<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:
    long long int miniCoinR(vector<int> &coins,int idx,int amount){
        if(amount==0){
            return 0;
        }
        if(idx==0){
            return INT_MAX;
        }
        if(coins[idx-1]>amount){
            return miniCoinR(coins,idx-1,amount);
        }
        return min(miniCoinR(coins,idx-1,amount),1+miniCoinR(coins,idx,amount-coins[idx-1]));
    }
    long long int miniCoinM(vector<int> &coins,int idx,int amount,vector<vector<int>> &dp){
        if(amount==0){
            return 0;
        }
        if(idx==0){
            return INT_MAX;
        }
        if(dp[idx][amount]!=-1){
            return dp[idx][amount];
        }
        if(coins[idx-1]>amount){
            return dp[idx][amount]=miniCoinM(coins,idx-1,amount,dp);
        }
        return dp[idx][amount]=min(miniCoinM(coins,idx-1,amount,dp),1+miniCoinM(coins,idx,amount-coins[idx-1],dp));
    }
    long long int miniCoinT(vector<int> &coins,int total){
        vector<vector<long long int>> dp(coins.size()+1,vector<long long int>(total+1,-1));
        for(int amount=0;amount<=total;amount++){
            dp[0][amount]=INT_MAX;
        }
        for(int idx=0;idx<=coins.size();idx++){
            dp[idx][0]=0;
        }
        for(int idx=1;idx<=coins.size();idx++){
            for(int amount=1;amount<=total;amount++){
                if(coins[idx-1]>amount){
                    dp[idx][amount]=dp[idx-1][amount];
                }
                else{
                    dp[idx][amount]=min(dp[idx-1][amount],1+dp[idx][amount-coins[idx-1]]);
                }
            }
        }
        return dp[coins.size()][total];
    }
    long long int miniCoinO(vector<int> &coins,int total){
        vector<long long int> dp(total+1,INT_MAX),temp(total+1,INT_MAX);
        dp[0]=0;
        temp[0]=0;
        for(int idx=1;idx<=coins.size();idx++){
            for(int amount=1;amount<=total;amount++){
                if(coins[idx-1]>amount){
                    temp[amount]=dp[amount];
                }
                else{
                    temp[amount]=min(dp[amount],1+temp[amount-coins[idx-1]]);
                }
            }
            dp=temp;
        }
        return dp[total];
    }
    int coinChange(vector<int>& coins, int amount) {
        if(amount==0){
            return 0;
        }
        // long long int val=miniCoinR(coins,coins.size(),amount);

        // vector<vector<int>> dp(coins.size()+1,vector<int>(amount+1,-1));
        // long long int val=miniCoinM(coins,coins.size(),amount,dp);

        // long long int val=miniCoinT(coins,amount);

        long long int val=miniCoinO(coins,amount);

        if(val>=INT_MAX){
            return -1;
        }
        return val;
    }
};
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