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+// 3116. Kth Smallest Amount With Single Denomination Combination
+#include "leetcode.h"
+
+/*
+ * you are given an integer array 'coins' representing coins of different
+ * denominations and an integer 'k'. you have an infinite number of coins of
+ * each denomination. however, you are not allowed to combine coins of different
+ * denominations. return the k'th smallest amount that can be made using these
+ * coins.
+ */
+
+int gcd(int a, int b) { return !b ? a : gcd(b, a % b); }
+
+int lcm(int a, int b) { return a / gcd(a, b) * b; }
+
+int cnt(int *coins, int coinsSize, int x) {
+ int sum = 0;
+ for (int mask = 1; mask < (1 << coinsSize); mask++) {
+ int bits = __builtin_popcountll(mask);
+ int least_common = 1;
+ for (int j = 0; j < coinsSize; j++)
+ if (mask & (1 << j))
+ least_common = lcm(least_common, coins[j]);
+ if (bits & 1)
+ sum += x / least_common;
+ else
+ sum -= x / least_common;
+ }
+ return sum;
+}
+
+int bin_search(int *coins, int coinsSize, int k) {
+ int left = 1, right = 25LL * 2e9;
+ while (left < right) {
+ int mid = left + (right - left) / 2;
+ if (cnt(coins, coinsSize, mid) < k)
+ left = mid + 1;
+ else
+ right = mid;
+ }
+ return left;
+}
+
+long long findKthSmallest(int *coins, int coinsSize, int k) {
+ return bin_search(coins, coinsSize, k);
+}
+
+int main() {
+ int c1[] = {3, 6, 9}, c2[] = {5, 2};
+ printf("%lld\n", findKthSmallest(c1, ARRAY_SIZE(c1), 3)); // expect: 9
+ printf("%lld\n", findKthSmallest(c2, ARRAY_SIZE(c2), 7)); // expect: 12
+}