{"segments": [{"id": 1, "seek": 2422, "start": 0.72, "end": 24.22, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة الرقم 11 لمساق رياضيات من فصلة لطلاب طالبات الجامعة الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة المتنقلة بدأنا حديثنا في المحاضرة العاشرة السابقة على اللي هو ال graphs", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 34892, 4587, 2304, 2975, 32767, 3794, 995, 4587, 12602, 1829, 46958, 1829, 9307, 9154, 6156, 9381, 37977, 5296, 9566, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 6055, 19452, 12610, 29245, 25528, 9673, 30241, 20498, 9307, 12174, 38251, 21542, 2407, 35457, 3660, 9673, 2655, 1863, 4587, 37977, 47525, 10721, 8315, 11331, 16254, 12984, 8315, 8978, 9673, 5016, 46958, 25720, 18863, 33599, 25720, 21136, 16758, 28671, 15844, 13672, 1829, 31439, 2423, 24877], "avg_logprob": -0.09624334773484697, "compression_ratio": 1.8571428571428572, 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حاكينا عن الـ undirected graph بعدين أخدنا أمثلة على كل هذه الموضوعات وجينا أخدنا اللي هو النظرية اللي بتقول دايما اللي هو المجموع اللي هو ال degree لل vertices على كل ال vertices اللي في ال V بتساوي 2 فحاصل ضرب اللي هو عدد الخطوط أو عدد ال edges اللي في الشكل", "tokens": [9566, 3555, 3615, 995, 9122, 8315, 11331, 995, 4117, 1829, 8315, 18871, 2423, 39184, 674, 11890, 292, 4295, 39182, 9957, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 15844, 28242, 29538, 9673, 2407, 11242, 45367, 9307, 49610, 1829, 8315, 5551, 9778, 3215, 8315, 13672, 1829, 31439, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 39648, 11778, 47302, 15042, 13672, 1829, 31439, 9673, 7435, 2304, 45367, 13672, 1829, 31439, 2423, 4314, 24976, 32053, 15844, 28242, 2423, 32053, 13672, 1829, 8978, 2423, 691, 39894, 3794, 995, 45865, 568, 6156, 5016, 33546, 1211, 48812, 25513, 13672, 1829, 31439, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 34051, 6225, 3215, 3215, 2423, 8819, 13672, 1829, 8978, 25124, 28820], 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"end": 102.01, "word": " عدد", "probability": 0.9944661458333334}, {"start": 102.01, "end": 102.13, "word": " ال", "probability": 0.9765625}, {"start": 102.13, "end": 102.53, "word": " edges", "probability": 0.84765625}, {"start": 102.53, "end": 103.05, "word": " اللي", "probability": 0.987060546875}, {"start": 103.05, "end": 103.33, "word": " في", "probability": 0.98095703125}, {"start": 103.33, "end": 104.37, "word": " الشكل", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 5, "seek": 11903, "start": 104.79, "end": 119.03, "text": "و بعدين أخدنا أمثلة على هيك و أخدنا بعد هيك شو معنى .. شو معنات اللي هو ال directed graph اللي بيكون .. قولنا بيسير اللي هو الخط اللي هو directed from نقطة إلى نقطة أخرى", "tokens": [2407, 39182, 9957, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 15844, 39896, 4117, 4032, 5551, 9778, 3215, 8315, 39182, 39896, 4117, 13412, 2407, 20449, 1863, 7578, 4386, 13412, 2407, 20449, 8315, 2655, 13672, 1829, 31439, 2423, 12898, 4295, 13672, 1829, 4724, 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"end": 144.93, "word": " نشوف", "probability": 0.8649088541666666}, {"start": 144.93, "end": 145.15, "word": " إيش", "probability": 0.732666015625}, {"start": 145.15, "end": 145.93, "word": " يعرفناه", "probability": 0.62957763671875}], "temperature": 1.0}, {"id": 7, "seek": 16652, "start": 146.46, "end": 166.52, "text": "بقول لو كان عندى graph g1 is a sub graph يعني هذا g1 بنقول عنه sub graph من مين of another graph g يعني g1 عبارة عن sub graph او graph جزئي من ال graph g if and only if the vertex and edges sits of g1", "tokens": [3555, 39648, 45164, 25961, 43242, 7578, 4295, 290, 16, 307, 257, 1422, 4295, 37495, 22653, 23758, 290, 16, 44945, 39648, 18871, 3224, 1422, 4295, 9154, 3714, 9957, 295, 1071, 4295, 290, 37495, 22653, 290, 16, 6225, 3555, 9640, 3660, 18871, 1422, 4295, 1975, 2407, 4295, 10874, 11622, 19986, 1829, 9154, 2423, 4295, 290, 498, 293, 787, 498, 264, 28162, 293, 8819, 12696, 295, 290, 16], "avg_logprob": -0.32102271914482117, "compression_ratio": 1.5393939393939393, 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بنقول إن G1 sub graph من G إذا كان كل ال vertices اللي في G1 موجودة في vertices في G في ال V تبعتهم", "tokens": [38, 16, 366, 25009, 2090, 1385, 295, 264, 28162, 293, 8819, 295, 460, 8717, 5016, 1863, 8717, 2655, 5172, 26108, 14739, 460, 7251, 30544, 3714, 4117, 2407, 11703, 1863, 9154, 13412, 17082, 1211, 6055, 7649, 1829, 9154, 32053, 9154, 32053, 4032, 27842, 16490, 9566, 2407, 9566, 11933, 15730, 44945, 39648, 36145, 460, 16, 1422, 4295, 9154, 460, 11933, 15730, 25961, 28242, 2423, 32053, 13672, 1829, 8978, 460, 16, 3714, 29245, 23328, 3660, 8978, 32053, 8978, 