C Exercises: Colorful numbers

Last update on August 09 2025 12:46:50 (UTC/GMT +8 hours)

34. Colorful Number Test Subroutine Variants

A colorful number is a non-negative base 10 integer where the product of every sub group of consecutive digits is unique.
i.e.
24753 is a colorful number. 2, 4, 7, 5, 3, (2×4)8, (4×7)28, (7×5)35, (5×3)15, (2×4×7)56, (4×7×5)140, (7×5×3)105, (2×4×7×5)280, (4×7×5×3)420, (2×4×7×5×3)840
Every product is unique.
2346 is not a colorful number. 2, 3, 4, 6, (2×3)6, (3×4)12, (4×6)24, (2×3×4)48, (3×4×6)72, (2×3×4×6)14
The product 6 is repeated.
Single digit numbers are considered to be colorful. A colorful number larger than 9 cannot contain a repeated digit, the digit 0 or the digit 1. As a consequence, there is a firm upper limit for colorful numbers; no colorful number can have more than 8 digits.
Write a C program (subroutine, function, procedure, whatever it may be called in your language) to test if a number is a colorful number or not.
Use that routine to find all of the colorful numbers less than 100.
Use that routine to find the largest possible colorful number.

Sample Data:
Colorful numbers less than 100:
0 1 2 3 4 5 6 7 8 9
23 24 25 26 27 28 29 32 34 35
36 37 38 39 42 43 45 46 47 48
49 52 53 54 56 57 58 59 62 63
64 65 67 68 69 72 73 74 75 76
78 79 82 83 84 85 86 87 89 92
93 94 95 96 97 98

C Code:

//#Source shorturl.at/qvw79
#include <locale.h>
#include <stdbool.h>
#include <stdio.h>
#include <time.h>

bool colorful(int n) {
    // A colorful number cannot be greater than 98765432.
    if (n < 0 || n > 98765432)
        return false;
    int digit_count[10] = {};
    int digits[8] = {};
    int num_digits = 0;
    for (int m = n; m > 0; m /= 10) {
        int d = m % 10;
        if (n > 9 && (d == 0 || d == 1))
            return false;
        if (++digit_count[d] > 1)
            return false;
        digits[num_digits++] = d;
    }
    // Maximum number of products is (8 x 9) / 2.
    int products[36] = {};
    for (int i = 0, product_count = 0; i < num_digits; ++i) {
        for (int j = i, p = 1; j < num_digits; ++j) {
            p *= digits[j];
            for (int k = 0; k < product_count; ++k) {
                if (products[k] == p)
                    return false;
            }
            products[product_count++] = p;
        }
    }
    return true;
}

static int count[8];
static bool used[10];
static int largest = 0;

void count_colorful(int taken, int n, int digits) {
    if (taken == 0) {
        for (int d = 0; d < 10; ++d) {
            used[d] = true;
            count_colorful(d < 2 ? 9 : 1, d, 1);
            used[d] = false;
        }
    } else {
        if (colorful(n)) {
            ++count[digits - 1];
            if (n > largest)
                largest = n;
        }
        if (taken < 9) {
            for (int d = 2; d < 10; ++d) {
                if (!used[d]) {
                    used[d] = true;
                    count_colorful(taken + 1, n * 10 + d, digits + 1);
                    used[d] = false;
                }
            }
        }
    }
}

int main() {
    setlocale(LC_ALL, "");

    clock_t start = clock();

    printf("Colorful numbers less than 100:\n");
    for (int n = 0, count = 0; n < 100; ++n) {
        if (colorful(n))
            printf("%2d%c", n, ++count % 10 == 0 ? '\n' : ' ');
    }

    count_colorful(0, 0, 0);
    printf("\n\nLargest colorful number: %'d\n", largest);

    printf("\nCount of colorful numbers by number of digits:\n");
    int total = 0;
    for (int d = 0; d < 8; ++d) {
        printf("%d   %'d\n", d + 1, count[d]);
        total += count[d];
    }
    printf("\nTotal: %'d\n", total);

    clock_t end = clock();
    printf("\nElapsed time: %f seconds\n",
           (end - start + 0.0) / CLOCKS_PER_SEC);
    return 0;
}

Sample Output:

Colorful numbers less than 100:
 0  1  2  3  4  5  6  7  8  9
23 24 25 26 27 28 29 32 34 35
36 37 38 39 42 43 45 46 47 48
49 52 53 54 56 57 58 59 62 63
64 65 67 68 69 72 73 74 75 76
78 79 82 83 84 85 86 87 89 92
93 94 95 96 97 98 

Largest colorful number: 98,746,253

Count of colorful numbers by number of digits:
1   10
2   56
3   328
4   1,540
5   5,514
6   13,956
7   21,596
8   14,256

Total: 57,256

Elapsed time: 0.036510 seconds

Flowchart:

For more Practice: Solve these Related Problems:

Write a C program to test if a number is colorful and output "colorful" or "not colorful" based on product uniqueness.
Write a C program to generate a list of colorful numbers less than 100 and print them.
Write a C program to check a number's colorful property and list the products of all its contiguous digit subsequences.
Write a C program to implement a function that tests for colorful numbers and use it to filter a series of numbers.

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