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Applications od Complexity Analysis Added
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‎03_Complexity-Analysis/Problems_Applications-of-Complexity-Analysis.ipynb renamed to ‎03_Complexity-Analysis/Problems_Applications_of_Complexity_Analysis.ipynb

+303-1
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@@ -550,6 +550,79 @@
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"For the second query, we have 2 pairs in total that sum up to 10. They are, (2, 8) and (5, 5).\n",
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"'''\n",
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"\n",
553+
"# Solution-1\n",
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"\n",
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"from sys import stdin\n",
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"\n",
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"def pairSum(arr, n, num) :\n",
558+
" arr.sort()\n",
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" \n",
560+
" si = 0\n",
561+
" ei = n-1\n",
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" numpair = 0\n",
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" \n",
564+
" while si<ei:\n",
565+
" if arr[si]+arr[ei]<num:\n",
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" si+=1\n",
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" \n",
568+
" elif arr[si]+arr[ei]>num:\n",
569+
" ei-=1\n",
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" \n",
571+
" else:\n",
572+
" startele = arr[si]\n",
573+
" endele = arr[ei]\n",
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" \n",
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" if startele == endele: \n",
576+
" totalele = (ei-si)+1\n",
577+
" numpair += (totalele*(totalele-1)//2)\n",
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" \n",
579+
" return numpair\n",
580+
" \n",
581+
" tempsi = si+1\n",
582+
" tempei = ei-1\n",
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" \n",
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" while (tempsi<=tempei) and (arr[tempsi]==startele):\n",
585+
" tempsi += 1\n",
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" \n",
587+
" while (tempei>=tempsi) and (arr[tempei]==endele):\n",
588+
" tempei -= 1\n",
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" \n",
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" totalelefromstart = (tempsi-si)\n",
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" totalelefromend = (ei-tempei)\n",
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" \n",
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" numpair += (totalelefromstart * totalelefromend)\n",
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" \n",
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" si = tempsi\n",
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" ei = tempei\n",
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" \n",
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" return numpair\n",
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"\n",
600+
"#taking input using fast I/O method\n",
601+
"def takeInput() :\n",
602+
" n = int(stdin.readline().strip())\n",
603+
" if n == 0 :\n",
604+
" return list(), 0\n",
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"\n",
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" arr = list(map(int, stdin.readline().strip().split(\" \")))\n",
607+
" return arr, n\n",
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"\n",
609+
"def printList(arr, n) : \n",
610+
" for i in range(n) :\n",
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" print(arr[i], end = \" \")\n",
612+
" print()\n",
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"\n",
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"#main\n",
615+
"t = int(stdin.readline().strip())\n",
616+
"while t > 0 : \n",
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" arr, n = takeInput()\n",
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" num = int(stdin.readline().strip())\n",
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" print(pairSum(arr, n, num))\n",
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" t -= 1\n",
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"\n",
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" \n",
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"\n",
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"# Solution-2\n",
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"\n",
553626
"from sys import stdin\n",
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"from collections import OrderedDict\n",
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"\n",
@@ -609,6 +682,235 @@
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"source": [
688+
"'''\n",
689+
"Triplet sum\n",
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"\n",
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"You have been given a random integer array/list(ARR) and a number X. Find and return the triplet(s) in the array/list which sum \n",
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"to X.\n",
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"\n",
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"Note :\n",
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"Given array/list can contain duplicate elements.\n",
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"\n",
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"Input format :\n",
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"The first line contains an Integer 't' which denotes the number of test cases or queries to be run. Then the test cases follow.\n",
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"\n",
700+
"First line of each test case or query contains an integer 'N' representing the size of the first array/list.\n",
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"\n",
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"Second line contains 'N' single space separated integers representing the elements in the array/list.\n",
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"\n",
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"Third line contains an integer 'X'.\n",
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"\n",
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"Output format :\n",
707+
"For each test case, print the total number of triplets present in the array/list.\n",
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"\n",
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"Output for every test case will be printed in a separate line.\n",
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"\n",
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"Constraints :\n",
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"1 <= t <= 10^2\n",
713+
"0 <= N <= 10^3\n",
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"0 <= X <= 10^9\n",
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"Time Limit: 1 sec\n",
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"\n",
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"Sample Input 1:\n",
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"1\n",
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"7\n",
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"1 2 3 4 5 6 7 \n",
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"12\n",
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"Sample Output 1:\n",
