colorful_number.txt

/*
Determine whether a number is colorful or not. 263 is a colorful number because (2,6,3,2x6,6x3,2x3x6) are all different whereas 236 is not because (2,3,6,2x3,3x6,2x3x6) have 6 twice. So take all consecutive subsets of digits, take their product and ensure all the products are different
Hard one, didn't do that at first. BUT NOTE: we make the length of the production[] as 10, this might be insufficient for some large input. Just for simplicity, we set the size as 10. 
*/


# include <stdio.h>
# include <string.h>
# define N 10

bool is_colorful(int num, int * production, int len){
	int i;
	// check [0.len-1]
	for(i = 0; i < len; i++){
		if(production[i] == num)
			return false;
	}
	// inseart [len]
	production[len] = num;
	return true;
}

int main(){
	// input
	char str[N]; // note: char, easy to input
	int production[N]; // note: int, easy to compute: record production
	printf("Please input an integer: ");
	gets(str);
    
	// check input
	int i;
	for(i = 0; i < strlen(str); i++){
		if(str[i] < '0' || str[i] > '9'){
			printf("Invalid input integer: %c.\n", str[i]);
			return -1;
		}
	}
	
	// calculate: all continue substr
	int j, k, len, num;
	len = 0;
	//  i: start index
	for(i = 0; i < strlen(str); i++){
		// j: substr length
		for(j = 1; j < strlen(str)+1 - i; j++){
			// k: continuous product
			num = 1;
			k = 0;
			while(k < j){
				num = num * (str[i + k] - '0'); // note: char -> int
				k++;
			}
			if(!is_colorful(num, production, len)){
				printf("%s is not colorful.\n", str);
				return 0;
			}
			len++;
		}
	}
	
	// output
	printf("%s is colorful.\n", str);

}




REMARK:
1. In the code, i is the start index, j is the length of the substring, k is used to get the product, len is the current index of the production[N].The idea is to store the production we get into the array production[N]. We get the production in this way:
EXAMPLE, given 236, we check in this order:
2
2*3
2*3*6
3
3*6
6
and then check if this value are in the production[N].

2 FOLLOWUP:
What if we get rid of the condition "consecutive" and change the problem into " So take all consecutive subsets of digits, take their product and ensure all the products are different". How should we do that?