{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "07b6a432",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\anaconda3\\Lib\\site-packages\\nxviz\\__init__.py:18: UserWarning: \n",
      "nxviz has a new API! Version 0.7.4 onwards, the old class-based API is being\n",
      "deprecated in favour of a new API focused on advancing a grammar of network\n",
      "graphics. If your plotting code depends on the old API, please consider\n",
      "pinning nxviz at version 0.7.4, as the new API will break your old code.\n",
      "\n",
      "To check out the new API, please head over to the docs at\n",
      "https://ericmjl.github.io/nxviz/ to learn more. We hope you enjoy using it!\n",
      "\n",
      "(This deprecation message will go away in version 1.0.)\n",
      "\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import nxviz as nv \n",
    "\n",
    "def drawRNA(s,bps):\n",
    "    nodes = [(i, {\"nt\":s[i],\"label\":\"s\"}) for i in range(len(s))]\n",
    "    ax = plt.figure(figsize=(20,6))\n",
    "    G = nx.Graph()\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(bps)\n",
    "    nv.arc(G, node_color_by=\"nt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4204d2d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawRNA(\"AACCUUUGGA\",[(2,8),(3,7)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8dc10817",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'..((...)).'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def displaySS(bps, n):\n",
    "    l = [\".\" for i in range(n)]\n",
    "    for (i,j) in bps:\n",
    "        (l[i],l[j]) = (\"(\",\")\")\n",
    "    return \"\".join(l)\n",
    "\n",
    "ss = displaySS([(2,8),(3,7)],10)\n",
    "drawRNA(ss,[(2,8),(3,7)])\n",
    "ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c8e29a7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([(3, 7), (1, 8), (0, 9)], 10)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def parseSS(ss):\n",
    "    p = []\n",
    "    bps = []\n",
    "    for i,c in enumerate(ss):\n",
    "        if c==\"(\":\n",
    "            p.append(i)\n",
    "        elif c==\")\":\n",
    "            j = p.pop()\n",
    "            bps.append((j,i))\n",
    "    return (bps,len(ss))\n",
    "parseSS(\"((.(...)))\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "925313e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'((..)(...))(..)'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seq = \"((..)(...))(..)\"\n",
    "bps,n = parseSS(seq)\n",
    "displaySS(bps,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5e417878",
   "metadata": {},
   "outputs": [],
   "source": [
    "BP_ENERGIES = {\n",
    "    \"AU\":-2,\n",
    "    \"UA\":-2,\n",
    "    \"CG\":-3,\n",
    "    \"GC\":-3,\n",
    "    \"GU\":-1,\n",
    "    \"UG\":-1,\n",
    "}\n",
    "\n",
    "def canBP(c1,c2):\n",
    "    return c1+c2 in BP_ENERGIES\n",
    "\n",
    "def countSS(s, debug=False,theta=1):\n",
    "    n = len(s)\n",
    "    C = [[1 for j in range(n)] for i in range(n)]\n",
    "    for m in range(theta+2,n+1):\n",
    "        for i in range(0,n-m+1):\n",
    "            j = i+m-1\n",
    "            C[i][j] = C[i+1][j]\n",
    "            for k in range(i+theta+1,j+1):\n",
    "                if canBP(s[i],s[k]) or debug:\n",
    "                    A = C[i+1][k-1]\n",
    "                    B = 1\n",
    "                    if k<j:\n",
    "                        B = C[k+1][j]\n",
    "                    C[i][j] += A*B\n",
    "    return C\n",
    "\n",
    "import random\n",
    "def stochastic_backtrack(i,j,s,C,debug=False,theta=1):\n",
    "    if j-i+1 < theta+2:\n",
    "        return []\n",
    "    r = random.random()*C[i][j]\n",
    "    r -= C[i+1][j]\n",
    "    if r<0:\n",
    "        return stochastic_backtrack(i+1,j,s,C,debug,theta)\n",
    "    for k in range(i+theta+1,j+1):\n",
    "        if canBP(s[i],s[k]) or debug:\n",