460, 8978, 2423, 691, 6055, 3555, 34268, 16095], "avg_logprob": -0.26134673612458365, "compression_ratio": 1.536231884057971, "no_speech_prob": 0.00013780593872070312, "words": [{"start": 166.55, "end": 166.91, "word": "G1", "probability": 0.4434814453125}, {"start": 166.91, "end": 167.39, "word": " are", "probability": 0.315673828125}, {"start": 167.39, "end": 168.09, "word": " respectively", "probability": 0.78125}, 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15730, 2423, 3566, 4295], "avg_logprob": -0.2471726247242519, "compression_ratio": 1.9744897959183674, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 451.37, "end": 451.85, "word": "نجي", "probability": 0.4342447916666667}, {"start": 451.85, "end": 452.13, "word": " لكي", "probability": 0.572998046875}, {"start": 452.13, "end": 452.47, "word": " أربعة", "probability": 0.7205403645833334}, {"start": 452.47, "end": 452.69, "word": " كي", "probability": 0.685302734375}, {"start": 452.69, "end": 452.99, "word": " أربعة", "probability": 0.9228515625}, {"start": 452.99, "end": 453.11, "word": " اللي", "probability": 0.810791015625}, {"start": 453.11, "end": 453.23, "word": " هو", "probability": 0.57470703125}, {"start": 453.23, "end": 453.55, "word": " واحد", "probability": 0.93359375}, {"start": 453.55, "end": 454.05, "word": " تنين", "probability": 0.7513020833333334}, {"start": 454.05, "end": 454.57, "word": " تلاتة", "probability": 0.9400634765625}, {"start": 454.57, "end": 454.83, "word": " أربعة", "probability": 0.8224283854166666}, {"start": 454.83, "end": 455.11, "word": " فيها", "probability": 0.96630859375}, {"start": 455.11, "end": 455.39, "word": " أربع", "probability": 0.8434244791666666}, {"start": 455.39, "end": 455.63, "word": " عياش", "probability": 0.6392415364583334}, {"start": 455.63, "end": 456.11, "word": " نقاط", "probability": 0.91064453125}, {"start": 456.11, "end": 457.35, "word": " الأربع", "probability": 0.9187825520833334}, {"start": 457.35, "end": 458.07, "word": " نقاط", "probability": 0.9749348958333334}, {"start": 458.07, "end": 459.01, "word": " كلهم", "probability": 0.816162109375}, {"start": 459.01, "end": 459.99, "word": " بين", "probability": 0.927734375}, {"start": 459.99, "end": 460.47, "word": " هذه", "probability": 0.179443359375}, {"start": 460.47, "end": 460.85, "word": " و", "probability": 0.2381591796875}, {"start": 460.85, "end": 461.83, "word": " هذه", "probability": 0.66943359375}, {"start": 461.83, "end": 462.27, "word": " خط", "probability": 0.921875}, {"start": 462.27, "end": 462.53, "word": " و", "probability": 0.485107421875}, {"start": 462.53, "end": 462.91, "word": " بينها", "probability": 0.977294921875}, {"start": 462.91, "end": 462.99, "word": " و", "probability": 0.9482421875}, {"start": 462.99, "end": 463.33, "word": " بينها", "probability": 0.860107421875}, {"start": 463.33, "end": 463.49, "word": " دي", "probability": 0.6630859375}, {"start": 463.49, "end": 463.83, "word": " خط", "probability": 0.99462890625}, {"start": 463.83, "end": 464.01, "word": " و", "probability": 0.460205078125}, {"start": 464.01, "end": 464.41, "word": " بينها", "probability": 0.986572265625}, {"start": 464.41, "end": 464.51, "word": " و", "probability": 0.98828125}, {"start": 464.51, "end": 464.77, "word": " بينها", "probability": 0.984375}, {"start": 464.77, "end": 464.95, "word": " دي", "probability": 0.98876953125}, {"start": 464.95, "end": 465.29, "word": " خط", "probability": 0.99609375}, {"start": 465.29, "end": 465.95, "word": " يعني", "probability": 0.91259765625}, {"start": 465.95, "end": 466.33, "word": " كل", "probability": 0.9794921875}, {"start": 466.33, "end": 467.41, "word": " النقاط", "probability": 0.955078125}, {"start": 467.41, "end": 468.17, "word": " اللي", "probability": 0.98486328125}, {"start": 468.17, "end": 468.51, "word": " هم", "probability": 0.47802734375}, {"start": 468.51, "end": 469.17, "word": " adjacent", "probability": 0.88232421875}, {"start": 469.17, "end": 469.87, "word": " لبعض", "probability": 0.924072265625}, {"start": 469.87, "end": 470.57, "word": " عشان", "probability": 0.94775390625}, {"start": 470.57, "end": 470.79, "word": " هيك", "probability": 0.89306640625}, {"start": 470.79, "end": 471.49, "word": " بنسميه", "probability": 0.885986328125}, {"start": 471.49, "end": 471.83, "word": " graph", "probability": 0.68408203125}, {"start": 471.83, "end": 472.49, "word": " إذا", "probability": 0.6962890625}, {"start": 472.49, "end": 472.97, "word": " ال", "probability": 0.92138671875}, {"start": 472.97, "end": 473.41, "word": " complete", "probability": 0.7978515625}, {"start": 473.41, "end": 474.09, "word": " graph", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 