Added Dynamic Programming (Coin Change)

coin_change_dynamic_programming.cpp

@@ -0,0 +1,68 @@
+#include "bits/stdc++.h"
+using namespace std;
+
+typedef long long ll;
+typedef long double ld;
+#define blue ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
+#define mod 1000000007;
+
+/*
+
+Probelm Statement:
+    Given: A value N and some coins of marked denominations
+    Task: Count the number of ways to make change for the value N using these coins.
+    Conditions: You have infinite supply of coins of given denominations
+
+
+Solution:
+    Initially you have to make a value N using coins (c1, c2, .., cx)
+    where x = number of diffrent coins
+
+    Approach:
+        Either you select a specific coin or reject it,
+        if you select (N = N-coin(i) ) you can select again or may reject the second time (Remember infinite supply of coins)
+
+        if you reject a coin you move to next coin, this goes on untill your value to make i.e. N = 0
+                                    OR
+        You stop if you have tried all the coins
+*/
+
+int dp[1000][1000];
+
+int coin_change_dp(int coins[], int X, int N) {
+
+    for(int i=0;i<X;i++) dp[0][i]=1; //Initializing the preconditions
+
+    int include=0, exclude=0;
+
+    for(int i=1;i<=N;i++) { // Iterate for all values of N
+
+        for(int j=0;j<X;j++) { // Iterate for all the coins 
+
+            include=0,exclude=0;
+            if(i - coins[j] >= 0 ) include = dp[i-coins[j]][j]; // Count if we include coin number j (i.e. coins[j])
+
+            if(j >= 1) exclude = dp[i][j-1]; // Count if we exclude coin number j (i.e. coins[j])
+
+            dp[i][j] = include + exclude; // Total count is include + exclude
+        }
+    }
+    return dp[N][X-1];
+}
+
+int main() {
+    int N = 15; // Value to make change with coins
+
+    int X = 3; // Number of diffrent coins
+
+    int coins[] = {1, 2, 3}; // Values of coins
+
+    int total_number_of_ways_to_make_coin_change;
+
+    memset(dp,-1,sizeof(dp)); // Initializing the DP array with -1's
+
+    total_number_of_ways_to_make_coin_change = coin_change_dp(coins,X, N);
+
+    cout<<"The total number of ways to exchange "<<N<<" are: "<<total_number_of_ways_to_make_coin_change<<endl;
+}
+