大数乘法，快速傅里叶变换FFT

A3.cpp

@@ -0,0 +1,74 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+const double PI(acos(-1.0));
+typedef complex<double> C;
+
+const int N = (1 << 17);
+int ans[N];
+C a[N], b[N];
+char s[N], t[N];
+
+void bit_reverse_swap(C *a, int n) {
+    for (int i = 1, j = n >> 1, k; i < n - 1; ++i) {
+        if (i < j) swap(a[i], a[j]);
+        for (k = n >> 1; j >= k; j -= k, k >>= 1)  // inspect the highest "1"
+            ;
+        j += k;
+    }
+}
+
+void FFT(C *a, int n, int t) {
+    bit_reverse_swap(a, n);
+    for (int i = 2; i <= n; i <<= 1) {
+        C wi(cos(2.0 * t * PI / i), sin(2.0 * t * PI / i));
+        for (int j = 0; j < n; j += i) {
+            C w(1);
+            for (int k = j, h = i >> 1; k < j + h; ++k) {
+                C t = w * a[k + h], u = a[k];
+                a[k] = u + t;
+                a[k + h] = u - t;
+                w *= wi;
+            }
+        }
+    }
+    if (t == -1) {
+        for (int i = 0; i < n; ++i) {
+            a[i] /= n;
+        }
+    }
+}
+
+int trans(int x) {
+    return 1 << int(ceil(log(x) / log(2) - 1e-9));  // math.h/log() 以e为底
+}
+
+int main() {
+    int n, m, l;
+    for (; ~scanf("%s%s", s, t);) {
+        n = strlen(s);
+        m = strlen(t);
+        l = trans(n + m - 1);  // n次*m次不超过n+m-1次
+        for (int i = 0; i < n; ++i) a[i] = C(s[n - 1 - i] - '0');
+        for (int i = n; i < l; ++i) a[i] = C(0);
+        for (int i = 0; i < m; ++i) b[i] = C(t[m - 1 - i] - '0');
+        for (int i = m; i < l; ++i) b[i] = C(0);
+
+        FFT(a, l, 1);  //把A和B换成点值表达
+        FFT(b, l, 1);
+        for (int i = 0; i < l; ++i)  //点值做乘法
+            a[i] *= b[i];
+        FFT(a, l, -1);  //逆DFT
+        for (int i = 0; i < l; ++i) ans[i] = (int) (a[i].real() + 0.5);
+        ans[l] = 0;  // error-prone :'l' -> '1'
+        for (int i = 0; i < l; ++i) {
+            ans[i + 1] += ans[i] / 10;
+            ans[i] %= 10;
+        }
+        int p = l;
+        for (; p && !ans[p]; --p);
+        for (; ~p; putchar(ans[p--] + '0'));
+        puts("");
+    }
+    return 0;
+}