    "            A = C[i+1][k-1]\n",
    "            B = 1\n",
    "            if k<j:\n",
    "                B = C[k+1][j]\n",
    "            r -= A*B\n",
    "            if r<0:\n",
    "                lA = stochastic_backtrack(i+1,k-1,s,C,debug,theta)\n",
    "                lB = stochastic_backtrack(k+1,j,s,C,debug,theta)\n",
    "                return [(i,k)] + lA + lB\n",
    "    print(\"AAAaarararrrggghgh!!\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "65520314",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AAAAAAAAAAAA\n",
      "67 ((((.))..)).\n",
      "68 ..((......))\n",
      "69 .(((.)...).)\n",
      "72 (.(..(..).))\n",
      "74 (...(..)..).\n",
      "74 .(.(.(.))..)\n",
      "74 ..(.(.))(..)\n",
      "74 ..(.).......\n",
      "76 (..(.)(.)..)\n",
      "76 (..).(...)..\n",
      "76 ....(.).....\n",
      "77 ((.(.(..))))\n",
      "77 ....(.(.)..)\n",
      "78 ((.))....(.)\n",
      "78 (.)....(.)..\n",
      "78 .(.(.).(..))\n",
      "78 .(.)(.).....\n",
      "78 ..(...(.))..\n",
      "79 (((.).))....\n",
      "79 ((..(.))..).\n",
      "79 (.(.).....).\n",
      "79 (..(...).)..\n",
      "79 .(.).((.)..)\n",
      "79 ..(.(.(..)))\n",
      "80 (((...))..).\n",
      "80 ((..(.).).).\n",
      "80 (.(.)).(.)..\n",
      "80 (.)(.(.(.)))\n",
      "80 (.).(..)(.).\n",
      "80 (.)..(.....)\n",
      "80 (.)......(.)\n",
      "80 (..(.(..)).)\n",
      "80 (..)(.(..)).\n",
      "80 .((.)).((.))\n",
      "80 .((.)).(...)\n",
      "80 .(..)((.)..)\n",
      "80 ..(((..))..)\n",
      "80 ...(.)(.)...\n",
      "81 (((.).(.)).)\n",
      "81 ((..))(...).\n",
      "81 (.((.(.)).))\n",
      "81 (.(.)..)(.).\n",
      "81 (.).(...)(.)\n",
      "81 (...)..(..).\n",
      "81 .(((.)).)...\n",
      "81 .((....))...\n",
      "81 .(.(..).(.))\n",
      "81 .(..(.(.).))\n",
      "81 ..(.(.))....\n",
      "81 ..(.(..(.)))\n",
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      "109 .(..(...).).\n",
      "109 ..((...(.)))\n",
      "109 ..(.(.))(.).\n",
      "109 ..(.(..).)..\n",
      "109 ..(.)(.(..))\n",
      "109 ..(.).(.(.))\n",
      "109 ..(.).(....)\n",
      "109 ..(..((.))).\n",
      "109 ..(........)\n",
      "109 ...((((.))))\n",
      "109 ...((..))(.)\n",
      "110 (((.).)...).\n",
      "110 (((....)))..\n",
      "110 ((.)....)(.)\n",
      "110 ((..(.))...)\n",
      "110 ((..))((..))\n",
      "110 ((..)..)(..)\n",
      "110 ((..)...)(.)\n",
      "110 ((.....(.)))\n",
      "110 (.((..)))(.)\n",
      "110 (.(.((.)).))\n",
      "110 (.(.)((.)).)\n",
      "110 (.(.)(.).)..\n",
      "110 (.(...))(.).\n",
      "110 (.)((.).)(.)\n",
      "110 (.)(..)..(.)\n",
      "110 (.)..((..).)\n",
      "110 (..(.(..))).\n",
      "110 (..(..))(..)\n",
      "110 (..)...(...)\n",
      "110 (...(.)(.)).\n",
      "110 (...(.).)...\n",
      "110 (.....).....\n",
      "110 (......(.)).\n",
      "110 .(((.))(..))\n",
      "110 .((.(..))..)\n",
      "110 .((.)((..)))\n",
      "110 .((.)(...).)\n",
      "110 .((.))(.)(.)\n",
      "110 .((.)...(.))\n",
      "110 .((..)(.)..)\n",
      "110 .((..)).(..)\n",
      "110 .(.((.).)..)\n",
      "110 .(.(.)(..).)\n",
      "110 .(.)(.(..)).\n",
      "110 .(.).(.)....\n",
      "110 .(...(.).)..\n",
      "110 .(....)(.)..\n",
      "110 ..(.(.).(.))\n",
      "110 ..(...).....\n",
      "110 ..(....(.)).\n",
      "110 ......(.)(.)\n",
      "111 ((((.)(.))))\n",
      "111 (((.(.).))).\n",
      "111 (((.(...))))\n",
      "111 (((.).).(.))\n",
      "111 (((..)))(.).\n",
      "111 (((....).)).\n",
      "111 ((.((.).)).)\n",
      "111 ((.(.)(..)))\n",
      "111 ((.)(.)).(.)\n",
      "111 ((.).(.)(.))\n",
      "111 ((.).(.)...)\n",
      "111 ((.)..).....\n",
      "111 ((..)(...).)\n",
      "111 ((..)).(...)\n",
      "111 ((...)..)...\n",
      "111 ((....)(.).)\n",
      "111 (.((.)))(.).\n",
      "111 (.(.(..).)).\n",
      "111 (.(...))(..)\n",
