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# Burst Balloons in C++

Suppose we have n balloons, these are indexed from 0 to n-1. Here each balloon is painted with a number on it represented by one array called nums. we have to burst all the balloons. If we burst balloon i we will get nums[i – 1] * nums[i] * nums[i + 1] number of coins. After the burst, the i – 1 and i + 1 then becomes adjacent. We have to find the maximum coins to collect by bursting the balloons wisely.

So if the input is like [3,1,5,7], then the result will be 148. Initially the array is like [3,1,5,7], then after bursting 1, we will get 3 * 1 * 5 = 15, then the array is [3,5,7], then burst 5, so we will get (3 * 5 * 7) = 105, then array is like [3,7], then burst 3, so we will get (1*3*7) = 21, finally the array is [7], so after bursting, we will get 7, so the total is 15 + 105 + 21 + 7 = 148.

To solve this, we will follow these steps −

n := size of a

if (n is non-zero) is false, then,

return 0

Define one 2D array dp of order n x n

for initializing l := n - 1, when l >= 0, decrease l by 1 do −

for initializing r := l, when r < n, increase r by 1 do −

for initializing i := l, when i <= r, increase i by 1 do −

y := dp[i + 1, r] if i + 1 < n, otherwise 0

z := a[l - 1] if l - 1 >= 0 otherwise 1

w := a[r + 1] if r + 1 < n otherwise 1

x := dp[l, i - 1] if i - 1 > = 0, otherwise 0 + y + (z * w * a[i])

dp[l, r] := max of dp[l, r] and x

return dp[0, n - 1]

## Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h> using namespace std; class Solution { public: int maxCoins(vector<int>& a) { int n = a.size(); if(!n)return 0; vector < vector <int>> dp(n,vector <int> (n)); for(int l = n-1;l>=0;l--){ for(int r=l;r<n;r++){ for(int i =l;i<=r;i++){ dp[l][r] = max(dp[l][r],(i-1>=0?dp[l][i-1]:0) +(i+1<n?dp[i+1][r]:0)+((l-1>=0?a[l-1]:1 )*(r+1<n?a[r+1]:1)*a[i])); } } } return dp[0][n-1]; } }; main(){ Solution ob; vector<int> v = {3,1,5,7}; cout << (ob.maxCoins(v)); }

## Input

[3,1,5,7]

## Output

148

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