<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:

    int solveRec(int ind,vector<int> &coins,int amount){
        if(ind == 0){
            if(amount % coins[ind] == 0){
                return (amount/coins[ind]);
            }
            else{
                return 1e9;
            }
        }
        
        int notPick = 0 + solveRec(ind-1,coins,amount);
        int pick = INT_MAX;
        if(coins[ind] <= amount){
            pick = 1 + solveRec(ind,coins,amount-coins[ind]);
        }

        return min(pick,notPick);
    }


    int solveMem(int ind,vector<int> &coins,int amount,vector<vector<int> > &dp){
        if(ind == 0){
            if(amount % coins[ind] == 0){
                return (amount/coins[ind]);
            }
            else{
                return 1e9;
            }
        }
        if(dp[ind][amount] != -1){
            return dp[ind][amount];
        }
        
        int notPick = 0 + solveMem(ind-1,coins,amount,dp);
        int pick = INT_MAX;
        if(coins[ind] <= amount){
            pick = 1 + solveMem(ind,coins,amount-coins[ind],dp);
        }

        return dp[ind][amount] = min(pick,notPick);
    }


    int solveTab(vector<int> &coins,int amount){
        int n = coins.size();
        vector<vector<int> > dp(n,vector<int> (amount+1,0));

        for(int i=0 ; i<=amount ; i++){
            if(i % coins[0] == 0){
                dp[0][i] = i/coins[0];
            }
            else{
                dp[0][i] = 1e9;
            }
        }

        for(int i=1 ; i<n ; i++){
            for(int T=0 ; T<=amount ; T++){
                int notPick = 0 + dp[i-1][T];
                int pick = INT_MAX;
                if(T >= coins[i]){
                    pick = 1 + dp[i][T - coins[i]];
                }
                dp[i][T] = min(pick,notPick);
            }
        }
        return dp[n-1][amount];
    }

    int coinChange(vector<int>& coins, int amount) {
        int n = coins.size();
        // int ans = solveRec(n-1,coins,amount);
        // if(ans >= 1e9){
        //     return -1;
        // }
        // return ans;

        // vector<vector<int> > dp(n,vector<int> (amount+1,-1));
        // int ans = solveMem(n-1,coins,amount,dp);
        // if(ans >= 1e9){
        //     return -1;
        // }
        // return ans;

        int ans = solveTab(coins,amount);
        if(ans >= 1e9){
            return -1;
        }
        return ans;
    }
};
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