      "111 (.(...)).(.)\n",
      "111 (.(.....).).\n",
      "111 (.)((...))..\n",
      "111 (.).(.(...))\n",
      "111 (.).(...)...\n",
      "111 (..(..)(..))\n",
      "111 (..)((..))..\n",
      "111 (..)(..)....\n",
      "111 (..).((.))..\n",
      "111 (..)...((.))\n",
      "111 (...((.).).)\n",
      "111 (...(.))....\n",
      "111 (...(...))..\n",
      "111 (...)(..(.))\n",
      "111 (....(.).)..\n",
      "111 (....)(.)...\n",
      "111 (....).(.)..\n",
      "111 (.....(.))..\n",
      "111 (......(..))\n",
      "111 .(((..).).).\n",
      "111 .((.(..).).)\n",
      "111 .((.)(....))\n",
      "111 .((.).)..(.)\n",
      "111 .(.((.)))(.)\n",
      "111 .(.((..)))..\n",
      "111 .(.(.)).....\n",
      "111 .(.(.).....)\n",
      "111 .(.(..)...).\n",
      "111 .(.(......))\n",
      "111 .(.).....(.)\n",
      "111 .(..((.).)).\n",
      "111 .(..).((.)).\n",
      "111 .(..).(.)(.)\n",
      "111 .(...(.)...)\n",
      "111 .(...)(.)(.)\n",
      "111 .(...)(..)..\n",
      "111 .(....((.)))\n",
      "111 ..((.(.).)).\n",
      "111 ..((...))(.)\n",
      "111 ..(.((...)))\n",
      "111 ..(.(..))(.)\n",
      "111 ..(.(....).)\n",
      "111 ..(.)...(.).\n",
      "111 ...((..(.)))\n",
      "111 ...(.((.).))\n",
      "111 ...(.(...).)\n",
      "111 ...(.)..(.).\n",
      "111 ...(..(.))..\n",
      "111 ...(.....)..\n",
      "112 ((((.).).)).\n",
      "112 (((.))(..)).\n",
      "112 (((.)).).(.)\n",
      "112 (((.)..(.)))\n",
      "112 (((.....)).)\n",
      "112 ((.)(.).)(.)\n",
      "112 ((.))((.)..)\n",
      "112 ((.).((.)).)\n",
      "112 ((.)..)..(.)\n",
      "112 ((..)(.).)..\n",
      "112 ((..)......)\n",
      "112 ((...((.))))\n",
      "112 ((...).....)\n",
      "112 ((....(..)))\n",
      "112 ((....))(..)\n",
      "112 (.((.).)(.))\n",
      "112 (.((..))..).\n",
      "112 (.((..).)..)\n",
      "112 (.(.))((..))\n",
      "112 (.(.))(..)..\n",
      "112 (.(...)....)\n",
      "112 (.)(.(.).)..\n",
      "112 (.)(.)(.)...\n",
      "112 (.)(.)..(.).\n",
      "112 (.)....(...)\n",
      "112 (..(.)).(.).\n",
      "112 (..(..(.)).)\n",
      "112 (...((.)))..\n",
      "112 (...(..).)..\n",
      "112 (...).((.)).\n",
      "112 (...).((.).)\n",
      "112 (.....(..).)\n",
      "112 .(((.))....)\n",
      "112 .((.((.)).))\n",
      "112 .((.)..)....\n",
      "112 .((..(.)).).\n",
      "112 .(.)((.(.)))\n",
      "112 .(.).((...))\n",
      "112 .(..)(....).\n",
      "112 ..((.(.)..))\n",
      "112 ..((..).(.))\n",
      "112 ..(.)..(..).\n",
      "112 ..(..)..(.).\n",
      "112 ...((.))....\n",
      "112 ...((..)(.))\n",
      "112 ...(.(.(.)))\n",
      "112 ......(.)...\n",
      "113 (((.).(..)))\n",
      "113 (((.)...))..\n",
      "113 (((..)....))\n",
      "113 ((.).)..(.).\n",
      "113 ((..(.(.))))\n",
      "113 ((...(...)))\n",
      "113 (.)((.)(..))\n",
      "113 (.)(.)(...).\n",
      "113 (.)(.).((.))\n",
      "113 (.)..(..)...\n",
      "113 (..(.....).)\n",
      "113 (..)....(..)\n",
      "113 (...((.)).).\n",
      "113 (....(..)..)\n",
      "113 .(((..).)..)\n",
      "113 .((.((.)))).\n",
      "113 .(.(.))..(.)\n",
      "113 .(.(..(.).))\n",
      "113 .(.(..)(.)).\n",
      "113 .(.).(.(..))\n",
      "113 .(.).(..)(.)\n",
      "113 .(..)(.)(..)\n",
      "113 ..((..(..)))\n",
      "113 ..((....).).\n",
      "113 ..(.(...)..)\n",
      "113 ..(..((.)).)\n",
      "113 ...(..)(...)\n",
      "113 ....((.))...\n",
      "113 ....((..))..\n",
      "113 ....(.(..)).\n",
      "113 .....((..).)\n",
      "113 .....(.).(.)\n",
      "113 .........(.)\n",
      "114 (((.).)(..))\n",
      "114 (((.).))(..)\n",
      "114 ((.(.)..).).\n",
      "114 ((.))(.)....\n",
      "114 ((..(.)).)..\n",
      "114 ((..)(.)...)\n",
      "114 ((..)..).(.)\n",
      "114 (.((....)).)\n",
      "114 (.)(..(..)).\n",
      "114 (.)(....)...\n",
      "114 (.).(.(.)..)\n",
      "114 (..((....)))\n",
