Count Nice Pairs in an Array

Count Nice Pairs in an Array - Problem

You are given an array nums that consists of non-negative integers. Let us define rev(x) as the reverse of the non-negative integer x. For example, rev(123) = 321, and rev(120) = 21.

A pair of indices (i, j) is nice if it satisfies all of the following conditions:

0 <= i < j < nums.length
nums[i] + rev(nums[j]) == nums[j] + rev(nums[i])

Return the number of nice pairs of indices. Since that number can be too large, return it modulo 10⁹ + 7.

Input & Output

Example 1 — Basic Case

$ Input: nums = [42,11,1,97]

› Output: 2

💡 Note: The two nice pairs are (0,3) and (1,2). For (0,3): 42 + rev(97) = 42 + 79 = 121, and 97 + rev(42) = 97 + 24 = 121. For (1,2): 11 + rev(1) = 11 + 1 = 12, and 1 + rev(11) = 1 + 11 = 12.

Example 2 — Single Nice Pair

$ Input: nums = [13,10,35,24,76]

› Output: 4

💡 Note: Multiple pairs satisfy the nice condition when nums[i] - rev(nums[i]) equals nums[j] - rev(nums[j]).

Example 3 — No Nice Pairs

$ Input: nums = [123,456]

› Output: 1

💡 Note: 123 + rev(456) = 123 + 654 = 777, and 456 + rev(123) = 456 + 321 = 777. Since both sums are equal, this forms 1 nice pair. Using the difference approach: 123-321=-198, 456-654=-198, so they have the same difference and form 1 nice pair.

Constraints

1 ≤ nums.length ≤ 10⁵
0 ≤ nums[i] ≤ 10⁹

Visualization

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Asked in

F Facebook 25 G Google 18

The key insight is transforming the equation nums[i] + rev(nums[j]) = nums[j] + rev(nums[i]) into nums[i] - rev(nums[i]) = nums[j] - rev(nums[j]). Best approach uses hash map frequency counting. Time: O(n), Space: O(n)

Common Approaches

✓ Brute Force

⏱️ Time: O(n²) Space: O(1)

For each pair of indices (i,j) where i < j, calculate rev(nums[i]) and rev(nums[j]), then check if nums[i] + rev(nums[j]) equals nums[j] + rev(nums[i]). Count all valid pairs.

Hash Map with Frequency Count

⏱️ Time: O(n) Space: O(n)

The key insight is that nums[i] + rev(nums[j]) = nums[j] + rev(nums[i]) can be rearranged to nums[i] - rev(nums[i]) = nums[j] - rev(nums[j]). We calculate this difference for each number and count how many numbers have the same difference.

Brute Force — Algorithm Steps

Iterate through all pairs (i,j) where i < j
For each pair, reverse both numbers
Check if nums[i] + rev(nums[j]) == nums[j] + rev(nums[i])
Count valid pairs and return modulo 10^9 + 7

Visualization

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Step-by-Step Walkthrough

Check Pair (0,1)

nums[0] + rev(nums[1]) vs nums[1] + rev(nums[0])

Check Pair (0,2)

Continue with next pair

Count Valid

Increment counter for each nice pair found

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int reverseNum(int x) {
    int result = 0;
    while (x > 0) {
        result = result * 10 + x % 10;
        x /= 10;
    }
    return result;
}

int solution(int* nums, int numsSize) {
    const int MOD = 1000000007;
    long long count = 0;
    
    for (int i = 0; i < numsSize; i++) {
        for (int j = i + 1; j < numsSize; j++) {
            if (nums[i] + reverseNum(nums[j]) == nums[j] + reverseNum(nums[i])) {
                count = (count + 1) % MOD;
            }
        }
    }
    
    return (int)count;
}

void parseArray(const char* str, int* arr, int* size) {
    *size = 0;
    const char* p = str;
    while (*p && *p != '[') p++;
    if (*p == '[') p++;
    while (*p && *p != ']') {
        while (*p == ' ' || *p == ',') p++;
        if (*p == ']' || *p == '\0') break;
        arr[(*size)++] = (int)strtol(p, (char**)&p, 10);
    }
}

int main() {
    char line[100000];
    fgets(line, sizeof(line), stdin);
    
    int nums[1000];
    int count = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[count++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    printf("%d\n", solution(nums, count));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

Nested loops check all pairs - outer loop runs n times, inner loop runs up to n times

⚠ Quadratic Growth

Space Complexity

O(1)

Only uses constant extra variables for counting and calculations

✓ Linear Space

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Constraints

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Common Approaches

Brute Force — Algorithm Steps

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Code -

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