 (UTC+08)

Register Now > ## Starter Package

SSD Cloud server and data transfer for only \$2.50 a month

Get Started > ## Alibaba Cloud Free Trial

Learn and experience the power of Alibaba Cloud with a free trial worth \$300-1200 USD