      "114 (..(.(.)..))\n",
      "114 (..(.)(..).)\n",
      "114 (..(.))((.))\n",
      "114 (......)....\n",
      "114 .(((.))).(.)\n",
      "114 .(((.)).(.))\n",
      "114 .(((.).)(.))\n",
      "114 .((.))(.)...\n",
      "114 .((.).)(...)\n",
      "114 .((...(.).))\n",
      "114 .(.(.)(...))\n",
      "114 .(.)(((.)).)\n",
      "114 .(.)..(.(.))\n",
      "114 .(..)..(.)..\n",
      "114 .(...(.))...\n",
      "114 .(.....(.)).\n",
      "114 ..((.)(..).)\n",
      "114 ..((..)).(.)\n",
      "114 ...(((.))..)\n",
      "114 ...(.)......\n",
      "115 ((((.))...))\n",
      "115 ((((..).)).)\n",
      "115 (((.))((.)))\n",
      "115 (((..)).)(.)\n",
      "115 ((.((..))).)\n",
      "115 ((.(.)).)(.)\n",
      "115 ((.(.)....))\n",
      "115 ((.))..(..).\n",
      "115 ((..))..(..)\n",
      "115 ((..).)(..).\n",
      "115 ((...))((.))\n",
      "115 (.(((..)).))\n",
      "115 (.(.(.)).)..\n",
      "115 (.(..(...)))\n",
      "115 (.)((.)).(.)\n",
      "115 (.)((..)..).\n",
      "115 (.)(.(.))...\n",
      "115 (.).(.).(..)\n",
      "115 (..(.(...)))\n",
      "115 (..(.)).....\n",
      "115 (..(..)(.)).\n",
      "115 (..)(.).(.).\n",
      "115 (..).(..)(.)\n",
      "115 (..)..((..))\n",
      "115 (..........)\n",
      "115 .((((.)).)).\n",
      "115 .(((.)))....\n",
      "115 .(((.))...).\n",
      "115 .(.)((.)(.))\n",
      "115 ..((.)(...))\n",
      "115 ...((.(.)).)\n",
      "115 ...((.....))\n",
      "115 .....((..)).\n",
      "116 (((.).)....)\n",
      "116 (((..(.))).)\n",
      "116 ((.((..).)))\n",
      "116 ((.)((.).)).\n",
      "116 ((.)(.)..)..\n",
      "116 ((.).....)..\n",
      "116 ((..)((.))).\n",
      "116 ((....)...).\n",
      "116 (.(.).(.))..\n",
      "116 (.(.).(..)).\n",
      "116 (.(..).)(..)\n",
      "116 (..((...)).)\n",
      "116 (..(..)).(.)\n",
      "116 (..).(..)...\n",
      "116 (...(..))(.)\n",
      "116 .(((....)).)\n",
      "116 .((.))((.)).\n",
      "116 .((..(..))).\n",
      "116 .(.)(..(.).)\n",
      "116 .(.)...(...)\n",
      "116 .(..)(.(.).)\n",
      "116 .(...)...(.)\n",
      "116 .(.....).(.)\n",
      "116 ..(((.)...))\n",
      "116 ...(......).\n",
      "117 (((((.)).)))\n",
      "117 (((.).).)...\n",
      "117 (((.)...).).\n",
      "117 ((.((...))))\n",
      "117 ((.))((.))..\n",
      "117 ((...)).....\n",
      "117 (.((..)(.)))\n",
      "117 (.(.)(...).)\n",
      "117 (.(.)).((.))\n",
      "117 (.(..))(.)..\n",
      "117 (..(....).).\n",
      "117 .((.))......\n",
      "117 .((.).((.)))\n",
      "117 .((.)......)\n",
      "117 .((..)(.).).\n",
      "117 .(.).((..)).\n",
      "117 .(..)..(..).\n",
      "117 .(...((.).))\n",
      "117 ..((...)..).\n",
      "117 ..(....).(.)\n",
      "117 ...(.)(.(.))\n",
      "118 ((((.)).)..)\n",
      "118 (((..)..))..\n",
      "118 (((...))...)\n",
      "118 (.(.))(.(.))\n",
      "118 (.(.))(.)(.)\n",
      "118 (..(.)(.))..\n",
      "118 (..(.).....)\n",
      "118 (....((.)).)\n",
      "118 .((((.)..)))\n",
      "118 .(((.(.)).))\n",
      "118 .(((..)..)).\n",
      "118 .(..).((..))\n",
      "118 ..((.)(.))..\n",
      "118 ..((..)...).\n",
      "118 ..(..(.)...)\n",
      "118 ..(..)...(.)\n",
      "118 ....(...)...\n",
      "119 (((.)).(..))\n",
      "119 (((.)..).)..\n",
      "119 ((.(.(.)).))\n",
      "119 ((.)(.)....)\n",
      "119 ((.).)(.)(.)\n",
      "119 ((..(.).))..\n",
      "119 ((..)((.).))\n",
      "119 ((..).).(..)\n",
      "119 ((...)(..).)\n",
      "119 (.(.)).(..).\n",
      "119 (.)((((.))))\n",
      "119 (.)(((.)).).\n",
      "119 (.).(((..)))\n",
      "119 (.....)(...)\n",
      "119 .((..)..(.))\n",
      "119 .(.(....))..\n",
      "119 .(.)((....))\n",
      "119 .(.).((.))..\n",
      "119 .(.)..(..)..\n",
      "119 ..(..(...)).\n",
      "119 ..(...(...))\n",
      "119 .....(.(..))\n",
      "120 ((.)(..))(.)\n",
      "120 (.(.(.))..).\n",
      "120 (.(..)...)..\n",
