@@ -0,0 +1,65 @@
+const MOD = BigInt(1e9 + 7);
+
+var countBalancedPermutations = function (num) {
+let tot = 0;
+const n = num.length;
+const cnt = new Array(10).fill(0);
+
+// Count the frequency of each digit in num
+for (const ch of num) {
+const d = parseInt(ch);
+cnt[d]++;
+tot += d; // Total sum of digits
+}
+
+// If the total sum is odd, we cannot divide it into two equal parts
+if (tot % 2 !== 0) {
+return 0;
+}
+
+const target = tot / 2; // Half of the total sum
+const maxOdd = Math.floor((n + 1) / 2); // Maximum possible odd positions
+
+// Precompute binomial coefficients using Pascal's triangle
+const comb = new Array(maxOdd + 1);
+for (let i = 0; i <= maxOdd; i++) {
+comb[i] = new Array(maxOdd + 1).fill(0n);
+comb[i][i] = comb[i][0] = 1n;
+for (let j = 1; j < i; j++) {
+comb[i][j] = (comb[i - 1][j] + comb[i - 1][j - 1]) % MOD;
+}
+}
+
+// DP table to store results: f[curr][oddCnt] is the number of ways to get sum 'curr' with 'oddCnt' odd digits
+const f = new Array(Number(target) + 1);
+for (let i = 0; i <= Number(target); i++) {
+f[i] = new Array(maxOdd + 1).fill(0n);
+}
+f[0][0] = 1n;
+
+let psum = 0, totSum = 0;
+
+// Loop through each digit from 0 to 9
+for (let i = 0; i <= 9; i++) {
+psum += cnt[i]; // Sum of the number of digits <= i
+totSum += i * cnt[i]; // Total sum of digits <= i
+
+// Try all combinations of odd and even positioned digits
+for (let oddCnt = Math.min(psum, maxOdd); oddCnt >= Math.max(0, psum - (n - maxOdd)); oddCnt--) {
+const evenCnt = psum - oddCnt;
+
+for (let curr = Math.min(totSum, target); curr >= Math.max(0, totSum - target); curr--) {
+let res = 0n;
+// Try all valid splits of the current digit into odd and even positions
+for (let j = Math.max(0, cnt[i] - evenCnt); j <= Math.min(cnt[i], oddCnt) && i * j <= curr; j++) {
+const ways = (comb[oddCnt][j] * comb[evenCnt][cnt[i] - j]) % MOD;
+res = (res + ((ways * f[curr - i * j][oddCnt - j]) % MOD)) % MOD;
+}
+f[curr][oddCnt] = res % MOD;
+}
+}
+}
+
+// Return the result for the target sum with the maximum number of odd digits
+return Number(f[target][maxOdd]);
+};