feat : coin-change

Author: ekgns33

coin-change/ekgns33.java

@@ -0,0 +1,48 @@
+/*
+input : array of integers each element represents coins, single integer amount
+output : fewest number of coin to make up the amount
+constraint
+1) elements are positive?
+yes
+2) coins are in integer range?
+yes
+3) range of amoutn
+integer range?
+[0, 10^4]
+4) at least one valid answer exists?
+nope. if there no exist than return -1
+
+edge. case
+1) if amount == 0 return 0;
+
+ solution 1) top-down approach
+
+amount - each coin
+    until amount == 0
+    return min
+tc : O(n * k) when n is amount, k is unique coin numbers
+sc : O(n) call stack
+
+solution 2) bottom-up
+tc : O(n*k)
+sc : O(n)
+let dp[i] the minimum number of coins to make up amount i
+
+ */
+class Solution {
+  public int coinChange(int[] coins, int amount) {
+    //edge
+    if(amount == 0) return 0;
+    int[] dp = new int[amount+1];
+    dp[0] = 0;
+    for(int i = 1; i<= amount; i++) {
+      dp[i] = amount+1;
+      for(int coin: coins) {
+        if(i - coin >= 0) {
+          dp[i] = Math.min(dp[i], dp[i-coin] + 1);
+        }
+      }
+    }
+    return dp[amount] == amount+1 ? -1 : dp[amount];
+  }
+}