<p>You are given two <strong>0-indexed</strong> integer arrays,&nbsp;<code>cost</code> and <code>time</code>, of size <code>n</code> representing the costs and the time taken to paint <code>n</code> different walls respectively. There are two painters available:</p>

<ul>
	<li>A<strong>&nbsp;paid painter</strong>&nbsp;that paints the <code>i<sup>th</sup></code> wall in <code>time[i]</code> units of time and takes <code>cost[i]</code> units of money.</li>
	<li>A<strong>&nbsp;free painter</strong> that paints&nbsp;<strong>any</strong> wall in <code>1</code> unit of time at a cost of <code>0</code>. But the&nbsp;free painter can only be used if the paid painter is already <strong>occupied</strong>.</li>
</ul>

<p>Return <em>the minimum amount of money required to paint the </em><code>n</code><em>&nbsp;walls.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> cost = [1,2,3,2], time = [1,2,3,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The walls at index 0 and 1 will be painted by the paid painter, and it will take 3 units of time; meanwhile, the free painter will paint the walls at index 2 and 3, free of cost in 2 units of time. Thus, the total cost is 1 + 2 = 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> cost = [2,3,4,2], time = [1,1,1,1]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The walls at index 0 and 3 will be painted by the paid painter, and it will take 2 units of time; meanwhile, the free painter will paint the walls at index 1 and 2, free of cost in 2 units of time. Thus, the total cost is 2 + 2 = 4.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= cost.length &lt;= 500</code></li>
	<li><code>cost.length == time.length</code></li>
	<li><code>1 &lt;= cost[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= time[i] &lt;= 500</code></li>
</ul>

typedef int ll;
#define vll vector<ll>
#define vvll vector<vll>
class Solution {
public:
    // cost, time
    vvll dp;
    static bool cmp(const vll &a, const vll &b) {
        if (a[0] == b[0]) {
            return a[1] > b[1];
        }
        return a[0]<b[0];
    }
    ll f(ll i, ll tsum, ll &n, vvll &data) {
        
        if (i == n) {
            if (tsum-n < 0) {
                return dp[i][tsum] = INT_MAX;
            }
            return dp[i][tsum] = 0;
        }
        // cout<<tsum<<endl;
        if (dp[i][tsum] != -1) return dp[i][tsum];
        // if (n-i-1 <= tsum) {
        //     return dp[i][tsum] = f(i+1, tsum-1, n, data);
        // }
        ll a = f(i+1, min(2*n, tsum + data[i][1]), n, data);
        if (a != INT_MAX) { 
            a+=data[i][0];
        }
        ll b = f(i+1, tsum-1, n, data);
        return dp[i][tsum] = min(a,b);
    }
    int paintWalls(vector<int>& c, vector<int>& t) {
        vvll data;
        ll n = c.size();
        ll tsum=0;
        for (int i = 0; i < n; i++) {
            data.push_back({c[i], t[i]});
            tsum+=t[i];
        }
        sort(data.begin(), data.end(), cmp);
        dp = vvll(n+1, vll(n+n + 1, -1));
        return f(0, n, n, data);
    }
};
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