We have been given N balloons, each with a number of coins associated with it. On bursting a balloon i, the number of coins gained is equal to A[i-1]*A[i]*A[i+1]. Also, balloons i-1 and i+1 now become adjacent. Find the maximum possible profit earned after bursting all the balloons. Assume an extra 1 at each boundary.
Input : 5, 10 Output : 60 Explanation - First Burst 5, Coins = 1*5*10 Then burst 10, Coins+= 1*10*1 Total = 60 Input : 1, 2, 3, 4, 5 Output : 110
A recursive solution is discussed here. We can solve this problem using dynamic programming.
First, consider a sub-array from indices Left to Right(inclusive).
If we assume the balloon at index Last to be the last balloon to be burst in this sub-array, we would say the coined gained to be-A[left-1]*A[last]*A[right+1].
Also, the total Coin Gained would be this value, plus dp[left][last – 1] + dp[last + 1][right], where dp[i][j] means maximum coin gained for sub-array with indices i, j.
Therefore, for each value of Left and Right, we need find and choose a value of Last with maximum coin gained, and update the dp array.
Our Answer is the value at dp[N].
- Number of paths with exactly k coins
- Buy minimum items without change and given coins
- Probability of getting at least K heads in N tosses of Coins
- Find minimum number of coins that make a given value
- Collect maximum coins before hitting a dead end
- Probability of getting two consecutive heads after choosing a random coin among two different types of coins
- Maximize the value of x + y + z such that ax + by + cz = n
- Maximize arr[j] - arr[i] + arr[l] - arr[k], such that i < j < k < l
- Maximize the number of subarrays with XOR as zero
- Maximize the bitwise OR of an array
- Maximize the number of sum pairs which are divisible by K
- Maximize the total profit of all the persons
- Maximize the number of segments of length p, q and r
- Maximize the product of four factors of a Number
- Remove array end element to maximize the sum of product
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.