3550. Smallest Index With Digit Sum Equal to Index

3550. Smallest Index With Digit Sum Equal to Index

Difficulty: Easy

Topics: Mid Level, Array, Math, Weekly Contest 450

You are given an integer array nums.

Return the smallest index i such that the sum of the digits of nums[i] is equal to i.

If no such index exists, return -1.

Example 1:

• Input: nums = [1,3,2]
• Output: 2
• Explanation: For nums[2] = 2, the sum of digits is 2, which is equal to index i = 2. Thus, the output is 2.

Example 2:

• Input: nums = [1,10,11]
• Output: 1
• Explanation:
  • For nums[1] = 10, the sum of digits is 1 + 0 = 1, which is equal to index i = 1.
  • For nums[2] = 11, the sum of digits is 1 + 1 = 2, which is equal to index i = 2.
  • Since index 1 is the smallest, the output is 1.

Example 3:

• Input: nums = [1,2,3]
• Output: -1
• Explanation: Since no index satisfies the condition, the output is -1.

Example 4:

• Input: nums = [0]
• Output: 0

Example 5:

• Input: nums = [0, 1]
• Output: 0

Example 6:

• Input: nums = [9, 10]
• Output: 1

Example 7:

• Input: nums = [5, 6, 7, 8, 9, 10]
• Output: 5

Example 8:

• Input: nums = [1000]
• Output: -1

Constraints:

• 1 <= nums.length <= 100
• 0 <= nums[i] <= 1000

Hint:

1. Simulate as described

Solution:

We scan the array from left to right, compute the sum of digits for each nums[i], and return the first index i where that digit sum equals i. If no index satisfies the condition, we return -1.

Approach

• Iterate through nums using foreach ($nums as $i => $num).
• For each number, compute its digit sum by repeatedly taking % 10 and dividing by 10.
• Compare the computed digit sum with the current index i.
• Return i immediately when a match is found, because scanning left-to-right guarantees the smallest index.
• If the loop finishes without a match, return -1.

Let's implement this solution in PHP: 3550. Smallest Index With Digit Sum Equal to Index

<?php
/**
 * @param Integer[] $nums
 * @return Integer
 */
function smallestIndex(array $nums): int
{
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Test cases
echo smallestIndex([1,3,2]) .  "\n";                    // Output: 2
echo smallestIndex([1,10,11]) .  "\n";                  // Output: 1
echo smallestIndex([1,2,3]) .  "\n";                    // Output: -1
echo smallestIndex([0]) .  "\n";                        // Output: 0
echo smallestIndex([0,1]) .  "\n";                      // Output: 0
echo smallestIndex([9,10]) .  "\n";                     // Output: 1
echo smallestIndex([5, 6, 7, 8, 9, 10]) .  "\n";        // Output: 5
echo smallestIndex([1000]) .  "\n";                     // Output: -1
?>

Explanation:

• Index i starts from 0.
• For a number like 10, the digit sum is 1 + 0 = 1.
• For nums[i] = 0, the digit sum is 0, which is handled correctly because the while ($x > 0) loop simply does not run.
• Since we return on the first valid index, no extra comparison or storage is needed.

Complexity Analysis

• Time Complexity: O(n * d), where n is the length of nums and d is the maximum number of digits in nums[i]. Since nums[i] <= 1000, d <= 4, so this is effectively O(n).
• Space Complexity: O(1), because only a few integer variables are used.

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