Completed DP1

src/CoinChange.java

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+/*
+COIN CHANGE I (LeetCode 322)
+
+Problem:
+Given coin denominations and a target amount, return the minimum number of coins
+required to make that amount. If it is not possible, return -1.
+
+This class demonstrates FOUR different approaches to solve the problem,
+starting from brute force recursion and gradually optimizing to Dynamic Programming.
+
+Approaches implemented:
+1. Pure Recursive (Brute Force)            -> Exponential Time
+2. Top-Down DP (Recursion + Memoization)  -> O(coins * amount)
+3. Bottom-Up DP (2D Table)                -> O(coins * amount)
+4. Bottom-Up DP (1D Optimized)             -> O(coins * amount), Space O(amount)
+*/
+
+public class CoinChange {
+
+    // Used for memoization in Top-Down DP
+    int[][] memo;
+
+    /*1. PURE RECURSIVE SOLUTION (BRUTE FORCE)
+       Try all possibilities:
+       - Either skip the current coin
+       - Or take the current coin and reduce the amount
+       Time Complexity: Exponential (very slow)
+       Space Complexity: Recursion stack
+    */
+    public int recursiveCoinChange(int[] coins, int amount) {
+        int result = recursiveHelper(coins, amount, 0);
+        return (result >= Integer.MAX_VALUE - 10) ? -1 : result;
+    }
+
+    private int recursiveHelper(int[] coins, int amount, int idx) {
+        // Base cases
+        if (amount == 0) return 0;
+        if (idx == coins.length || amount < 0) return Integer.MAX_VALUE - 10;
+
+        // Choice 1: Do not take current coin
+        int notChoose = recursiveHelper(coins, amount, idx + 1);
+
+        // Choice 2: Take current coin (unbounded)
+        int choose = recursiveHelper(coins, amount - coins[idx], idx);
+
+        return Math.min(notChoose, choose);
+    }
+
+    /* 2. TOP-DOWN DP (MEMOIZATION)
+       Same recursive logic, but we store results for each state
+       (idx, amount) to avoid recomputation.
+       Time Complexity: O(coins * amount)
+       Space Complexity: O(coins * amount)
+    */
+    public int coinChangeTopDown(int[] coins, int amount) {
+        memo = new int[coins.length][amount + 1];
+        int result = topDownHelper(coins, amount, 0);
+        return (result >= Integer.MAX_VALUE - 10) ? -1 : result;
+    }
+
+    private int topDownHelper(int[] coins, int amount, int idx) {
+        if (amount == 0) return 0;
+        if (idx == coins.length || amount < 0) return Integer.MAX_VALUE - 10;
+
+        if (memo[idx][amount] != 0) {
+            return memo[idx][amount];
+        }
+
+        int notChoose = topDownHelper(coins, amount, idx + 1);
+        int choose = 1 + topDownHelper(coins, amount - coins[idx], idx);
+
+        memo[idx][amount] = Math.min(notChoose, choose);
+        return memo[idx][amount];
+    }
+
+    /* 3. BOTTOM-UP DP (2D TABLE)
+       dp[i][j] = minimum coins needed to make amount j
+                  using first i coin types
+       Time Complexity: O(coins * amount)
+       Space Complexity: O(coins * amount)
+    */
+    public int coinChange2D(int[] coins, int amount) {
+        int m = coins.length;
+        int INF = 99999;
+
+        int[][] dp = new int[m + 1][amount + 1];
+
+        // Base case: no coins, positive amount impossible
+        for (int j = 1; j <= amount; j++) {
+            dp[0][j] = INF;
+        }
+
+        // Fill DP table
+        for (int i = 1; i <= m; i++) {
+            for (int j = 0; j <= amount; j++) {
+                if (j < coins[i - 1]) {
+                    dp[i][j] = dp[i - 1][j]; // cannot take coin
+                } else {
+                    dp[i][j] = Math.min(
+                            dp[i - 1][j],               // skip coin
+                            1 + dp[i][j - coins[i - 1]] // take coin
+                    );
+                }
+            }
+        }
+
+        return dp[m][amount] == INF ? -1 : dp[m][amount];
+    }
+
+    /* 4. BOTTOM-UP DP (1D OPTIMIZED)
+       dp[j] = minimum coins needed to make amount j
+       Optimizes space by reusing previous results.
+       Time Complexity: O(coins * amount)
+       Space Complexity: O(amount)
+    */
+    public int coinChange1D(int[] coins, int amount) {
+        int INF = 99999;
+        int[] dp = new int[amount + 1];
+
+        dp[0] = 0;
+        for (int j = 1; j <= amount; j++) {
+            dp[j] = INF;
+        }
+
+        for (int coin : coins) {
+            for (int j = coin; j <= amount; j++) {
+                dp[j] = Math.min(dp[j], 1 + dp[j - coin]);
+            }
+        }
+
+        return dp[amount] == INF ? -1 : dp[amount];
+    }
+}

