Update coin_change_2.cpp

cpp/neetcode_150/14_2-d_dynamic_programming/coin_change_2.cpp

@@ -7,7 +7,7 @@
  Time: O(m x n)
  Space: O(m x n)
 */
-
+/*
 class Solution {
 public:
  int change(int amount, vector<int>& coins) {
@@ -37,3 +37,47 @@ class Solution {
  return dp[{i, sum}];
  }
 };
+*/
+// DP programming solution using a matrix
+/*
+class Solution {
+public:
+ int change(int amount, vector<int>& coins) {
+ vector<vector<int>> DP(coins.size() + 1, vector<int>(amount+1));
+ 
+ for (int i = 0; i < coins.size() + 1; ++i)
+ DP[i][0] = 1;
+
+ for (int i = 1; i <= coins.size(); ++i){
+ for (int j = 0; j <= amount; ++j){
+ DP[i][j] = DP[i-1][j];
+ if (j - coins[i-1] >= 0)
+ DP[i][j] += DP[i][j - coins[i-1]];
+ }
+ }
+
+ return DP[coins.size()][amount];
+ }
+};
+// O(m) space solution
+*/
+class Solution {
+public:
+ int change(int amount, vector<int>& coins) {
+ vector<int> prev(amount+1);
+ vector<int> curr(amount+1);
+
+ prev[0] = 1;
+
+ for (int i = 0; i < coins.size(); ++i){
+ for (int j = 0; j <= amount; ++j){
+ curr[j] = prev[j];
+ if (j - coins[i] >= 0)
+ curr[j] += curr[j - coins[i]];
+ }
+ prev = curr;
+ }
+
+ return curr[amount];
+ }
+};