      "120 (..(.)..(.))\n",
      "120 (..(.)...)..\n",
      "120 .((.(.))(.))\n",
      "121 ((((...).)))\n",
      "121 ((.)(.)...).\n",
      "121 (.(..(..))).\n",
      "121 .((.).).(.).\n",
      "122 (((.)..))(.)\n",
      "122 (...(..)(.))\n",
      "122 ..(.(..)(.))\n",
      "122 ...(.(...)).\n",
      "122 ....((..).).\n",
      "123 (..).(.(.).)\n",
      "123 .(.(..).)(.)\n",
      "123 ....((....))\n",
      "123 ....(.)((.))\n",
      "123 ........(..)\n",
      "124 (..)((.))(.)\n",
      "124 .(..)..((.))\n",
      "125 (.(.(.).)..)\n",
      "125 (.(..))(..).\n",
      "125 (.(...)(..))\n",
      "125 (.)(.(.)(.))\n",
      "125 (.)(.(.))(.)\n",
      "125 ...((.)...).\n",
      "126 ((.)..).(..)\n",
      "126 .(((.).).)..\n",
      "126 .(.)(.)..(.)\n",
      "126 ....(.).(..)\n",
      "127 ((.(..))(.))\n",
      "127 .((.))(..)..\n",
      "127 .(....(.))..\n",
      "127 ...((....)).\n",
      "128 .((..(.))..)\n",
      "129 ((.(.....)))\n",
      "130 ((..)(....))\n",
      "132 (.(.).)(..).\n",
      "132 .(.((..)..))\n",
      "136 .(.(...)..).\n"
     ]
    }
   ],
   "source": [
    "SAMPLES = 228300\n",
    "for s,d in [#(\"A\",False),\n",
    "            #(\"CAG\",False),\n",
    "            #(\"CAGU\",False),\n",
    "            #(\"AAAA\",True),\n",
    "            #(\"AAAAAAAA\",True),\n",
    "            (\"AAAAAAAAAAAA\",True),\n",
    "            #(\"AAAAAAAAAAAA\"*10,True)\n",
    "           ]:\n",
    "    print(s)\n",
    "    C = countSS(s,d)\n",
    "    stats = {}\n",
    "    for i in range(SAMPLES):\n",
    "        bps = stochastic_backtrack(0,len(s)-1,s,C,d)\n",
    "        ss = displaySS(bps,len(s))\n",
    "        if ss not in stats:\n",
    "            stats[ss] = 0\n",
    "        stats[ss] += 1\n",
    "    for nb,ss in sorted([(stats[s],s) for s in stats]):\n",
    "        print(nb,ss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "05e9ce21",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math \n",
    "\n",
    "RT = 0.001986*(273+2237)\n",
    "\n",
    "def BF(E):\n",
    "    return math.exp(-E/RT)\n",
    "\n",
    "def partition_function(s, theta=1):\n",
    "    n = len(s)\n",
    "    C = [[1 for j in range(n)] for i in range(n)]\n",
    "    for m in range(theta+2,n+1):\n",
    "        for i in range(0,n-m+1):\n",
    "            j = i+m-1\n",
    "            C[i][j] = C[i+1][j]\n",
    "            for k in range(i+theta+1,j+1):\n",
    "                if canBP(s[i],s[k]):\n",
    "                    A = BF(BP_ENERGIES[s[i]+s[k]]) * C[i+1][k-1]\n",
    "                    B = 1\n",
    "                    if k<j:\n",
    "                        B = C[k+1][j]\n",
    "                    C[i][j] += A*B\n",
    "    return C\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "399d09a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "258.5965029004957"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seq = \"GGGGAAACCCC\"\n",
    "C = partition_function(seq)\n",
    "C[0][len(seq)-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fe40b2a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def stochastic_backtrack_PF(i,j,s,C,theta=1):\n",
    "    if j-i+1 < theta+2:\n",
    "        return []\n",
    "    r = random.random()*C[i][j]\n",
    "    r -= C[i+1][j]\n",
    "    if r<0:\n",
    "        return stochastic_backtrack_PF(i+1,j,s,C,theta)\n",
    "    for k in range(i+theta+1,j+1):\n",
    "        if canBP(s[i],s[k]):\n",
    "            A = BF(BP_ENERGIES[s[i]+s[k]]) * C[i+1][k-1]\n",
    "            B = 1\n",
    "            if k<j:\n",
    "                B = C[k+1][j]\n",
    "            r -= A*B\n",
    "            if r<0:\n",
    "                lA = stochastic_backtrack_PF(i+1,k-1,s,C,theta)\n",
    "                lB = stochastic_backtrack_PF(k+1,j,s,C,theta)\n",
    "                return [(i,k)] + lA + lB\n",