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"5\n",
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"\n",
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"Sample Input 2:\n",
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"2\n",
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"7\n",
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"1 2 3 4 5 6 7 \n",
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"19\n",
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"9\n",
731+
"2 -5 8 -6 0 5 10 11 -3\n",
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"10\n",
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"Sample Output 2:\n",
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"0\n",
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"5\n",
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"\n",
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"Explanation for Input 2:\n",
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"Since there doesn't exist any triplet with sum equal to 19 for the first query, we print 0.\n",
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"\n",
740+
"For the second query, we have 5 triplets in total that sum up to 10. They are, (2, 8, 0), (2, 11, -3), (-5, 5, 10), \n",
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"(8, 5, -3) and (-6, 5, 11)\n",
742+
"'''\n",
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"\n",
744+
"from sys import stdin\n",
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"\n",
746+
"def tripletSum(arr, n, num) :\n",
747+
" arr.sort()\n",
748+
" numtriplets = 0\n",
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" \n",
750+
" for i in range(n):\n",
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" pairsumfor = num-arr[i]\n",
752+
" numpairs = pairSum(arr,i+1,n-1,pairsumfor)\n",
753+
" numtriplets +=numpairs\n",
754+
" return numtriplets\n",
755+
" \n",
756+
" \n",
757+
"def pairSum(arr, si, ei, num) :\n",
758+
" \n",
759+
" numpair=0\n",
760+
" while si <ei:\n",
761+
" if arr[si]+arr[ei]<num:\n",
762+
" si+=1\n",
763+
" elif arr[si]+arr[ei]>num:\n",
764+
" ei-=1\n",
765+
" else:\n",
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" startele=arr[si]\n",
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" endele=arr[ei]\n",
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" \n",
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" if startele == endele: \n",
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" totalele=(ei-si)+1\n",
771+
" numpair+=(totalele*(totalele-1)//2)\n",
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" \n",
773+
" return numpair\n",
774+
" \n",
775+
" tempsi=si+1\n",
776+
" tempei=ei-1\n",
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" \n",
778+
" while (tempsi<=tempei) and (arr[tempsi]==startele):\n",
779+
" tempsi+=1\n",
780+
" \n",
781+
" while (tempei>=tempsi) and (arr[tempei]==endele):\n",
782+
" tempei-=1\n",
783+
" \n",
784+
" totalelefromstart=(tempsi-si)\n",
785+
" totalelefromend=(ei-tempei)\n",
786+
" \n",
787+
" numpair+=(totalelefromstart * totalelefromend)\n",
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" \n",
789+
" si=tempsi\n",
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" ei=tempei\n",
791+
" \n",
792+
" return numpair\n",
793+
"\n",
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"\n",
795+
"def takeInput() :\n",
796+
" n = int(stdin.readline().strip())\n",
797+
" if n == 0 :\n",
798+
" return list(), 0\n",
799+
"\n",
800+
" arr = list(map(int, stdin.readline().strip().split(\" \")))\n",
801+
" return arr, n\n",
802+
"\n",
803+
"def printList(arr, n) : \n",
804+
" for i in range(n) :\n",
805+
" print(arr[i], end = \" \")\n",
806+
" print()\n",
807+
"\n",
808+
"#main\n",
809+
"t = int(stdin.readline().strip())\n",
810+
"while t > 0 : \n",
811+
" arr, n = takeInput()\n",
812+
" num = int(stdin.readline().strip())\n",
813+
" print(tripletSum(arr, n, num))\n",
814+
" t -= 1"
815+
],
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"metadata": {
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"id": "-oX-8TjPeBU8"
818+
},
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"source": [
825+
"'''\n",
826+
"Rotate array\n",
827+
"\n",
828+
"You have been given a random integer array/list(ARR) of size N. Write a function that rotates the given array/list by D elements(towards the left).\n",
829+
"\n",
830+
"Note:\n",
831+
"Change in the input array/list itself. You don't need to return or print the elements.\n",
832+
"\n",
833+
"Input format :\n",
834+
"The first line contains an Integer 't' which denotes the number of test cases or queries to be run. Then the test cases follow.\n",
835+
"\n",
836+
"First line of each test case or query contains an integer 'N' representing the size of the array/list.\n",
837+
"\n",
838+
"Second line contains 'N' single space separated integers representing the elements in the array/list.\n",
839+
"\n",
840+
"Third line contains the value of 'D' by which the array/list needs to be rotated.\n",
841+
"\n",
842+
"Output Format :\n",
843+
"For each test case, print the rotated array/list in a row separated by a single space.\n",
844+
"\n",
845+
"Output for every test case will be printed in a separate line.\n",
846+
"\n",
847+
"Constraints :\n",
848+
"1 <= t <= 10^4\n",
849+
"0 <= N <= 10^6\n",
850+
"0 <= D <= N\n",
851+
"Time Limit: 1 sec\n",
852+
"\n",
853+
"Sample Input 1:\n",
854+
"1\n",
855+
"7\n",
856+
"1 2 3 4 5 6 7\n",
857+
"2\n",
858+
"Sample Output 1:\n",
859+
"3 4 5 6 7 1 2\n",
860+
"\n",
861+
"Sample Input 2:\n",
862+
"2\n",
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"7\n",
864+
"1 2 3 4 5 6 7\n",
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"0\n",
866+
"4\n",
867+
"1 2 3 4\n",
868+
"2\n",
869+
"Sample Output 2:\n",
870+
"1 2 3 4 5 6 7\n",
871+
"3 4 1 2\n",
872+
"'''\n",
873+
"\n",
874+
"from sys import stdin\n",
875+
"\n",
876+
"def rotate(arr, n, d):\n",
877+
" \n",
878+
" if d>n:\n",
879+
" d = d%n\n",
880+
" \n",
881+
" arr[:] = arr[d:] + arr[:n]\n",
882+
" \n",
883+
" return arr\n",
884+
"\n",
885+
"#Taking Input Using Fats I/O\n",
886+
"def takeInput() :\n",
887+
" n = int(stdin.readline().rstrip())\n",
888+
" if n == 0:\n",
889+
" return list(), 0\n",
890+
" arr = list(map(int, stdin.readline().rstrip().split(\" \")))\n",
891+
" return arr, n\n",
892+
"\n",
893+
"#to print the array/list \n",
894+
"def printList(arr, n) : \n",
895+
" for i in range(n) :\n",
896+
" print(arr[i], end = \" \")\n",
897+
" print()\n",
898+
"\n",
899+
"#main\n",
900+
"t = int(stdin.readline().rstrip())\n",
901+
"while t > 0 :\n",
902+
" arr, n = takeInput()\n",
903+
" d = int(stdin.readline().rstrip())\n",
904+
" rotate(arr, n, d)\n",
905+
" printList(arr, n)\n",
906+
" t -= 1"
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],
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"metadata": {
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"id": "U9v5HMwvoabf"
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},
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"source": [
@@ -700,7 +1002,7 @@
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"id": "RmnDHeXiRand",
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"outputId": "416db181-8893-4cd8-bdd6-86f4a5b11269"
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},
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"execution_count": 1,
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",

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