Created add-digit-dp-problem.java (#362)

Here's a solution to the open issue add digit dp problem

Author: Aman5989

Add-digit-dp-problem.java

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+
+import java.util.ArrayList;
+
+import java.util.Arrays;
+ 
+// Given two integers a and b. The task is to print
+// sum of all the digits appearing in the
+// integers between a and b
+
+public class AMAN {
+ 
+
+    // Memoization for the state results
+
+    static long dp[][][] = new long[20][180][2];
+ 
+
+    // Stores the digits in x in a vector digit
+
+    static void getDigits(long x, ArrayList<Integer> digit)
+
+    {
+
+        while (x != 0) {
+
+            digit.add((int)(x % 10));
+
+            x /= 10;
+
+        }
+
+    }
+ 
+
+    // Return sum of digits from 1 to integer in
+
+    // digit vector
+
+    static long digitSum(int idx, int sum, int tight,
+
+                         ArrayList<Integer> digit)
+
+    {
+
+        // base case
+
+        if (idx == -1)
+
+            return sum;
+ 
+
+        // checking if already calculated this state
+
+        if (dp[idx][sum][tight] != -1 && tight != 1)
+
+            return dp[idx][sum][tight];
+ 
+
+        long ret = 0;
+ 
+
+        // calculating range value
+
+        int k = (tight != 0) ? digit.get(idx) : 9;
+ 
+
+        for (int i = 0; i <= k; i++) {
+
+            // calculating newTight value for next state
+
+            int newTight
+
+                = (digit.get(idx) == i) ? tight : 0;
+ 
+
+            // fetching answer from next state
+
+            ret += digitSum(idx - 1, sum + i, newTight,
+
+                            digit);
+
+        }
+ 
+
+        if (tight != 0)
+
+            dp[idx][sum][tight] = ret;
+ 
+
+        return ret;
+
+    }
+ 
+
+    // Returns sum of digits in numbers from a to b.
+
+    static int rangeDigitSum(int a, int b)
+
+    {
+
+        // initializing dp with -1
+
+        for (int i = 0; i < 20; i++)
+
+            for (int j = 0; j < 180; j++)
+
+                for (int k = 0; k < 2; k++)
+
+                    dp[i][j][k] = -1;
+ 
+
+        // storing digits of a-1 in digit vector
+
+        ArrayList<Integer> digitA
+
+            = new ArrayList<Integer>();
+
+        getDigits(a - 1, digitA);
+ 
+
+        // Finding sum of digits from 1 to "a-1" which is
+
+        // passed as digitA.
+
+        long ans1
+
+            = digitSum(digitA.size() - 1, 0, 1, digitA);
+ 
+
+        // Storing digits of b in digit vector
+
+        ArrayList<Integer> digitB
+
+            = new ArrayList<Integer>();
+
+        getDigits(b, digitB);
+ 
+
+        // Finding sum of digits from 1 to "b" which is
+
+        // passed as digitB.
+
+        long ans2
+
+            = digitSum(digitB.size() - 1, 0, 1, digitB);
+ 
+
+        return (int)(ans2 - ans1);
+
+    }
+ 
+
+    // driver function to call above function
+
+    public static void main(String[] args)
+
+    {
+
+        int a = 123, b = 1024;
+
+        System.out.println("digit sum for given range : "
+
+                           + rangeDigitSum(a, b));
+
+    }
+}