21, "seek": 49611, "start": 474.69, "end": 496.11, "text": "هو graph عادي كل نقطين فيه adjacent يعني كل نقطين فيه graph حالة خاصة من هذول ال complete graph اللي هي عائلة من ال graphs اسمها kn ايش ال kn هذه اللي هي عددها n من اللي هو ال vertices فيها؟", "tokens": [3224, 2407, 4295, 6225, 995, 16254, 28242, 8717, 47432, 9957, 8978, 3224, 24441, 37495, 22653, 28242, 8717, 47432, 9957, 8978, 3224, 4295, 11331, 6027, 3660, 16490, 33546, 3660, 9154, 8032, 8848, 12610, 2423, 3566, 4295, 13672, 1829, 39896, 6225, 16373, 37977, 9154, 2423, 24877, 24525, 2304, 11296, 444, 1975, 1829, 8592, 2423, 444, 29538, 13672, 1829, 39896, 6225, 3215, 3215, 11296, 297, 9154, 13672, 1829, 31439, 2423, 32053, 8978, 11296, 22807], "avg_logprob": -0.2291666679084301, "compression_ratio": 1.686046511627907, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 474.69, "end": 475.21, "word": "هو", "probability": 0.90185546875}, {"start": 475.21, "end": 475.67, "word": " graph", "probability": 0.35498046875}, {"start": 475.67, "end": 476.25, "word": " عادي", "probability": 0.8971354166666666}, {"start": 476.25, "end": 476.81, "word": " كل", "probability": 0.892578125}, {"start": 476.81, "end": 477.83, "word": " نقطين", "probability": 0.8074544270833334}, {"start": 477.83, "end": 478.41, "word": " فيه", "probability": 0.941650390625}, {"start": 478.41, "end": 478.89, "word": " adjacent", "probability": 0.75439453125}, {"start": 478.89, "end": 479.45, "word": " يعني", "probability": 0.818115234375}, {"start": 479.45, "end": 479.69, "word": " كل", "probability": 0.94580078125}, {"start": 479.69, "end": 480.17, "word": " نقطين", "probability": 0.9812825520833334}, {"start": 480.17, "end": 480.43, "word": " فيه", "probability": 0.88623046875}, {"start": 480.43, "end": 480.91, "word": " graph", "probability": 0.68408203125}, {"start": 480.91, "end": 482.05, "word": " حالة", "probability": 0.8043619791666666}, {"start": 482.05, "end": 482.69, "word": " خاصة", "probability": 0.9814453125}, {"start": 482.69, "end": 482.89, "word": " من", "probability": 0.98291015625}, {"start": 482.89, "end": 483.43, "word": " هذول", "probability": 0.5713297526041666}, {"start": 483.43, "end": 483.59, "word": " ال", "probability": 0.379638671875}, {"start": 483.59, "end": 484.05, "word": " complete", "probability": 0.470458984375}, {"start": 484.05, "end": 484.65, "word": " graph", "probability": 0.87060546875}, {"start": 484.65, "end": 485.47, "word": " اللي", "probability": 0.8212890625}, {"start": 485.47, "end": 485.73, "word": " هي", "probability": 0.697265625}, {"start": 485.73, "end": 486.45, "word": " عائلة", "probability": 0.9962565104166666}, {"start": 486.45, "end": 486.99, "word": " من", "probability": 0.9453125}, {"start": 486.99, "end": 487.27, "word": " ال", "probability": 0.650390625}, {"start": 487.27, "end": 487.81, "word": " graphs", "probability": 0.8251953125}, {"start": 487.81, "end": 488.43, "word": " اسمها", "probability": 0.9503580729166666}, {"start": 488.43, "end": 488.85, "word": " kn", "probability": 0.320556640625}, {"start": 488.85, "end": 489.23, "word": " ايش", "probability": 0.7300618489583334}, {"start": 489.23, "end": 489.35, "word": " ال", "probability": 0.95751953125}, {"start": 489.35, "end": 489.69, "word": " kn", "probability": 0.5732421875}, {"start": 489.69, "end": 490.21, "word": " هذه", "probability": 0.71826171875}, {"start": 490.21, "end": 490.91, "word": " اللي", "probability": 0.97119140625}, {"start": 490.91, "end": 491.23, "word": " هي", "probability": 0.88525390625}, {"start": 491.23, "end": 492.45, "word": " عددها", "probability": 0.8580322265625}, {"start": 492.45, "end": 492.95, "word": " n", "probability": 0.51318359375}, {"start": 492.95, "end": 493.97, "word": " من", "probability": 0.958984375}, {"start": 493.97, "end": 494.49, "word": " اللي", "probability": 0.9189453125}, {"start": 494.49, "end": 494.77, "word": " هو", "probability": 0.93017578125}, {"start": 494.77, "end": 494.89, "word": " ال", "probability": 0.90771484375}, {"start": 494.89, "end": 495.37, "word": " vertices", "probability": 0.97509765625}, {"start": 495.37, "end": 496.11, "word": " فيها؟", "probability": 0.9581705729166666}], "temperature": 1.0}, {"id": 22, "seek": 51874, "start": 496.46, "end": 518.74, "text": "و بيعملين complete graph يعني كل النقاط are adjacent ده نشوف اللي بعدها هاي K خمسة مثلا بخمسة هاي عندى خمس نقاط واحدة تنتهي من تلاتة اربعة خمسة واضح ان كل النقاط كل واحدة بيطلع منها اربع خطوط للاخرين فعشان هيك بنسميها complete graph من النوع K", "tokens": [2407, 4724, 1829, 25957, 1211, 9957, 3566, 4295, 37495, 22653, 28242, 28239, 4587, 41193, 366, 24441, 11778, 3224, 8717, 8592, 38688, 13672, 1829, 39182, 11296, 