 modular arithmetic || functional js 
IntuitionThe problem asks us to determine if two substrings, formed from the given string s, have the same sum when combined with a certain combinatorial functi
# Intuition
The problem asks us to determine if two substrings, formed from the given string `s`, have the same sum when combined with a certain combinatorial function. The idea here involves understanding how to efficiently calculate these sums using modular arithmetic and binomial coefficients modulo 5 and 10.

---

# Approach
1. **Binomial Coefficient Modulo Calculations:**  
   - Two helper functions are defined: `binomMod5` and `binomMod10`, which calculate binomial coefficients modulo 5 and 10, respectively.
     - `binomMod5` uses a precomputed table for binomial coefficients modulo 5, reducing computational complexity.
     - `binomMod10` utilizes both `binomMod5` and some additional conditions to compute the result modulo 10.
   
2. **Iterating Over Substrings:**  
   - We loop over all positions in the string `s` and compute a weighted sum of the digits using the binomial coefficient results.
   - We accumulate values `x` and `y` from the two substrings based on their weighted sums.

3. **Comparison:**  
   - If the two sums, `x` and `y`, are equal, return `true`. Otherwise, return `false`.

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# Complexity
- **Time complexity:**  
  $$O(n)$$ — Iterating through the string and performing constant-time binomial calculations for each digit.
  
- **Space complexity:**  
  $$O(1)$$ — Only a few integer variables and precomputed tables are used.

---

# Code
```javascript
const hasSameDigits = s => {
    const binomMod5 = (n, r) => {
        const table = [
            [1, 0, 0, 0, 0],
            [1, 1, 0, 0, 0],
            [1, 2, 1, 0, 0],
            [1, 3, 3, 1, 0],
            [1, 4, 1, 4, 1]
        ];
        let res = 1;
        while (n || r) {
            const n_digit = n % 5;
            const r_digit = r % 5;
            if (r_digit > n_digit) return 0;
            res = (res * table[n_digit][r_digit]) % 5;
            n = Math.floor(n / 5);
            r = Math.floor(r / 5);
        }
        return res;
    };

    const binomMod10 = (k, j) => {
        const r2 = ((j & ~k) === 0) ? 1 : 0;
        const r5 = binomMod5(k, j);
        return (5 * r2 + 6 * r5) % 10;
    };

    const n = s.length;
    const k = n - 2;
    let x = 0;
    let y = 0;

    for (let j = 0; j <= k; j++) {
        const c = binomMod10(k, j);
        x = (x + c * (s[j] - '0')) % 10;
        y = (y + c * (s[j + 1] - '0')) % 10;
    }

    return x === y;
};
```






['JavaScript']