chore(CPlusPlus): add coin change problem (#552)

algorithms/CPlusPlus/Dynamic-Programming/coin-change-problem.cpp

@@ -0,0 +1,72 @@
+/*
+Coin Change Problem
+You are given an infinite supply of coins of each of denominations D = {D0, D1, D2, D3, ...... Dn-1}. 
+You need to figure out the total number of ways W, in which you can make a change for Value V using coins of denominations D.
+Note : Return 0, if change isn't possible.
+W can be pretty large so output the answer % mod(10^9 + 7)
+
+Input Format
+Line 1 : Integer n i.e. total number of denominations
+Line 2 : N integers i.e. n denomination values
+Line 3 : Value V
+
+Output Format
+For each test case print the number of ways (W) % mod(10^9 +7) in new line.
+
+Constraints:
+1 <= N <= 10
+1 <= V <= 5000
+
+Approach:
+1)sort the coins, this will reduce the time complexity.
+2)Using every coin count the number of ways of making total value V.
+
+Time Complexity: O(NV)
+Space Complexity: O(V)
+
+Input:
+3
+1 2 3
+9
+
+Output:
+12
+*/
+
+#include<iostream>
+#include<algorithm>
+using namespace std;
+
+const int mod = (int)1e9 + 7;
+
+int main() {
+
+    cout<<"Enter the total number of coin denominations: ";
+    int n;
+    cin >> n;
+    int *coins = new int[n];
+    for (int i = 0; i < n; i++) {
+        cin >> coins[i];
+    }
+
+    sort(coins, coins + n);
+
+    cout<<"Enter the target value: ";
+    int V;
+    cin >> V;
+
+    int dp[V + 1];
+    for (int i = 0; i <= V; i++)dp[i] = 0;
+
+    dp[0] = 1;
+
+    for (int i = 0; i < n; i++) {
+        for (int j = coins[i]; j <= V; j++) {
+            dp[j] = (dp[j] + dp[j - coins[i]]) % mod;
+        }
+    }
+    cout << "Total number of ways to make target value are: " << dp[V] << endl;
+
+    return 0;
+}
+

algorithms/CPlusPlus/README.md

@@ -26,6 +26,8 @@
 - [0/1-knapsack](Dynamic-Programming/01-knapsack.cpp)
 - [Matrix chain Multiplication](Dynamic-Programming/matrix-chain-multiplication.cpp)
 - [Edit Distance](Dynamic-Programming/edit-distance.cpp)
+- [Coin Change](Dynamic-Programming/coin-change-problem.cpp)
+
 
 ## Graphs
 - [Bellman Ford Algorithm](Graphs/bellman-ford.cpp)
@@ -134,3 +136,4 @@
 - [Sum of all elements of an array](Recursion/Sum-of-all-elements-in-an-array.cpp)
 - [Decimal number to Binary conversion](Recursion/decimal-to-binary-conversion.cpp)
 - [Sum of digits of a decimal integer](Recursion/sum-of-digits-of-an-integer.cpp)
+