8032, 47302, 591, 16490, 2304, 3794, 3660, 50113, 15040, 4724, 9778, 2304, 3794, 3660, 8032, 47302, 43242, 7578, 16490, 2304, 3794, 8717, 4587, 41193, 36764, 24401, 3660, 6055, 29399, 3224, 1829, 9154, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 16490, 2304, 3794, 3660, 4032, 46958, 5016, 16472, 28242, 28239, 4587, 41193, 28242, 36764, 24401, 3660, 4724, 1829, 9566, 1211, 3615, 9154, 11296, 1975, 25513, 3615, 16490, 9566, 2407, 9566, 24976, 47283, 2288, 9957, 6156, 3615, 8592, 7649, 39896, 4117, 44945, 38251, 1829, 11296, 3566, 4295, 9154, 28239, 45367, 591], "avg_logprob": -0.25883150929990023, "compression_ratio": 1.7901785714285714, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 496.46, "end": 496.7, "word": "و", "probability": 0.67138671875}, {"start": 496.7, "end": 498.6, "word": " بيعملين", "probability": 0.52908935546875}, {"start": 498.6, "end": 498.92, "word": " complete", "probability": 0.426513671875}, {"start": 498.92, "end": 499.44, "word": " graph", "probability": 0.919921875}, {"start": 499.44, "end": 499.72, "word": " يعني", "probability": 0.825439453125}, {"start": 499.72, "end": 500.0, "word": " كل", "probability": 0.87451171875}, {"start": 500.0, "end": 502.26, "word": " النقاط", "probability": 0.72509765625}, {"start": 502.26, "end": 502.68, "word": " are", "probability": 0.68505859375}, {"start": 502.68, "end": 503.46, "word": " adjacent", "probability": 0.96337890625}, {"start": 503.46, "end": 503.98, "word": " ده", "probability": 0.59716796875}, {"start": 503.98, "end": 504.24, "word": " نشوف", "probability": 0.8046061197916666}, {"start": 504.24, "end": 504.38, "word": " اللي", "probability": 0.929443359375}, {"start": 504.38, "end": 505.0, "word": " بعدها", "probability": 0.74462890625}, {"start": 505.0, "end": 505.32, "word": " هاي", "probability": 0.51177978515625}, {"start": 505.32, "end": 505.44, "word": " K", "probability": 0.74169921875}, {"start": 505.44, "end": 505.82, "word": " خمسة", "probability": 0.8345947265625}, {"start": 505.82, "end": 506.52, "word": " مثلا", "probability": 0.941162109375}, {"start": 506.52, "end": 507.52, "word": " بخمسة", "probability": 0.8131591796875}, {"start": 507.52, "end": 507.78, "word": " هاي", "probability": 0.5389404296875}, {"start": 507.78, "end": 508.2, "word": " عندى", "probability": 0.743896484375}, {"start": 508.2, "end": 508.7, "word": " خمس", "probability": 0.9601236979166666}, {"start": 508.7, "end": 509.02, "word": " نقاط", "probability": 0.96533203125}, {"start": 509.02, "end": 509.32, "word": " واحدة", "probability": 0.9210611979166666}, {"start": 509.32, "end": 509.64, "word": " تنتهي", "probability": 0.5738525390625}, {"start": 509.64, "end": 509.76, "word": " من", "probability": 0.5703125}, {"start": 509.76, "end": 510.14, "word": " تلاتة", "probability": 0.756103515625}, {"start": 510.14, "end": 510.36, "word": " اربعة", "probability": 0.8243815104166666}, {"start": 510.36, "end": 510.72, "word": " خمسة", "probability": 0.92236328125}, {"start": 510.72, "end": 511.0, "word": " واضح", "probability": 0.9664713541666666}, {"start": 511.0, "end": 511.14, "word": " ان", "probability": 0.666015625}, {"start": 511.14, "end": 511.44, "word": " كل", "probability": 0.91552734375}, {"start": 511.44, "end": 511.9, "word": " النقاط", "probability": 0.8225911458333334}, {"start": 511.9, "end": 512.1, "word": " كل", "probability": 0.91357421875}, {"start": 512.1, "end": 512.36, "word": " واحدة", "probability": 0.98681640625}, {"start": 512.36, "end": 512.6, "word": " بيطلع", "probability": 0.83779296875}, {"start": 512.6, "end": 512.9, "word": " منها", "probability": 0.994384765625}, {"start": 512.9, "end": 513.3, "word": " اربع", "probability": 0.7669270833333334}, {"start": 513.3, "end": 513.72, "word": " خطوط", "probability": 0.97705078125}, {"start": 513.72, "end": 514.66, "word": " للاخرين", "probability": 0.8802490234375}, {"start": 514.66, "end": 515.42, "word": " فعشان", "probability": 0.9566650390625}, {"start": 515.42, "end": 515.66, "word": " هيك", "probability": 0.7100830078125}, {"start": 515.66, "end": 516.48, "word": " بنسميها", "probability": 0.916748046875}, {"start": 516.48, "end": 517.14, "word": " complete", "probability": 0.8115234375}, {"start": 517.14, "end": 517.94, "word": " graph", "probability": 0.9580078125}, {"start": 517.94, "end": 518.14, "word": " من", "probability": 0.9873046875}, {"start": 518.14, "end": 518.4, "word": " النوع", "probability": 0.945068359375}, {"start": 518.4, "end": 518.74, "word": " K", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 23, "seek": 53926, "start": 519.72, "end": 539.26, "text": "لو واحد بدى يرسم K6 بتقدر ترسمها بنفس الاسم و K7 طبعا بتغلب شوية