<p>You are given an integer array <code>coins</code> representing coins of different denominations and an integer <code>amount</code> representing a total amount of money.</p>

<p>Return <em>the fewest number of coins that you need to make up that amount</em>. If that amount of money cannot be made up by any combination of the coins, return <code>-1</code>.</p>

<p>You may assume that you have an infinite number of each kind of coin.</p>

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

<pre>
<strong>Input:</strong> coins = [1,2,5], amount = 11
<strong>Output:</strong> 3
<strong>Explanation:</strong> 11 = 5 + 5 + 1
</pre>

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

<pre>
<strong>Input:</strong> coins = [2], amount = 3
<strong>Output:</strong> -1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> coins = [1], amount = 0
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= coins.length &lt;= 12</code></li>
	<li><code>1 &lt;= coins[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>0 &lt;= amount &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    vector<vector<int>>dp;
    int chk(int st,int en, vector<int>&coins, int a) {
        if(a==0)
            return 0;
        if(st>=en)
            return INT_MAX;
        if(dp[st][a]!=-1)
            return dp[st][a];
        if(a<coins[st])
            return dp[st][a] = INT_MAX;

        int u = chk(st,en,coins,a-coins[st]);
        int v = chk(st+1,en,coins,a-coins[st]);
        int w = chk(st+1,en,coins,a);

        if(u==INT_MAX && v==INT_MAX && w==INT_MAX)
            return dp[st][a] = INT_MAX;
        u = min(u,v);
        if(u==INT_MAX){
            dp[st][a] = w;
            return dp[st][a];
        }
        dp[st][a] = min(1+u,w);
        return dp[st][a];

    }
    int coinChange(vector<int>& coins, int amount) {
        sort(coins.begin(),coins.end());
        dp = vector<vector<int>>(coins.size()+1,vector<int>(amount+1,-1));
        int x = chk(0,coins.size(),coins,amount);
        if(x == INT_MAX)
            return -1;
        return x;
    }
};
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