Create 2400-number-of-ways-to-reach-a-position-after-exactly-k-steps.js

Author: everthis

2400-number-of-ways-to-reach-a-position-after-exactly-k-steps.js

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+/**
+ * @param {number} startPos
+ * @param {number} endPos
+ * @param {number} k
+ * @return {number}
+ */
+var numberOfWays = function(startPos, endPos, k) {
+  const ll = BigInt, mod = ll(1e9 + 7), N = 1005;
+
+  let fact, ifact, inv;
+  const comb_init = () => {
+      fact = Array(N).fill(0);
+      ifact = Array(N).fill(0);
+      inv = Array(N).fill(0);
+      fact[0] = ifact[0] = inv[1] = 1n;
+      for (let i = 2; i < N; i++) inv[i] = (mod - mod / ll(i)) * inv[mod % ll(i)] % mod;
+      for (let i = 1; i < N; i++) {
+          fact[i] = fact[i - 1] * ll(i) % mod;
+          ifact[i] = ifact[i - 1] * inv[i] % mod;
+      }
+  };
+
+  const comb = (n, k) => {
+      if (n < k || k < 0) return 0;
+      return fact[n] * ifact[k] % mod * ifact[n - k] % mod;
+  };
+
+  comb_init();
+  let res = 0n;
+  for (let i = 0; i <= k; i++) {
+      let moveRight = i, moveLeft = k - i;
+      if (startPos + moveRight - moveLeft == endPos) res += comb(k, i);
+  }
+  return res;
+  
+};