لكن بتظلها في نفس النطاق هذه بنسميها complete graphs او مثل على ال complete graphs اللي هي العائلة اللي سميناها KN", "tokens": [1211, 2407, 36764, 24401, 47525, 7578, 7251, 2288, 38251, 591, 21, 39894, 28543, 2288, 6055, 2288, 38251, 11296, 44945, 36178, 2423, 32277, 2304, 4032, 591, 22, 23032, 3555, 3615, 995, 39894, 17082, 46152, 13412, 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"word": " يعني", "probability": 0.816650390625}, {"start": 609.2, "end": 609.52, "word": " خط", "probability": 0.92822265625}, {"start": 609.52, "end": 609.72, "word": " بين", "probability": 0.95166015625}, {"start": 609.72, "end": 610.1, "word": " V1", "probability": 0.97509765625}, {"start": 610.1, "end": 610.22, "word": " و", "probability": 0.99365234375}, {"start": 610.22, "end": 610.68, "word": " V2", "probability": 0.959228515625}, {"start": 610.68, "end": 610.86, "word": " و", "probability": 0.90771484375}, {"start": 610.86, "end": 611.08, "word": " خط", "probability": 0.9169921875}, {"start": 611.08, "end": 611.28, "word": " بين", "probability": 0.935546875}, {"start": 611.28, "end": 611.7, "word": " V2", "probability": 0.990966796875}, {"start": 611.7, "end": 611.82, "word": " و", "probability": 0.99609375}, {"start": 611.82, "end": 612.24, "word": " V3", "probability": 0.958251953125}], "temperature": 1.0}, {"id": 28, "seek": 63692, "start": 612.59, "end": 636.93, "text": "و خط بين V3 و V4 لما أصل عند خط بين اللي هي النقطة الأخيرة VN و برجع لمين لل V1 و كإن إيش بسكر و بعمله cycle زي دائرة أو اللي هو دورة كاملة ماشي the cycles C3, C4, C5, C6 are displaced انفجارا هى وهذه وهذه", "tokens": [2407, 16490, 9566, 49374, 691, 18, 4032, 691, 19, 5296, 15042, 5551, 36520, 43242, 16490, 9566, 49374, 13672, 1829, 39896, 28239, 47432, 3660, 16247, 9778, 48923, 691, 45, 4032, 4724, 47341, 3615, 32767, 9957, 24976, 691, 16, 4032, 9122, 28814, 1863, 11933, 1829, 8592, 4724, 3794, 37983, 4032, 4724, 25957, 43761, 6586, 30767, 1829, 11778, 16373, 25720, 34051, 13672, 1829, 31439, 11778, 13063, 3660, 9122, 10943, 37977, 3714, 33599, 1829, 264, 17796, 383, 18, 11, 383, 19, 11, 383, 20, 11, 383, 21, 366, 33692, 16472, 5172, 7435, 9640, 995, 8032, 7578, 37037, 24192, 37037, 24192], "avg_logprob": -0.2931701129244775, "compression_ratio": 1.4722222222222223, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 612.59, "end": 612.95, "word": "و", "probability": 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adjacent يعني ال cycle ممكن تكون complete يعني مثال على complete graph نجي للي بعدها C4", "tokens": [6027, 20292, 39896, 691, 16, 691, 17, 691, 17, 691, 18, 691, 18, 691, 16, 11933, 15730, 14111, 23758, 6586, 20328, 9640, 6024, 48506, 23758, 2423, 4295, 3566, 5551, 3224, 3566, 5296, 33456, 3224, 28242, 3714, 17082, 9566, 9957, 24441, 37495, 22653, 2423, 6586, 3714, 43020, 6055, 30544, 3566, 37495, 22653, 50113, 6027, 15844, 3566, 4295, 8717, 7435, 1829, 5296, 20292, 39182, 11296, 383, 19], "avg_logprob": -0.2340198838801095, "compression_ratio": 1.4885057471264367, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 638.01, "end": 638.35, "word": "اللي", "probability": 0.4923095703125}, {"start": 638.35, "end": 638.79, "word": " هي", "probability": 0.884765625}, {"start": 638.79, "end": 640.39, "word": " V1", "probability": 0.727294921875}, {"start": 640.39, "end": 641.01, "word": " V2", "probability": 0.754638671875}, {"start": 641.01, "end": 641.67, "word": " V2", 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تحت ال degree لكل واحدة تلاتة لإنه بيطلع بينها تلت خطوط فبكون مجموع ال degrees اللي تحت 18 يعني اللي تحت 18 و اللي فوق 18 بيطلع عن 36 36 هنا ضعف عدد الخطوط زي ما عكينا قبل شوية هذا هي this complete bipartite", "tokens": [5172, 3555, 30544, 3714, 7435, 2304, 45367, 2423, 5310, 24976, 1863, 4587, 41193, 13672, 1829, 6156, 30543, 2443, 2423, 7649, 2423, 1386, 13672, 1829, 6055, 33753, 2423, 4314, 5296, 28820, 36764, 24401, 3660, 6055, 1211, 9307, 3660, 5296, 28814, 1863, 3224, 4724, 1829, 9566, 1211, 3615, 49374, 11296, 6055, 1211, 2655, 16490, 9566, 2407, 9566, 6156, 3555, 30544, 3714, 7435, 2304, 45367, 2423, 5310, 13672, 1829, 6055, 33753, 2443, 37495, 22653, 13672, 1829, 6055, 33753, 2443, 4032, 13672, 1829, 6156, 30543, 2443, 4724, 1829, 9566, 1211, 3615, 18871, 8652, 8652, 34105, 48812, 3615, 5172, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 30767, 1829, 19446, 6225, 4117, 1829, 8315, 12174, 36150, 13412, 2407, 10632, 23758, 39896, 341, 3566, 28741, 642], "avg_logprob": 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with degree تلاتة و تلاتة vertices with degree ستة زي ما وضحت قبل و شوية الان مدموع ال degree لكل ال V اللي هما الستة والتلاتة ستة", "tokens": [38, 2662, 575, 2309, 32053, 37495, 