Update manhattan-distances-of-all-arrangements-of-pieces.cpp

kamyu104 · Jan 20, 2025 · 11eb3ca · 11eb3ca
1 parent b677454
commit 11eb3ca
Showing 1 changed file with 35 additions and 35 deletions.
diff --git a/C++/manhattan-distances-of-all-arrangements-of-pieces.cpp b/C++/manhattan-distances-of-all-arrangements-of-pieces.cpp
@@ -4,9 +4,44 @@
 
 // combinatorics
 static const uint32_t MOD = 1e9 + 7;
+
+uint32_t addmod(uint32_t a, uint32_t b) {  // avoid overflow
+    a %= MOD, b %= MOD;
+    if (MOD - a <= b) {
+        b -= MOD;  // relied on unsigned integer overflow in order to give the expected results
+    }
+    return a + b;
+}
+
+// reference: https://stackoverflow.com/questions/12168348/ways-to-do-modulo-multiplication-with-primitive-types
+uint32_t mulmod(uint32_t a, uint32_t b)  {  // avoid overflow
+    a %= MOD, b %= MOD;
+    uint32_t result = 0;
+    if (a < b) {
+        swap(a, b);
+    }
+    while (b > 0)  { 
+        if (b & 1) {
+            result = addmod(result, a);
+        }
+        a = addmod(a, a);
+        b >>= 1;
+    } 
+    return result; 
+} 
+
 vector<int> FACT = {1, 1};
 vector<int> INV = {1, 1};
 vector<int> INV_FACT = {1, 1};
+int nCr(int n, int k) {
+    while (size(INV) <= n) {  // lazy initialization
+        FACT.emplace_back(mulmod(FACT.back(), size(INV)));
+        INV.emplace_back(mulmod(INV[MOD % size(INV)], MOD - MOD / size(INV)));  // https://cp-algorithms.com/algebra/module-inverse.html
+        INV_FACT.emplace_back(mulmod(INV_FACT.back(), INV.back()));
+    }
+    return mulmod(mulmod(FACT[n], INV_FACT[n - k]), INV_FACT[k]);
+}
+
 class Solution {
 public:
     int distanceSum(int m, int n, int k) {
@@ -27,39 +62,4 @@ class Solution {
         const auto y = mulmod(mulmod(f(m) % MOD, n), n);
         return mulmod(x + y, nCr(m * n - 2, k - 2));
     }
-
-private:
-    int nCr(int n, int k) {
-        while (size(INV) <= n) {  // lazy initialization
-            FACT.emplace_back(mulmod(FACT.back(), size(INV)));
-            INV.emplace_back(mulmod(INV[MOD % size(INV)], MOD - MOD / size(INV)));  // https://cp-algorithms.com/algebra/module-inverse.html
-            INV_FACT.emplace_back(mulmod(INV_FACT.back(), INV.back()));
-        }
-        return mulmod(mulmod(FACT[n], INV_FACT[n - k]), INV_FACT[k]);
-    }
-
-    uint32_t addmod(uint32_t a, uint32_t b) {  // avoid overflow
-        a %= MOD, b %= MOD;
-        if (MOD - a <= b) {
-            b -= MOD;  // relied on unsigned integer overflow in order to give the expected results
-        }
-        return a + b;
-    }
-
-    // reference: https://stackoverflow.com/questions/12168348/ways-to-do-modulo-multiplication-with-primitive-types
-    uint32_t mulmod(uint32_t a, uint32_t b)  {  // avoid overflow
-        a %= MOD, b %= MOD;
-        uint32_t result = 0;
-        if (a < b) {
-            swap(a, b);
-        }
-        while (b > 0)  { 
-            if (b & 1) {
-                result = addmod(result, a);
-            }
-            a = addmod(a, a);
-            b >>= 1;
-        } 
-        return result; 
-    } 
 };