    "    print(\"AAAaarararrrggghgh!!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f7d74c82",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "(0, 17) 0.00718\n",
      "(5, 17) 0.00756\n",
      "(12, 28) 0.00756\n",
      "(19, 31) 0.00798\n",
      "(14, 31) 0.00824\n",
      "(0, 12) 0.00836\n",
      "(0, 21) 0.00866\n",
      "(2, 24) 0.00886\n",
      "(10, 26) 0.00888\n",
      "(7, 24) 0.00906\n",
      "(14, 26) 0.00914\n",
      "(10, 21) 0.00922\n",
      "(5, 21) 0.0094\n",
      "(17, 28) 0.00952\n",
      "(15, 31) 0.01028\n",
      "(10, 31) 0.01062\n",
      "(2, 19) 0.0107\n",
      "(12, 24) 0.01102\n",
      "(7, 19) 0.01112\n",
      "(2, 10) 0.01116\n",
      "(17, 29) 0.01126\n",
      "(5, 26) 0.01164\n",
      "(0, 26) 0.01214\n",
      "(16, 28) 0.0124\n",
      "(7, 28) 0.01254\n",
      "(14, 30) 0.01268\n",
      "(2, 28) 0.01316\n",
      "(5, 31) 0.01354\n",
      "(0, 7) 0.01406\n",
      "(2, 18) 0.01524\n",
      "(24, 31) 0.01546\n",
      "(10, 17) 0.01548\n",
      "(7, 14) 0.01582\n",
      "(5, 12) 0.01584\n",
      "(17, 24) 0.01586\n",
      "(14, 21) 0.01616\n",
      "(21, 28) 0.01628\n",
      "(1, 17) 0.01632\n",
      "(3, 19) 0.01666\n",
      "(19, 26) 0.01666\n",
      "(11, 31) 0.01678\n",
      "(12, 19) 0.0169\n",
      "(12, 32) 0.01702\n",
      "(4, 12) 0.01748\n",
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      "(2, 15) 0.02274\n",
      "(4, 17) 0.0228\n",
      "(3, 14) 0.02364\n",
      "(18, 26) 0.024\n",
      "(17, 25) 0.02454\n",
      "(7, 25) 0.02476\n",
      "(20, 28) 0.02514\n",
      "(7, 29) 0.02542\n",
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      "(8, 26) 0.0256\n",
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      "(12, 29) 0.02602\n",
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      "(5, 23) 0.02838\n",
      "(0, 13) 0.02864\n",
      "(5, 16) 0.02878\n",
      "(5, 27) 0.02878\n",
      "(17, 32) 0.02894\n",
      "(6, 28) 0.02942\n",
      "(11, 21) 0.02958\n",
      "(12, 22) 0.0297\n",
      "(0, 20) 0.0298\n",
      "(15, 26) 0.03034\n",
      "(0, 23) 0.03054\n",
      "(21, 29) 0.03054\n",
      "(7, 15) 0.0313\n",
      "(9, 19) 0.0316\n",
      "(18, 31) 0.03188\n",
      "(10, 20) 0.032\n",
      "(19, 30) 0.0324\n",
      "(16, 24) 0.0335\n",
      "(3, 24) 0.03396\n",
      "(13, 28) 0.03402\n",
      "(1, 12) 0.03544\n",
      "(14, 27) 0.03614\n",
      "(25, 31) 0.03658\n",
      "(7, 22) 0.03686\n",
      "(0, 9) 0.03696\n",
      "(26, 32) 0.03706\n",
      "(8, 21) 0.03812\n",
      "(9, 24) 0.03866\n",
      "(21, 32) 0.03958\n",
      "(12, 18) 0.03968\n",
      "(5, 20) 0.03998\n",
      "(9, 28) 0.04022\n",
      "(8, 31) 0.04072\n",
      "(24, 30) 0.04102\n",
      "(10, 23) 0.0412\n",
      "(11, 26) 0.0413\n",
      "(2, 11) 0.04186\n",
      "(3, 28) 0.042\n",
      "(11, 17) 0.04242\n",
      "(15, 21) 0.04284\n",
      "(10, 27) 0.04324\n",
      "(10, 16) 0.04358\n",
      "(12, 25) 0.0439\n",
      "(2, 25) 0.044\n",
      "(3, 10) 0.04544\n",
      "(6, 19) 0.0458\n",
      "(1, 7) 0.04648\n",
      "(2, 8) 0.04692\n",
      "(5, 30) 0.04692\n",
      "(7, 32) 0.04786\n",
      "(22, 31) 0.04828\n",
      "(7, 18) 0.04866\n",
      "(14, 20) 0.0494\n",
      "(1, 26) 0.0498\n",
      "(13, 24) 0.04998\n",
      "(13, 19) 0.05012\n",
      "(2, 29) 0.05128\n",
      "(8, 17) 0.05174\n",
      "(22, 26) 0.05228\n",
      "(7, 11) 0.05348\n",
      "(21, 25) 0.05388\n",
      "(8, 12) 0.05418\n",
      "(14, 23) 0.05464\n",
      "(4, 31) 0.05472\n",
      "(21, 24) 0.0568\n",
      "(14, 17) 0.0584\n",
      "(28, 31) 0.0594\n",
      "(2, 5) 0.05962\n",
      "(7, 10) 0.05994\n",
      "(0, 27) 0.0615\n",
      "(0, 6) 0.0628\n",
      "(20, 24) 0.06306\n",
      "(19, 23) 0.06314\n",
      "(5, 9) 0.06418\n",
      "(6, 10) 0.06696\n",
      "(26, 29) 0.0703\n",
      "(0, 3) 0.07072\n",
      "(0, 30) 0.0714\n",
      "(4, 7) 0.07366\n",
