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upper, pyramid
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@DavidLeoni
DavidLeoni committed Oct 12, 2018
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Showing 1 changed file with 150 additions and 27 deletions.
177 changes: 150 additions & 27 deletions exercises/matrices/matrices-solution.ipynb
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" <iframe\n",
" width=\"900\"\n",
" height=\"650\"\n",
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" src=\"https://pythontutor.com/iframe-embed.html#py=3&code=%0A%23+WARNING%3A+WRONG+CODE%0Adef+deep_clone_wrong%28mat%29%3A%0A++++%22%22%22+RETURN+a+NEW+list+of+lists+which+is+a+COMPLETE+DEEP+clone%0A++++++++of+mat+%28which+is+a+list+of+lists%29%0A++++%22%22%22%0A++++return+mat%5B%3A%5D+%23+NOT+SUFFICIENT+%21%0A++++++++++++++++++%23+This+is+a+SHALLOW+clone%2C+it%27s+only+copying+the+_external_+list%0A++++++++++++++++++%23+and+not+also+the+internal+ones+%21%0A%0Am+%3D+%5B%0A++++++++%5B%27a%27%2C%27b%27%5D%2C%0A++++++++%5B%27b%27%2C%27d%27%5D%0A++++%5D+++++++%0A++++++++%0Ares+%3D+deep_clone_wrong%28m%29%0A%0A%23+Notice+you+will+have+arrows+in+res+list+going+to+the+_original_+mat.+We+don%27t+want+this+%21%0A&cumulative=false&curInstr=0\"\n",
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"assert m1 == res\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def is_utriang(mat):\n",
" \"\"\" Takes a RETURN True if the provided nxn matrix is upper triangular, that is, it has all the entries \n",
" below the diagonal set to zero\n",
" \"\"\"\n",
" #jupman-raise\n",
" n = len(mat)\n",
" m = len(mat[0])\n",
" \n",
" for i in range(1,n):\n",
" for j in range(0, i // 2):\n",
" if mat[i][j] != 0:\n",
" return False\n",
" return True\n",
" #/jupman-raise\n",
" \n",
"assert is_utriang([\n",
" [1]\n",
" ]) == True\n",
"assert is_utriang([\n",
" [3,2,5],\n",
" [0,6,2],\n",
" [0,0,4]\n",
"]) == True\n",
"\n",
"assert is_utriang([\n",
" [3,2,5],\n",
" [0,6,2],\n",
" [1,0,4]\n",
"]) == False\n",
"\n",
"assert is_utriang([\n",
" [3,2,5],\n",
" [0,6,2],\n",
" [1,1,4]\n",
"]) == False\n",
"\n",
"assert is_utriang([\n",
" [3,2,5],\n",
" [1,6,2],\n",
" [1,0,4]\n",
"]) == False\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
Expand All @@ -1111,7 +1160,7 @@
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 26,
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 27,
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"### transpose\n",
"### transpose_1\n",
"\n",
"Transpose a matrix _in-place_. The transpose $M^T$ of a matrix $M$ is defined as "
]
Expand All @@ -1237,7 +1286,7 @@
},
{
"cell_type": "code",
"execution_count": 28,
"execution_count": 29,
"metadata": {},
"outputs": [
{
Expand All @@ -1246,7 +1295,7 @@
"[3, 4, 5, 6]"
]
},
"execution_count": 28,
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1264,7 +1313,7 @@
},
{
"cell_type": "code",
"execution_count": 29,
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "code",
"execution_count": 30,
"execution_count": 31,
"metadata": {},
"outputs": [
{
Expand All @@ -1341,7 +1390,7 @@
"[0, 0, 0]"
]
},
"execution_count": 30,
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1366,7 +1415,7 @@
},
{
"cell_type": "code",
"execution_count": 31,
"execution_count": 32,
"metadata": {},
"outputs": [
{
Expand All @@ -1375,7 +1424,7 @@
"[[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]"
]
},
"execution_count": 31,
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1394,7 +1443,7 @@
},
{
"cell_type": "code",
"execution_count": 32,
"execution_count": 33,
"metadata": {},
"outputs": [
{
Expand All @@ -1404,17 +1453,17 @@
" <iframe\n",
" width=\"900\"\n",
" height=\"225\"\n",
" src=\"https://pythontutor.com/iframe-embed.html#code=bad+%3D+%5B%5B0%5D%2A3%5D%2A5%0A&py=3&cumulative=false&curInstr=0\"\n",
" src=\"https://pythontutor.com/iframe-embed.html#py=3&code=bad+%3D+%5B%5B0%5D%2A3%5D%2A5%0A&cumulative=false&curInstr=0\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
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Expand All @@ -1435,7 +1484,7 @@
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"execution_count": 33,
"execution_count": 34,
"metadata": {},
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{
Expand All @@ -1444,7 +1493,7 @@
"[[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]"
]
},
"execution_count": 33,
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -1465,7 +1514,7 @@
},
{
"cell_type": "code",
"execution_count": 34,
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -1516,7 +1565,7 @@
},
{
"cell_type": "code",
"execution_count": 35,
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -1584,7 +1633,7 @@
},
{
"cell_type": "code",
"execution_count": 36,
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -1628,7 +1677,7 @@
},
{
"cell_type": "code",
"execution_count": 37,
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -1730,6 +1779,80 @@
" ]\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### pyramid"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"def pyramid(n):\n",
" \"\"\"\n",
" Takes a number n >= 1 and RETURN a matrix as list of lists containing numbers displaced like this\n",
" example for a pyramid of square 7:\n",
"\n",
" 1111111\n",
" 1222221 \n",
" 1233321 \n",
" 1234321\n",
" 1233321\n",
" 1222221\n",
" 1111111\n",
" \"\"\" \n",
" #jupman-raise\n",
" ret = [[0]*n for i in range(n)]\n",
" for i in range(n//2 + 1):\n",
" for j in range(n//2 +1):\n",
" ret[i][j] = min(i, j) + 1\n",
" ret[i][n-j-1] = min(i, j) + 1\n",
" ret[n-i-1][j] = min(i, j) + 1\n",
" ret[n-i-1][n-j-1] = min(i, j) + 1\n",
" \n",
" ret[n//2][n//2] = n // 2 + 1\n",
" return ret\n",
" #/jupman-raise\n",
"\n",
"\n",
"assert pyramid(1) == [\n",
" [1]\n",
" ]\n",
"\n",
"assert pyramid(3) == [\n",
" [1,1,1],\n",
" [1,2,1],\n",
" [1,1,1]\n",
" ]\n",
"\n",
"assert pyramid(4) == [\n",
" [1, 1, 1, 1], \n",
" [1, 3, 3, 1], \n",
" [1, 3, 3, 1], \n",
" [1, 1, 1, 1]\n",
"]\n",
"\n",
"assert pyramid(5) == [\n",
" [1, 1, 1, 1, 1],\n",
" [1, 2, 2, 2, 1], \n",
" [1, 2, 3, 2, 1], \n",
" [1, 2, 2, 2, 1], \n",
" [1, 1, 1, 1, 1]\n",
" ]\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
Expand Down

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