22653, 23758, 2423, 39184, 34687, 4724, 1829, 26890, 2655, 995, 36081, 2423, 39184, 21884, 13672, 1829, 12174, 1211, 8315, 18871, 3224, 30767, 1829, 13672, 1829, 33427, 3224, 46740, 8608, 2655, 3660, 32053, 365, 4314, 6055, 1211, 9307, 3660, 37495, 22653, 8608, 2655, 3660, 32053, 365, 4314, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 3660, 32053, 365, 4314, 8608, 2655, 3660, 30767, 1829, 19446, 4032, 11242, 33753, 12174, 36150, 4032, 13412, 2407, 10632, 2423, 7649, 3714, 40448, 45367, 2423, 4314, 5296, 28820, 2423, 691, 13672, 1829, 8032, 15042, 2423, 14851, 3660, 16070, 2655, 1211, 9307, 3660, 8608, 2655, 3660], "avg_logprob": -0.25707547113580526, "compression_ratio": 1.9275362318840579, "no_speech_prob": 3.933906555175781e-06, "words": [{"start": 1512.84, "end": 1513.44, "word": "Graph", "probability": 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"probability": 0.938232421875}, {"start": 1532.58, "end": 1532.82, "word": " هما", "probability": 0.580810546875}, {"start": 1532.82, "end": 1533.22, "word": " الستة", "probability": 0.7980143229166666}, {"start": 1533.22, "end": 1534.06, "word": " والتلاتة", "probability": 0.88544921875}, {"start": 1534.06, "end": 1535.02, "word": " ستة", "probability": 0.8888346354166666}], "temperature": 1.0}, {"id": 68, "seek": 155594, "start": 1535.76, "end": 1555.94, "text": "كل واحد ديجري تلاتة و تلاتة كل واحدة ديجري ستة بتطلع ل 36 يعني اتنين في عدد الخطوط اللي هو بيكون عدد الخطوط 18 خط لإن ال 36 زي ما انتوا عارفين يعني مضاعف عدد الخطوط جولنا اذا الكل بيكون عدد الخطوط عنا 18 خط", "tokens": [28820, 36764, 24401, 11778, 1829, 7435, 16572, 6055, 1211, 9307, 3660, 4032, 6055, 1211, 9307, 3660, 28242, 36764, 24401, 3660, 11778, 1829, 7435, 16572, 8608, 2655, 3660, 39894, 9566, 1211, 3615, 5296, 8652, 37495, 22653, 1975, 2655, 1863, 9957, 8978, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 13672, 1829, 31439, 4724, 1829, 30544, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 2443, 16490, 9566, 5296, 28814, 1863, 2423, 8652, 30767, 1829, 19446, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 37495, 22653, 3714, 11242, 45761, 5172, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 10874, 12610, 8315, 1975, 15730, 2423, 28820, 4724, 1829, 30544, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 6225, 8315, 2443, 16490, 9566], "avg_logprob": -0.20778508209868482, "compression_ratio": 2.0809248554913293, "no_speech_prob": 6.198883056640625e-06, "words": [{"start": 1535.76, "end": 1536.08, "word": "كل", "probability": 0.8076171875}, {"start": 1536.08, "end": 1536.3, "word": " واحد", "probability": 0.89892578125}, {"start": 1536.3, "end": 1536.62, "word": " ديجري", "probability": 0.639862060546875}, {"start": 1536.62, "end": 1537.24, "word": " تلاتة", "probability": 0.846923828125}, {"start": 1537.24, "end": 1537.88, "word": " و", "probability": 0.492919921875}, {"start": 1537.88, "end": 1538.3, "word": " تلاتة", "probability": 0.880859375}, {"start": 1538.3, "end": 1538.44, "word": " كل", "probability": 0.91162109375}, {"start": 1538.44, "end": 1538.68, "word": " واحدة", "probability": 0.8606770833333334}, {"start": 1538.68, "end": 1538.98, "word": " ديجري", "probability": 0.931640625}, {"start": 1538.98, "end": 1539.32, "word": " ستة", "probability": 0.9544270833333334}, {"start": 1539.32, "end": 1539.56, "word": " بتطلع", "probability": 0.69775390625}, {"start": 1539.56, "end": 1539.64, "word": " ل", "probability": 0.328857421875}, {"start": 1539.64, "end": 1540.02, "word": " 36", "probability": 0.4697265625}, {"start": 1540.02, "end": 1540.86, "word": " يعني", "probability": 0.86865234375}, {"start": 1540.86, "end": 1541.58, "word": " اتنين", "probability": 0.929443359375}, {"start": 1541.58, "end": 1542.06, "word": " في", "probability": 0.82958984375}, {"start": 1542.06, "end": 1542.68, "word": " عدد", "probability": 0.9811197916666666}, {"start": 1542.68, "end": 1543.38, "word": " الخطوط", "probability": 0.9866943359375}, {"start": 1543.38, "end": 1544.2, "word": " اللي", "probability": 0.94775390625}, {"start": 1544.2, "end": 1544.44, "word": " هو", "probability": 0.9765625}, {"start": 1544.44, "end": 1544.92, "word": " بيكون", "probability": 0.7316080729166666}, {"start": 1544.92, "end": 1545.26, "word": " عدد", "probability": 0.99658203125}, {"start": 1545.26, "end": 1545.58, "word": " الخطوط", "probability": 0.9903564453125}, {"start": 1545.58, "end": 1545.94, "word": " 18", "probability": 0.2384033203125}, {"start": 1545.94, "end": 1546.64, "word": " خط", "probability": 0.92578125}, {"start": 1546.64, "end": 1547.06, "word": " لإن", "probability": 0.7842610677083334}, {"start": 1547.06, "end": 1547.4, "word": " ال", "probability": 