      "(12, 15) 0.07386\n",
      "(1, 31) 0.0756\n",
      "(2, 32) 0.0756\n",
      "(17, 22) 0.0783\n",
      "(0, 31) 0.08076\n",
      "(0, 2) 0.082\n",
      "(26, 28) 0.08202\n",
      "(12, 14) 0.08374\n",
      "(5, 7) 0.0849\n",
      "(9, 14) 0.0878\n",
      "(23, 28) 0.08912\n",
      "(17, 19) 0.0892\n",
      "(16, 19) 0.09248\n",
      "(19, 21) 0.10314\n",
      "(10, 12) 0.10382\n",
      "(24, 26) 0.10636\n",
      "(18, 21) 0.10648\n",
      "(24, 27) 0.12546\n",
      "(10, 13) 0.12988\n",
      "(2, 4) 0.14116\n",
      "(29, 31) 0.14218\n",
      "(15, 17) 0.1532\n",
      "(14, 16) 0.1794\n",
      "(28, 30) 0.18928\n",
      "(3, 5) 0.19168\n"
     ]
    }
   ],
   "source": [
    "seq = \"GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\"\n",
    "SAMPLES = 50000\n",
    "C = partition_function(seq)\n",
    "stats = {}\n",
    "for i in range(SAMPLES):\n",
    "    bps = stochastic_backtrack_PF(0,len(seq)-1,seq,C)\n",
    "    for (i,j) in bps:        \n",
    "        if (i,j) not in stats:\n",
    "            stats[(i,j)] = 0\n",
    "        stats[(i,j)] += 1\n",
    "for nb,ss in sorted([(stats[s],s) for s in stats]):\n",
    "    print(ss,nb/SAMPLES)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a4f0f852",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mfe(s, theta=1):\n",
    "    n = len(s)\n",
    "    C = [[0 for j in range(n)] for i in range(n)]\n",
    "    for m in range(theta+2,n+1):\n",
    "        for i in range(0,n-m+1):\n",
    "            j = i+m-1\n",
    "            C[i][j] = C[i+1][j]\n",
    "            for k in range(i+theta+1,j+1):\n",
    "                if canBP(s[i],s[k]):\n",
    "                    A = BP_ENERGIES[s[i]+s[k]] + C[i+1][k-1]\n",
    "                    B = 0\n",
    "                    if k<j:\n",
    "                        B = C[k+1][j]\n",
    "                    C[i][j] = min(C[i][j], A + B)\n",
    "    return C\n",
    "\n",
    "def backtrack_mfe(i,j,s,C,theta=1):\n",
    "    if j-i+1 < theta+2:\n",
    "        return []\n",
    "    if C[i][j] == C[i+1][j]:\n",
    "        return backtrack_mfe(i+1,j,s,C,theta)\n",
    "    for k in range(i+theta+1,j+1):\n",
    "        if canBP(s[i],s[k]):\n",
    "            A = BP_ENERGIES[s[i]+s[k]] + C[i+1][k-1]\n",
    "            B = 0\n",
    "            if k<j:\n",
    "                B = C[k+1][j]\n",
    "            if C[i][j] == A+B:\n",
    "                lA = backtrack_mfe(i+1,k-1,s,C,theta)\n",
    "                lB = backtrack_mfe(k+1,j,s,C,theta)\n",
    "                return [(i,k)] + lA + lB\n",
    "    print(\"AAAaarararrrggghgh!!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d4a75d4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\n",
      "..(.((.(.((((((.)(.(.)).))))))))) -12\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BP_ENERGIES = {\n",
    "    \"AU\":-1,\n",
    "    \"UA\":-1,\n",
    "    \"CG\":-1,\n",
    "    \"GC\":-1,\n",
    "    \"GU\":-1,\n",
    "    \"UG\":-1,\n",
    "}\n",
    "seq = \"GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\"\n",
    "theta=1\n",
    "C = mfe(seq,theta)\n",
    "bps = backtrack_mfe(0,len(seq)-1,seq,C,theta=theta)\n",
    "ss = displaySS(bps,len(seq))\n",
    "print(seq)\n",
    "print(ss,C[0][len(seq)-1])\n",
    "drawRNA(ss,bps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "642439ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\n",
      "(..)((.(.((((((((..).).))))))))). -31\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BP_ENERGIES = {\n",
    "    \"AU\":-2,\n",
    "    \"UA\":-2,\n",
    "    \"CG\":-3,\n",
    "    \"GC\":-3,\n",
    "    \"GU\":-1,\n",
    "    \"UG\":-1,\n",
    "}\n",
    "C = mfe(seq,theta)\n",
    "bps = backtrack_mfe(0,len(seq)-1,seq,C,theta=theta)\n",
    "ss = displaySS(bps,len(seq))\n",
    "print(seq)\n",
    "print(ss,C[0][len(seq)-1])\n",
