From f68ee5e7ec6984dfbac0f8916df087bba4b4241e Mon Sep 17 00:00:00 2001
From: chayan das <110921638+Chayandas07@users.noreply.github.com>
Date: Mon, 11 Nov 2024 23:40:15 +0530
Subject: [PATCH] Create 2601. Prime Subtraction Operation

---
 2601. Prime Subtraction Operation | 36 +++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)
 create mode 100644 2601. Prime Subtraction Operation

diff --git a/2601. Prime Subtraction Operation b/2601. Prime Subtraction Operation
new file mode 100644
index 0000000..76708ab
--- /dev/null
+++ b/2601. Prime Subtraction Operation	
@@ -0,0 +1,36 @@
+const int N = 1000;
+vector<int> lp(N + 1);
+vector<int> pr;
+
+void linearSieve() {
+    for (int i = 2; i <= N; ++i) {
+        if (lp[i] == 0) {
+            lp[i] = i;
+            pr.push_back(i);
+        }
+        for (int j = 0; i * pr[j] <= N; ++j) {
+            lp[i * pr[j]] = pr[j];
+            if (pr[j] == lp[i]) {
+                break;
+            }
+        }
+    }
+}
+
+class Solution {
+public:
+    bool primeSubOperation(vector<int>& nums) {
+        int n = nums.size();
+        if (n == 1) return true;
+        linearSieve();
+        for (int i = n - 2; i >= 0; --i) {
+            if (nums[i] >= nums[i + 1]) {
+                int target = nums[i] - nums[i + 1] + 1;
+                auto it = lower_bound(pr.begin(), pr.end(), target);
+                if (it == pr.end() || *it >= nums[i]) return false;
+                nums[i] -= *it;
+            }
+        }
+        return true;
+    }
+};