add algo6.6~6.9

Author: oldherd

第六章代码.ipynb

@@ -64,7 +64,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
@@ -228,7 +228,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -282,13 +282,198 @@
     "                rec[i][j] = \"LU\"\n",
     "    return D[n][m], rec\n",
     "\n",
-    "\n",
     "if __name__ == '__main__':\n",
     "    s1 = \"kittcjen\"\n",
     "    s2 = \"kitchen\"\n",
     "    ans, rec = minimal_edit_distance(s1, s2)\n",
     "    print_MED(rec, s1, s2, len(s1), len(s2))"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 算法 6.6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2\n",
+      "[['L', 'L', 'L', 'L', 'L', 'L', 'L', 'L'], ['U', 'LU', 'L', 'L', 'L', 'L', 'L', 'L'], ['U', 'U', 'LU', 'L', 'L', 'L', 'L', 'L'], ['U', 'U', 'U', 'LU', 'L', 'L', 'L', 'L'], ['U', 'U', 'U', 'U', 'LU', 'L', 'L', 'L'], ['U', 'U', 'U', 'U', 'LU', 'L', 'L', 'L'], ['U', 'U', 'U', 'U', 'U', 'LU', 'L', 'L'], ['U', 'U', 'U', 'U', 'U', 'U', 'LU', 'L'], ['U', 'U', 'U', 'U', 'U', 'U', 'U', 'LU']]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def MED_scrolling_array(s : str, t : str):\n",
+    "    n = len(s)\n",
+    "    m = len(t)\n",
+    "    D = [[0 for _ in range(m + 1)] for __ in range(m + 1)]\n",
+    "    rec = [[0 for _ in range(m + 1)] for __ in range(n + 1)]\n",
+    "    for i in range(n + 1):\n",
+    "        rec[i][0] = \"U\"\n",
+    "    for j in range(m + 1):\n",
+    "        D[0][j] = j\n",
+    "        rec[0][j] = \"L\"\n",
+    "    \n",
+    "    for i in range(1, n + 1):\n",
+    "        id = i & 1\n",
+    "        D[id][0] = i\n",
+    "        for j in range(1, m + 1):\n",
+    "            ansDel = D[id ^ 1][j] + 1\n",
+    "            ansIns = D[id][j - 1] + 1\n",
+    "            ansRep = D[id ^ 1][j - 1] + (0 if s[i - 1] == t[j - 1] else 1)\n",
+    "            D[id][j] = min(ansDel, ansIns, ansRep)\n",
+    "            if D[id][j] == ansDel:\n",
+    "                rec[i][j] = \"U\"\n",
+    "            elif D[id][j] == ansIns:\n",
+    "                rec[i][j] = \"L\"\n",
+    "            else:\n",
+    "                rec[i][j] = \"LU\"\n",
+    "    return D[n & 1][m], rec\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    s1 = \"kittcjen\"\n",
+    "    s2 = \"kitchen\"\n",
+    "    ans, rec = MED_scrolling_array(s1, s2)\n",
+    "    print(ans)\n",
+    "    print(rec)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 算法 6.7"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "27\n",
+      "[2, 2, 6]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def rod_cutting(p, n):\n",
+    "    dp = [0 for _ in range(n + 1)]\n",
+    "    rec = [0 for _ in range(n + 1)]\n",
+    "    dp[0] = 0\n",
+    "    for i in range(1, n + 1):\n",
+    "        best = i\n",
+    "        for j in range(1, i):\n",
+    "            if p[best] + dp[i - best] < p[j] + dp[i - j]:\n",
+    "                best = j\n",
+    "        dp[i] = dp[i - best] + p[best]\n",
+    "        rec[i] = best\n",
+    "    \n",
+    "    solution = []\n",
+    "    p = n\n",
+    "    while p != 0:\n",
+    "        solution.append(rec[p])\n",
+    "        p -= rec[p]\n",
+    "\n",
+    "    return dp[n], solution\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    p = [0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 24]\n",
+    "    n = 10\n",
+    "    ans, solution = rod_cutting(p, n)\n",
+    "    print(ans)\n",
+    "    print(solution)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 算法 6.8"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2800\n"
+     ]
+    }
+   ],
+   "source": [
+    "def chain_of_matrix(p):\n",
+    "    n = len(p) - 1\n",
+    "    dp = [[(-1 if i != j else 0) for j in range(n + 1)] for i in range(n + 1)]\n",
+    "    for l in range(2, n + 1):\n",
+    "        for i in range(1, n - l + 2):\n",
+    "            j = i + l - 1\n",
+    "            for k in range(i, j):\n",
+    "                cur = dp[i][k] + dp[k + 1][j] + p[i - 1] * p[k] * p[j]\n",
+    "                if dp[i][j] == -1 or cur < dp[i][j]:\n",
+    "                    dp[i][j] = cur\n",
+    "                    rec[i][j] = k\n",
+    "    return dp[1][n], rec\n",
+    "\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    p = [40, 8, 30, 5]\n",
+    "    n = 3\n",
+    "    ans, rec = chain_of_matrix(p)\n",
+    "    print(ans)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 算法 6.9"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(M1)((M2)(M3))\n"
+     ]
+    }
+   ],
+   "source": [
+    "def print_matrix_chain(rec, U, n, i, j):\n",
+    "    if i == j:\n",
+    "        return U[i - 1]\n",
+    "    left = print_matrix_chain(rec, U, n, i, rec[i][j])\n",
+    "    right = print_matrix_chain(rec, U, n, rec[i][j] + 1, j)\n",
+    "    return ''.join(['(', left, ')(', right, ')'])\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    p = [40, 8, 30, 5]\n",
+    "    n = 3\n",
+    "    ans, rec = chain_of_matrix(p)\n",
+    "    U = [\"M1\", \"M2\", \"M3\"]\n",
+    "    solution = print_matrix_chain(rec, U, n, 1, n)\n",
+    "    print(solution)"
+   ]
   }
  ],
  "metadata": {