    "drawRNA(ss,bps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f5e4d84c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def backtrack_subopt(i,j,delta,s,C,theta=1):\n",
    "    if j-i+1 < theta+2:\n",
    "        return [([],0.)]\n",
    "    subopts = []\n",
    "    if C[i+1][j] - C[i][j] <= delta:\n",
    "        delta_update = delta - (C[i+1][j] - C[i][j])\n",
    "        subopts += backtrack_subopt(i+1,j,delta_update,s,C,theta)\n",
    "    for k in range(i+theta+1,j+1):\n",
    "        if canBP(s[i],s[k]):\n",
    "            Ebp = BP_ENERGIES[s[i]+s[k]]\n",
    "            A =  Ebp + C[i+1][k-1]\n",
    "            B = 0\n",
    "            if k<j:\n",
    "                B = C[k+1][j]\n",
    "            if A+B - C[i][j] <= delta:\n",
    "                delta_update = delta - (A+B - C[i][j])\n",
    "                lA = backtrack_subopt(i+1,k-1,delta_update,s,C,theta)\n",
    "                lB = backtrack_subopt(k+1,j,delta_update,s,C,theta)\n",
    "                for bpA,EA in lA:\n",
    "                    for bpB,EB in lB:\n",
    "                        Ec = EA+EB+Ebp\n",
    "                        if Ec - C[i][j] <= delta:\n",
    "                            subopts.append(([(i,k)] + bpA + bpB, Ec))\n",
    "    return subopts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "38ef895b",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\n",
      "....((...)(.(((((..(...)).)))))). -24.0\n",
      "....((.(.((((((..(....)))))))))). -25.0\n",
      "....((.(.(((((((.....).))))))))). -25.0\n",
      "....(((...).(((((..(...)).)))))). -24.0\n",
      "...(.(...))((((((..(...)).)))).). -24.0\n",
      "..((.(...)))(((((..(...)).))))... -24.0\n",
      "..((.(...)))(((((..(...)).)))...) -24.0\n",
      "..(..(...)(.(((((..(...)).))))).) -24.0\n",
      "..(..(.(.((((((..(....))))))))).) -25.0\n",
      "..(..(.(.(((((((.....).)))))))).) -25.0\n",
      "..(..((...).(((((..(...)).))))).) -24.0\n",
      "..(.(..(.((((((..(....)))))))).)) -24.0\n",
      "..(.(..(.(((((((.....).))))))).)) -24.0\n",
      "..(.((...)(..((((..(...)).))).))) -24.0\n",
      "..(.((...)(.(((.(..(...))..)))))) -24.0\n",
      "..(.((...)(.((((.(.(...)).))))))) -24.0\n",
      "..(.((...)(.((((.(..(...))))))))) -25.0\n",
      "..(.((...)(.((((.(.(...).)))))))) -25.0\n",
      "..(.((...)(.(((((..(...)).))))))) -26.0\n",
      "..(.((...)(.((((((....).).))))))) -25.0\n",
      "..(.((...((((((..(....))))))).))) -25.0\n",
      "..(.((...(((((((.....).)))))).))) -25.0\n",
      "..(.((.(...)((((.(..(...))))))))) -24.0\n",
      "..(.((.(...)((((.(.(...).)))))))) -24.0\n",
      "..(.((.(...)(((((..(...)).))))))) -25.0\n",
      "..(.((.(...)((((((....).).))))))) -24.0\n",
      "..(.((.(..(((((..(....)))))).)))) -24.0\n",
      "..(.((.(..((((((.....).))))).)))) -24.0\n",
      "..(.((.(.(.((((..(....))))).))))) -24.0\n",
      "..(.((.(.(.(((((.....).)))).))))) -24.0\n",
      "..(.((.(.((.(((..(....)))).)))))) -25.0\n",
      "..(.((.(.((.((((.....).))).)))))) -25.0\n",
      "..(.((.(.(((.((..(....))).))))))) -25.0\n",
      "..(.((.(.(((.(((.....).)).))))))) -25.0\n",
      "..(.((.(.((((...(..(...)))))))))) -25.0\n",
      "..(.((.(.((((...((....).))))))))) -24.0\n",
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   "source": [
    "BP_ENERGIES = {\n",
    "    \"AU\":-2,\n",
    "    \"UA\":-2,\n",
    "    \"CG\":-3,\n",
    "    \"GC\":-3,\n",
    "    \"GU\":-1,\n",
    "    \"UG\":-1,\n",
    "}\n",
    "seq = \"GAUCAGCUACGAUCGACUAGCUACGAUCGACUA\"\n",
    "theta = 3\n",
    "C = mfe(seq,theta)\n",
    "delta = 3\n",
    "print(seq)\n",
    "for bps,E in backtrack_subopt(0,len(seq)-1,delta,seq,C,theta=theta):\n",
    "    ss = displaySS(bps,len(seq))\n",
    "    print(ss,E)\n",
    "    #drawRNA(ss,bps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cd1ea51",
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   "source": []
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