<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 memo(int i, vector<int>&coins, int amt, vector<vector<int>>&dp){
          if(i==0){
            if(amt%coins[0]==0) return amt/coins[0];
            else return 1e9;
          }
          
          if(dp[i][amt]!=-1) return dp[i][amt];

          int notPick = 0 + memo(i-1, coins, amt, dp);
          int pick = INT_MAX;
          if(amt>=coins[i]){
                pick = 1 + memo(i, coins, amt-coins[i], dp);
          }
        

          return dp[i][amt] = min(pick, notPick);
          
    }


    int tab(vector<int>&coins, int amt){
        int n = coins.size();
        vector<vector<int>>dp(n, vector<int>(amt+1,-1));
        
        for(int a = 0 ; a<=amt ; a++){
            if(a%coins[0]==0) dp[0][a] = a/coins[0];
            else dp[0][a] = 1e9;
        }

        for(int i=1 ; i<n ; i++){
            for(int a=0 ; a<=amt ; a++){
              int notPick = 0 + dp[i-1][a];
              int pick = 1e9;
          if(a>=coins[i]){
                pick = 1 + dp[i][a-coins[i]];
          }
        

         dp[i][a] = min(pick, notPick);
            }
        }
        return dp[n-1][amt];
    }

    int spaceOpt(vector<int>&coins, int amt){
        int n = coins.size();
        vector<int>prev(amt+1,0);

        for(int i=0 ; i<=amt ; i++){
           if(i%coins[0]==0) prev[i] = i/coins[0];
            else prev[i] = 1e9;
        }
        
         for(int i=1 ; i<n ; i++){
            vector<int>curr(amt+1,0);
            for(int a=0 ; a<=amt ; a++){
              int notPick = 0 + prev[a];
              int pick = 1e9;
          if(a>=coins[i]){
                pick = 1 + curr[a-coins[i]];
          }
        

         curr[a] = min(pick, notPick);
            }
            prev = curr;
        }
        return prev[amt];


    }   


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