MinStepTo1DP.cpp

#include <iostream>
using namespace std;

int minStepsHelper(int n, int *ans) {
	// Base case
	if(n <= 1) {
		return 0;
	}
	// Check if output already exists
	if(ans[n] != -1) {
		return ans[n];
	}
	// Calculate output
	int x = minStepsHelper(n - 1, ans);
	int y = INT_MAX, z = INT_MAX;
	if(n % 2 == 0) {
		y = minStepsHelper(n/2, ans);
	}
	if(n % 3 == 0) {
		z = minStepsHelper(n/3, ans);
	}
	int output = min(x, min(y, z)) + 1;
	// Save output for future use
	ans[n] = output;
	return output;
}

int minSteps(int n) {
	int *ans = new int[n+1];
	for(int i = 0; i <= n; i++) {
		ans[i] = -1;
	}
	return minStepsHelper(n, ans);
}

int main() {
	int n;
	cin >> n;

	cout << minSteps(n) << endl;
}

/*    USING RECURSION ONLY
int minSteps(int n) {
	// Base case
	if(n <= 1) {
		return 0;
	}
	// Recursive call
	int x = minSteps(n - 1);
	int y = INT_MAX, z = INT_MAX;
	if(n % 2 == 0) {
		y = minSteps(n/2);
	}

	if(n % 3 == 0) {
		z = minSteps(n/3);
	}

	// Calculate final output
	int ans = min(x, min(y, z)) + 1;

	return ans;

}
*/