0.61572265625}, {"start": 1547.4, "end": 1547.86, "word": " 36", "probability": 0.837890625}, {"start": 1547.86, "end": 1548.16, "word": " زي", "probability": 0.83349609375}, {"start": 1548.16, "end": 1548.2, "word": " ما", "probability": 0.9111328125}, {"start": 1548.2, "end": 1548.38, "word": " انتوا", "probability": 0.8103841145833334}, {"start": 1548.38, "end": 1548.72, "word": " عارفين", "probability": 0.979736328125}, {"start": 1548.72, "end": 1549.16, "word": " يعني", "probability": 0.61669921875}, {"start": 1549.16, "end": 1550.4, "word": " مضاعف", "probability": 0.80767822265625}, {"start": 1550.4, "end": 1550.74, "word": " عدد", "probability": 0.9759114583333334}, {"start": 1550.74, "end": 1551.16, "word": " الخطوط", "probability": 0.98828125}, {"start": 1551.16, "end": 1551.52, "word": " جولنا", "probability": 0.5801595052083334}, {"start": 1551.52, "end": 1551.86, "word": " اذا", "probability": 0.6324462890625}, {"start": 1551.86, "end": 1552.9, "word": " الكل", "probability": 0.7027587890625}, {"start": 1552.9, "end": 1553.6, "word": " بيكون", "probability": 0.9195963541666666}, {"start": 1553.6, "end": 1553.88, "word": " عدد", "probability": 0.9930013020833334}, {"start": 1553.88, "end": 1554.28, "word": " الخطوط", "probability": 0.9912109375}, {"start": 1554.28, "end": 1554.5, "word": " عنا", "probability": 0.745361328125}, {"start": 1554.5, "end": 1554.98, "word": " 18", "probability": 0.8759765625}, {"start": 1554.98, "end": 1555.94, "word": " خط", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 69, "seek": 156891, "start": 1556.55, "end": 1568.91, "text": "So that K36 has 18 edges تقريبا 18 خط degree sequence نعرف حاجة اسمها degree sequence نشوف ايش degree sequence", "tokens": [6455, 300, 591, 11309, 575, 2443, 8819, 6055, 4587, 16572, 3555, 995, 2443, 16490, 9566, 4314, 8310, 8717, 3615, 28480, 11331, 26108, 3660, 24525, 2304, 11296, 4314, 8310, 8717, 8592, 38688, 1975, 1829, 8592, 4314, 8310], "avg_logprob": -0.4400337870056565, "compression_ratio": 1.2432432432432432, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1556.55, "end": 1556.87, "word": "So", "probability": 0.280029296875}, {"start": 1556.87, "end": 1557.29, "word": " that", 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"probability": 0.8846028645833334}, {"start": 1564.57, "end": 1564.91, "word": " degree", "probability": 0.943359375}, {"start": 1564.91, "end": 1566.15, "word": " sequence", "probability": 0.9833984375}, {"start": 1566.15, "end": 1567.89, "word": " نشوف", "probability": 0.80908203125}, {"start": 1567.89, "end": 1568.07, "word": " ايش", "probability": 0.86083984375}, {"start": 1568.07, "end": 1568.37, "word": " degree", "probability": 0.7373046875}, {"start": 1568.37, "end": 1568.91, "word": " sequence", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 70, "seek": 159292, "start": 1570.2, "end": 1592.92, "text": "الشعر الله سهل يعني suppose that D1 وD2 وDn are degree of the vertices of a graph يعني في عندنا graph بيسيده graph زي ال graph تبعت المرة الفاتة عندنا graph G هذا ال graph جينا حسبنا اللي هي فيه N من ال vertices حسبنا أول واحدة لجينا انها degree D1 التانية D2 التلاتة Dn", "tokens": [6027, 8592, 3615, 2288, 21984, 8608, 3224, 1211, 37495, 22653, 7297, 300, 413, 16, 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"end": 1571.82, "word": " suppose", "probability": 0.2369384765625}, {"start": 1571.82, "end": 1572.16, "word": " that", "probability": 0.58544921875}, {"start": 1572.16, "end": 1572.68, "word": " D1", "probability": 0.6444091796875}, {"start": 1572.68, "end": 1573.38, "word": " وD2", "probability": 0.845703125}, {"start": 1573.38, "end": 1574.08, "word": " وDn", "probability": 0.7870279947916666}, {"start": 1574.08, "end": 1574.5, "word": " are", "probability": 0.7578125}, {"start": 1574.5, "end": 1575.06, "word": " degree", "probability": 0.7939453125}, {"start": 1575.06, "end": 1575.92, "word": " of", "probability": 0.96923828125}, {"start": 1575.92, "end": 1576.1, "word": " the", "probability": 0.73974609375}, {"start": 1576.1, "end": 1576.78, "word": " vertices", "probability": 0.97021484375}, {"start": 1576.78, "end": 1577.02, "word": " of", "probability": 0.97119140625}, {"start": 1577.02, "end": 1577.2, "word": " a", "probability": 0.640625}, {"start": 1577.2, "end": 1577.34, "word": " graph", "probability": 0.9541015625}, {"start": 1577.34, "end": 1577.68, "word": " يعني", "probability": 0.860107421875}, {"start": 1577.68, "end": 1577.82, "word": " في", "probability": 0.81396484375}, {"start": 1577.82, "end": 1578.14, "word": " عندنا", "probability": 0.85009765625}, {"start": 1578.14, "end": 1578.44, "word": " graph", "probability": 0.8056640625}, {"start": 