Added a file named 'digit_dp.cpp' that implements digit dynamic programming alogrithm in c++ language.

Dynamic Programming/digit dp/digit_dp.cpp

@@ -0,0 +1,64 @@
+#include "bits/stdc++.h" 
+using namespace std; 
+
+long long dp[20][180][2]; 
+
+long long getDigits(long long x, vector <int> &digit) 
+{ 
+	while (x) 
+	{ 
+		digit.push_back(x%10); 
+		x /= 10; 
+	} 
+} 
+
+long long digitSum(int idx, int sum, int tight, 
+						vector <int> &digit) 
+{ 
+	if (idx == -1) 
+	return sum; 
+
+	if (dp[idx][sum][tight] != -1 and tight != 1) 
+		return dp[idx][sum][tight]; 
+
+	long long ret = 0; 
+
+	int k = (tight)? digit[idx] : 9; 
+
+	for (int i = 0; i <= k ; i++) 
+	{ 
+		int newTight = (digit[idx] == i)? tight : 0; 
+
+		ret += digitSum(idx-1, sum+i, newTight, digit); 
+	} 
+
+	if (!tight) 
+	dp[idx][sum][tight] = ret; 
+
+	return ret; 
+} 
+
+int rangeDigitSum(int a, int b) 
+{ 
+	memset(dp, -1, sizeof(dp)); 
+
+	vector<int> digitA; 
+	getDigits(a-1, digitA); 
+
+	long long ans1 = digitSum(digitA.size()-1, 0, 1, digitA); 
+
+	vector<int> digitB; 
+	getDigits(b, digitB); 
+
+	long long ans2 = digitSum(digitB.size()-1, 0, 1, digitB); 
+
+	return (ans2 - ans1); 
+} 
+
+int main() 
+{ 
+	long long a = 123, b = 1024; 
+	cout << "digit sum for given range : "
+		<< rangeDigitSum(a, b) << endl; 
+	return 0; 
+}