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Burst Balloons

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the maximum coins you can collect by bursting balloons. You are given n balloons, indexed from 0 to n - 1. Each balloon is painted with a number on it represented by an array nums. You are asked to burst all the balloons. If you burst the i-th balloon, you will get nums[i - 1] * nums[i] * nums[i + 1] coins. If i - 1 or i + 1 goes out of bounds of the array, then treat it as if there is a balloon with a 1 painted on it. Return the maximum coins you can collect by bursting the balloons wisely.

Example 1
    
      
  • Input: nums = [3,1,5,8]
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  • Output: 167
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  • Explanation: 
    • Burst balloon at index 1 (value 1): coins = 3*1*5 = 15, remaining = [3,5,8]. 
    • Burst balloon at index 1 (value 5): coins = 3*5*8 = 120, remaining = [3,8]. 
    • Burst balloon at index 0 (value 3): coins = 1*3*8 = 24, remaining = [8]. 
    • Burst balloon at index 0 (value 8): coins = 1*8*1 = 8, remaining = []. 
    • Total coins = 15 + 120 + 24 + 8 = 167.
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Example 2
    
      
  • Input: nums = [1,5]
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  • Output: 10
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  • Explanation: 
    • Burst balloon at index 0 (value 1): coins = 1*1*5 = 5, remaining = [5]. 
    • Burst balloon at index 0 (value 5): coins = 1*5*1 = 5, remaining = []. 
    • Total coins = 5 + 5 = 10.
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Constraints
    
      
  • n == nums.length
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  • 1 ≤ n ≤ 300
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  • 0 ≤ nums[i] ≤ 100
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  • Time Complexity: O(n^3)
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  • Space Complexity: O(n^2)
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Hint
Solution

Solution Hints

    
      
  • Use dynamic programming with interval-based approach
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  • Add boundary balloons with value 1 at both ends
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  • For each interval [left, right], try bursting each balloon as the last one
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  • When bursting balloon k last in interval [left, right], multiply values[left] * values[k] * values[right]
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  • Use memoization to store results for overlapping subproblems
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  • Build solution bottom-up from smaller intervals to larger ones
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Steps to solve by this approach:

 Step 1: Add boundary balloons with value 1 at both ends of the array
 Step 2: Create a 2D memoization table to store results of subproblems
 Step 3: Use interval DP where dp[left][right] represents max coins from interval (left, right)
 Step 4: For each interval, try bursting each balloon as the last one in that interval
 Step 5: When balloon k is burst last, coins = values[left] * values[k] * values[right]
 Step 6: Add coins from left and right subintervals recursively
 Step 7: Use memoization to avoid recalculating same subproblems

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