打气球游戏

题目：打气球游戏

Given n balloons, indexed from 0 to n-1.Each balloon is painted with a number on it represented by array nums. You areasked to burst all the balloons. If the you burst balloon i you will getnums[left] * nums[i] * nums[right] coins. Here left and right are adjacentindices of i. After the burst, the left and right then becomes adjacent.

Find the maximum coins you can collect bybursting the balloons wisely.

Note:

(1) You may imagine nums[-1] = nums[n] = 1.They are 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]  -->  [8]  -->  []

   coins = 3*1*5     +    3*5*8   +   1*3*8  + 1*8*1 =  167

实现

public int maxCoins(int[] iNums) {

              int[]nums = new int[iNums.length + 2];

              intn = 1;

              for(int x : iNums)

                     if(x > 0)

                            nums[n++]= x;

              nums[0]= nums[n++] = 1;

              int[][]dp = new int[n][n];

              for(int k = 2; k < n; ++k)

                     for(int left = 0; left < n - k; ++left) {

                            intright = left + k;

                            for(int i = left + 1; i < right; ++i)

                                   dp[left][right]= Math.max(dp[left][right],

                                                 nums[left]* nums[i] * nums[right] + dp[left][i] + dp[i][right]);

                     }

              returndp[0][n - 1];

       }