Implemented the Coin Change algorithm in R. (#170)

Author: Sachinn-64

dynamic_programming/coin_change.r

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+# Coin Change Problem
+#
+# The Coin Change problem finds the minimum number of coins needed to make a certain amount
+# using a given set of coin denominations.
+#
+# Time Complexity: O(amount * n) where n = number of coin denominations
+# Space Complexity: O(amount)
+#
+# Applications:
+# - Currency and cash management
+# - Making change in vending machines or payment systems
+# - Dynamic resource allocation
+# - Minimum cost problems in algorithms
+
+# Function to compute minimum coins required
+coin_change <- function(coins, amount) {
+  #' Compute minimum number of coins needed to make the given amount
+  #' @param coins: Numeric vector of coin denominations
+  #' @param amount: Total amount to make
+  #' @return: Minimum number of coins required, or -1 if not possible
+  
+  # Initialize DP array
+  dp <- rep(Inf, amount + 1)
+  dp[0 + 1] <- 0  # zero coins needed for amount 0
+  
+  for (i in 1:amount) {
+    for (coin in coins) {
+      if (coin <= i) {
+        dp[i + 1] <- min(dp[i + 1], 1 + dp[i - coin + 1])
+      }
+    }
+  }
+  
+  if (dp[amount + 1] == Inf) {
+    return(-1)
+  } else {
+    return(dp[amount + 1])
+  }
+}
+
+# Function to print the DP table (for educational purposes)
+print_coin_change_dp <- function(dp, amount) {
+  cat("DP Table for Coin Change:\n")
+  for (i in 0:amount) {
+    cat(sprintf("Amount %2d: %s\n", i, dp[i + 1]))
+  }
+  cat("\n")
+}
+
+
+# Example Usage & Testing
+cat("=== Coin Change Problem ===\n\n")
+
+# Test 1: Basic Example
+coins <- c(1, 2, 5)
+amount <- 11
+cat("Coins:", paste(coins, collapse = ", "), "\n")
+cat("Amount:", amount, "\n")
+min_coins <- coin_change(coins, amount)
+cat("Minimum Coins Needed:", min_coins, "\n\n")
+
+# Test 2: No solution case
+coins <- c(2, 4)
+amount <- 7
+cat("Coins:", paste(coins, collapse = ", "), "\n")
+cat("Amount:", amount, "\n")
+min_coins <- coin_change(coins, amount)
+cat("Minimum Coins Needed:", min_coins, "\n\n")
+
+# Test 3: Larger dataset
+coins <- c(1, 3, 4, 5)
+amount <- 7
+cat("Coins:", paste(coins, collapse = ", "), "\n")
+cat("Amount:", amount, "\n")
+min_coins <- coin_change(coins, amount)
+cat("Minimum Coins Needed:", min_coins, "\n\n")