src/HouseRobber.java

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+/*
+HOUSE ROBBER (LeetCode 198)
+
+Problem:
+Given an array where each element represents money in a house,
+find the maximum amount you can rob without robbing two adjacent houses.
+
+This class demonstrates MULTIPLE approaches, starting from brute force
+and gradually optimizing to Dynamic Programming.
+
+Approaches implemented:
+1. Pure Recursive (Exhaustive Decision Tree)
+2. Top-Down DP (Recursion + Memoization)
+3. Bottom-Up DP (1D Array)
+4. Bottom-Up DP (O(1) Space Optimized)
+*/
+
+public class HouseRobber {
+
+    // Used for memoization in Top-Down DP
+    private int[] memo;
+
+    /* 1. PURE RECURSIVE SOLUTION (BRUTE FORCE)
+       At each house:
+       - Either rob it and skip next
+       - Or skip it and move to next
+
+       Time Complexity: O(2^n)
+       Space Complexity: O(n) recursion stack
+    */
+    public int robRecursive(int[] nums) {
+        return robHelper(nums, 0);
+    }
+
+    private int robHelper(int[] nums, int index) {
+        // Base case: out of bounds
+        if (index >= nums.length) return 0;
+
+        // Choice 1: Do not rob current house
+        int skip = robHelper(nums, index + 1);
+
+        // Choice 2: Rob current house
+        int rob = nums[index] + robHelper(nums, index + 2);
+
+        return Math.max(skip, rob);
+    }
+
+    /*2. TOP-DOWN DP (MEMOIZATION)
+       Same recursion, but store results to avoid recomputation.
+
+       Time Complexity: O(n)
+       Space Complexity: O(n)
+    */
+    public int robTopDown(int[] nums) {
+        memo = new int[nums.length];
+        return robHelperMemo(nums, 0);
+    }
+
+    private int robHelperMemo(int[] nums, int index) {
+        if (index >= nums.length) return 0;
+
+        if (memo[index] != 0) return memo[index];
+
+        int skip = robHelperMemo(nums, index + 1);
+        int rob = nums[index] + robHelperMemo(nums, index + 2);
+
+        memo[index] = Math.max(skip, rob);
+        return memo[index];
+    }
+
+    /* 3. BOTTOM-UP DP (1D ARRAY)
+       dp[i] = maximum money that can be robbed up to house i
+       Transition:
+       dp[i] = max(dp[i-1], nums[i] + dp[i-2])
+
+       Time Complexity: O(n)
+       Space Complexity: O(n)
+    */
+    public int robBottomUp(int[] nums) {
+        int n = nums.length;
+        if (n == 0) return 0;
+        if (n == 1) return nums[0];
+
+        int[] dp = new int[n];
+        dp[0] = nums[0];
+        dp[1] = Math.max(nums[0], nums[1]);
+
+        for (int i = 2; i < n; i++) {
+            dp[i] = Math.max(dp[i - 1], nums[i] + dp[i - 2]);
+        }
+
+        return dp[n - 1];
+    }
+
+    /* 4. BOTTOM-UP DP (SPACE OPTIMIZED)
+       Uses only two variables instead of dp array.
+       Time Complexity: O(n)
+       Space Complexity: O(1)
+    */
+    public int robOptimized(int[] nums) {
+        int prev2 = 0; // dp[i-2]
+        int prev1 = 0; // dp[i-1]
+
+        for (int money : nums) {
+            int curr = Math.max(prev1, prev2 + money);
+            prev2 = prev1;
+            prev1 = curr;
+        }
+
+        return prev1;
+    }
+}

src/TestDP1.java

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+import java.util.Arrays;
+
+public class TestDP1 {
+    public static void main(String[] args) {
+
+        CoinChange cc = new CoinChange();
+
+        int[][] coinsList = {
+                {1, 2, 5},
+                {2},
+                {1},
+                {1, 3, 4}
+        };
+        int[] amounts = {11, 3, 0, 6};
+        int[] expectedCC = {3, -1, 0, 2};
+
+        for (int i = 0; i < coinsList.length; i++) {
+            int r1 = cc.recursiveCoinChange(coinsList[i], amounts[i]);
+            int r2 = cc.coinChangeTopDown(coinsList[i], amounts[i]);
+            int r3 = cc.coinChange2D(coinsList[i], amounts[i]);
+            int r4 = cc.coinChange1D(coinsList[i], amounts[i]);
+
+            System.out.println(
+                    r1 == expectedCC[i] &&
+                            r2 == expectedCC[i] &&
+                            r3 == expectedCC[i] &&
+                            r4 == expectedCC[i]
+            );
+        }
+        System.out.println("Testing House Robber");
+
+        HouseRobber hr = new HouseRobber();
+
+        int[][] robberTests = {
+                {2, 7, 9, 3, 1},
+                {1, 2, 3, 1},
+                {2, 1, 1, 2},
+                {1},
+                {}
+        };
+
+        int[] expectedHR = {12, 4, 4, 1, 0};
+
+        for (int i = 0; i < robberTests.length; i++) {
+            int a = hr.robRecursive(robberTests[i]);
+            int b = hr.robTopDown(robberTests[i]);
+            int c = hr.robBottomUp(robberTests[i]);
+            int d = hr.robOptimized(robberTests[i]);
+
+            System.out.println(
+                    a == expectedHR[i] &&
+                            b == expectedHR[i] &&
+                            c == expectedHR[i] &&
+                            d == expectedHR[i]
+            );
+        }
+    }
+}