Leetcode Problem 312. Burst Balloons

312. Burst Balloons

Leetcode Solutions

Dynamic Programming (Bottom-Up)

  1. Add a balloon with value 1 at the beginning and end of the nums array to handle edge cases.
  2. Initialize a 2D DP array dp where dp[left][right] represents the maximum coins obtainable by bursting all balloons between left and right.
  3. Iterate over the length of the subarray from 1 to n.
  4. For each length, iterate over all possible starting points left.
  5. Calculate the ending point right based on the current length and starting point.
  6. For each position i between left and right, calculate the coins obtained by assuming the ith balloon is the last to burst.
  7. The coins gained are the sum of bursting all balloons to the left and right of i plus the coins from bursting the ith balloon itself, considering the neighbors.
  8. Update dp[left][right] with the maximum coins obtained for all positions i.
  9. Return dp[1][n-2] as the final answer, excluding the fake balloons added in step 1.
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Dynamic Programming (Top-Down)

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