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]

Return167

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

Links: http://leetcode.com/problems/burst-balloons/

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[0] = 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[0][len-1]; }}

Reference:

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

Https://leetcode.com/discuss/72186/c-dynamic-programming-o-n-3-32-ms-with-comments

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

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