<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 helper(int ind,int w,vector<int> &coins,vector<vector<int>> &dp){
    //     if(w == 0) return dp[ind][w] = 0;
    //     if(ind == 0){
    //         if(coins[0] == w) return dp[ind][w] = 1;
    //         else{
    //             if(w % coins[0] == 0) return dp[ind][w] = w / coins[0];
    //             return dp[ind][w] = -1;
    //         } 
    //     }
    //     if(dp[ind][w] != -2) return dp[ind][w];
    //     if(coins[ind] > w){
    //         return dp[ind][w] = helper(ind-1,w,coins,dp);
    //     }
    //     int pick_temp = helper(ind,w-coins[ind],coins,dp);
    //     int notpick = helper(ind-1,w,coins,dp);
    //     if(pick_temp == -1 && notpick == -1) return dp[ind][w] = -1;
    //     if(notpick == -1) return dp[ind][w] = 1 + pick_temp;
    //     if(pick_temp == -1) return dp[ind][w] = notpick;
    //     int pick = 1 + pick_temp;
    //     return dp[ind][w] = min(pick,notpick);  
    // }
    int coinChange(vector<int>& coins, int amount) {
        int n = coins.size();
        vector<int> dp(amount+1,-2);
        //helper(n-1,amount,coins,dp);
        dp[0] = 0;
        //for(int i = 0; i < n; i++) dp[i][0] = 0;
        for(int i = 0; i <= amount ; i++){
            if(i % coins[0] == 0) dp[i] = i / coins[0];
            else dp[i] = -1;
        }
        for(int i = 1; i < n; i++){
            vector<int> temp(amount+1,-2);
            for(int j = 0; j <= amount; j++){
                if(coins[i] > j){
                    temp[j] = dp[j];
                    continue;
                }
                int pick_temp = temp[j-coins[i]];
                int notpick = dp[j];
                if(pick_temp == -1 && notpick == -1) temp[j] = -1;
                else if(notpick == -1) temp[j] = 1 + pick_temp;
                else if(pick_temp == -1) temp[j] = notpick;
                else {
                    int pick = 1 + pick_temp;
                    temp[j] = min(pick,notpick);
                }

            }
            dp = temp;
        }
        return dp[amount];    
    }
};
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