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{ "cells": [ { "cell_type": "markdown", "id": "a469358e-2f57-4bd6-9c8d-c59f3d77920b", "metadata": {}, "source": [ "### Q53\n", "How many, not necessarily distinct, values of \\(\\binom{n}{r}\\), for \\(1 \\le n \\le 100\\), are greater than one-million?" ] }, { "cell_type": "code", "execution_count": 1, "id": "62ce1f5d-9a9e-4fca-9713-10e7c3085bbd", "metadata": {}, "outputs": [], "source": [ "def nCr_exceed_m(n,m):\n", " pascal_triangle = [[0 for i in range(n+1)] for j in range(n+1)]\n", " pascal_triangle[0][0] = 1\n", " match_count = 0\n", " for i in range(1,n+1):\n", " for j in range(i):\n", " pascal_triangle[i][j] += pascal_triangle[i-1][j]\n", " pascal_triangle[i][j+1] += pascal_triangle[i-1][j]\n", " for j in range(i+1):\n", " if pascal_triangle[i][j] > m:\n", " match_count += 1\n", " return match_count" ] }, { "cell_type": "code", "execution_count": 2, "id": "60a03530-995d-4e60-872e-ecc2f17520ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 933 µs, sys: 153 µs, total: 1.09 ms\n", "Wall time: 1.09 ms\n" ] }, { "data": { "text/plain": [ "4075" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%time\n", "nCr_exceed_m(100,1000000)" ] }, { "cell_type": "code", "execution_count": null, "id": "bd7ddc2f-5964-49c3-a927-774399b0b0a9", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }
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