1578.44, "end": 1578.9, "word": " بيسيده", "probability": 0.5139892578125}, {"start": 1578.9, "end": 1579.12, "word": " graph", "probability": 0.82275390625}, {"start": 1579.12, "end": 1579.32, "word": " زي", "probability": 0.96484375}, {"start": 1579.32, "end": 1579.44, "word": " ال", "probability": 0.50390625}, {"start": 1579.44, "end": 1579.6, "word": " graph", "probability": 0.462158203125}, {"start": 1579.6, "end": 1580.06, "word": " تبعت", "probability": 0.5350748697916666}, {"start": 1580.06, "end": 1580.4, "word": " المرة", "probability": 0.884765625}, {"start": 1580.4, "end": 1580.86, "word": " الفاتة", "probability": 0.6709798177083334}, {"start": 1580.86, "end": 1581.76, "word": " عندنا", "probability": 0.832275390625}, {"start": 1581.76, "end": 1582.3, "word": " graph", "probability": 0.8740234375}, {"start": 1582.3, "end": 1582.58, "word": " G", "probability": 0.806640625}, {"start": 1582.58, "end": 1583.32, "word": " هذا", "probability": 0.7802734375}, {"start": 1583.32, "end": 1583.48, "word": " ال", "probability": 0.86083984375}, {"start": 1583.48, "end": 1583.94, "word": " graph", "probability": 0.75146484375}, {"start": 1583.94, "end": 1584.54, "word": " جينا", "probability": 0.8308919270833334}, {"start": 1584.54, "end": 1585.24, "word": " حسبنا", "probability": 0.98486328125}, {"start": 1585.24, "end": 1585.94, "word": " اللي", "probability": 0.90185546875}, {"start": 1585.94, "end": 1586.18, "word": " هي", "probability": 0.587890625}, {"start": 1586.18, "end": 1586.6, "word": " فيه", "probability": 0.719482421875}, {"start": 1586.6, "end": 1586.82, "word": " N", "probability": 0.438232421875}, {"start": 1586.82, "end": 1587.02, "word": " من", "probability": 0.9912109375}, {"start": 1587.02, "end": 1587.2, "word": " ال", "probability": 0.9794921875}, {"start": 1587.2, "end": 1587.68, "word": " vertices", "probability": 0.98046875}, {"start": 1587.68, "end": 1588.92, "word": " حسبنا", "probability": 0.9842122395833334}, {"start": 1588.92, "end": 1589.36, "word": " أول", "probability": 0.95263671875}, {"start": 1589.36, "end": 1589.78, "word": " واحدة", "probability": 0.9436848958333334}, {"start": 1589.78, "end": 1590.06, "word": " لجينا", "probability": 0.7716064453125}, {"start": 1590.06, "end": 1590.26, "word": " انها", "probability": 0.58984375}, {"start": 1590.26, "end": 1590.54, "word": " degree", "probability": 0.9462890625}, {"start": 1590.54, "end": 1591.02, "word": " D1", "probability": 0.90625}, {"start": 1591.02, "end": 1591.56, "word": " التانية", "probability": 0.7150065104166666}, {"start": 1591.56, "end": 1592.0, "word": " D2", "probability": 0.967041015625}, {"start": 1592.0, "end": 1592.54, "word": " التلاتة", "probability": 0.8228759765625}, {"start": 1592.54, "end": 1592.92, "word": " Dn", "probability": 0.800048828125}], "temperature": 1.0}, {"id": 71, "seek": 160816, "start": 1593.1, "end": 1608.16, "text": "عندما نرتب تساعد تنازلي D1 أكبر سوى D2 أكبر سوى D3 أكبر سوى DN هذه الـ D1 وD2 وDN المرتبة اللي هي بشكل تنازلي", "tokens": [3615, 41260, 15042, 8717, 2288, 2655, 3555, 6055, 3794, 995, 22488, 6055, 1863, 31377, 20292, 413, 16, 5551, 4117, 26890, 8608, 2407, 7578, 413, 17, 5551, 4117, 26890, 8608, 2407, 7578, 413, 18, 5551, 4117, 26890, 8608, 2407, 7578, 21500, 29538, 2423, 39184, 413, 16, 4032, 35, 17, 4032, 35, 45, 9673, 43500, 49401, 13672, 1829, 39896, 4724, 8592, 28820, 6055, 1863, 31377, 20292], "avg_logprob": -0.39615384615384613, "compression_ratio": 1.6306306306306306, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1593.1, "end": 1593.62, "word": "عندما", "probability": 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هي واحد", "tokens": [2655, 1211, 9307, 3660, 4314, 371, 16, 38392, 39896, 36764, 24401, 1975, 2655, 1863, 9957, 4314, 371, 19, 38392, 39896, 36764, 24401], "avg_logprob": -0.28736412006875744, "compression_ratio": 1.380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1717.62, "end": 1718.6, "word": "تلاتة", "probability": 0.771697998046875}, {"start": 1718.6, "end": 1719.18, "word": " degree", "probability": 0.8740234375}, {"start": 1719.18, "end": 1720.14, "word": " v1", "probability": 0.608154296875}, {"start": 1720.14, "end": 1720.7, "word": " التي", "probability": 0.0906982421875}, {"start": 1720.7, "end": 1720.9, "word": " هي", "probability": 0.904296875}, {"start": 1720.9, "end": 1721.38, "word": " واحد", "probability": 0.8984375}, {"start": 1721.38, "end": 1722.1, "word": " اتنين", "probability": 0.8616943359375}, {"start": 1722.1, "end": 1723.48, "word": " degree", "probability": 0.931640625}, {"start": 1723.48, "end": 1724.44, "word": " v4", "probability": 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