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Given an n by m matrix of integers, find the submatrix with the maximum sum. Return the sum, left, right, top, bottom.
Raw
max_sum_submatrix.cpp
#include "max_sum_submatrix.h"
#include <iostream>
#include <vector>
int main()
{
std::vector<int> v = { 4,6,8,3,-233,6,5,-2,83,2,3,6,4 };
std::vector< std::vector<int> > matirx = {
{-41,2,-1, 4},
{8,-3,4,2},
{3,8,10,-8},
{-4,-1,1,7}
};
auto range = max_sum_subarray(v);
std::cout << "max_add: " << range.value<<" left: " << range.left << " right: " << range.right << std::endl;
range = max_sum_submatrix(matirx);
std::cout << "max_add: " << range.value << " left: " << range.left << " right: " << range.right
<< " top: " << range.top << " bottom: " << range.bottom << std::endl;
return 0;
}
Raw
max_sum_submatrix.h
#pragma once
#ifndef _MAX_SUM
#define _MAX_SUM
#include <vector>
#include <algorithm>
template<typename T>
struct MaxRange
{
unsigned left = 0, right = 0, top = 0, bottom = 0;
T value = 0;
};
template<typename T1, typename T2>
MaxRange<T1> max_sum_subarray(const std::vector<T2> & arr)
{
T1 endsum = 0;
MaxRange<T1> range;//if add many unsigned char, the result may be long long
unsigned endsum_left = 0, n = arr.size();
for (unsigned i = 0; i < n; ++i)
{
if (endsum <= 0)
{
endsum_left = i;
endsum = arr[i];
}
else
{
endsum += arr[i];
}
if (endsum >= range.value)
{
range.value = endsum;
range.left = endsum_left;
range.right = i + 1;
}
}
return range;
}
template<typename T>
MaxRange<int> max_sum_subarray(const std::vector<T> & arr)
{
return max_sum_subarray<int, T>(arr);
}
template<typename T1, typename T2>
MaxRange<T1> max_sum_submatrix(const std::vector< std::vector<T2> >& matrix)
{
MaxRange<T1> range;
unsigned row = matrix.size(), col = 0;
if (row > 0) col = matrix[0].size();
std::vector<T1> array(col, 0);
for (unsigned top = 0; top < row; ++top)
{
std::fill(array.begin(), array.end(), 0);
for (unsigned bottom = top; bottom < row; ++bottom)
{
unsigned i = 0;
for (auto & v : matrix[bottom])
{
array[i++] += v;
}
auto range_array = max_sum_subarray(array);
if (range_array.value >= range.value)
{
range.value = range_array.value;
range.top = top;
range.bottom = bottom + 1;
range.left = range_array.left;
range.right = range_array.right;
}
}
}
return range;
}
template<typename T2>
MaxRange<int> max_sum_submatrix(const std::vector< std::vector<T2> >& matrix)
{
return max_sum_submatrix<int, T2>(matrix);
}
#endif //_MAX_SUM
Display the source blob
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Raw
max_sum_submatrix.ipynb
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"</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 2, y: 4)&gt;\n",
"array([[-1, 0, 1, 2],\n",
" [ 3, 4, 5, 6]])\n",
"Dimensions without coordinates: x, y</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>x</span>: 2</li><li><span>y</span>: 4</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-30b34e3d-4a43-473d-babc-bad0c311b134' class='xr-array-in' type='checkbox' checked><label for='section-30b34e3d-4a43-473d-babc-bad0c311b134' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-1 0 1 2 3 4 5 6</span></div><div class='xr-array-data'><pre>array([[-1, 0, 1, 2],\n",
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"source": [
"import numpy as np\n",
"\n",
"import pandas as pd\n",
"\n",
"import xarray as xr\n",
"\n",
"a = [[-1,0,1,2], \n",
" [ 3,4,5,6]]\n",
"data = xr.DataArray(a, dims=(\"x\", \"y\"))\n",
"\n",
"data\n"
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" --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
" --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
" --xr-border-color: #1F1F1F;\n",
" --xr-disabled-color: #515151;\n",
" --xr-background-color: #111111;\n",
" --xr-background-color-row-even: #111111;\n",
" --xr-background-color-row-odd: #313131;\n",
"}\n",
"\n",
".xr-wrap {\n",
" display: block !important;\n",
" min-width: 300px;\n",
" max-width: 700px;\n",
"}\n",
"\n",
".xr-text-repr-fallback {\n",
" /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
" display: none;\n",
"}\n",
"\n",
".xr-header {\n",
" padding-top: 6px;\n",
" padding-bottom: 6px;\n",
" margin-bottom: 4px;\n",
" border-bottom: solid 1px var(--xr-border-color);\n",
"}\n",
"\n",
".xr-header > div,\n",
".xr-header > ul {\n",
" display: inline;\n",
" margin-top: 0;\n",
" margin-bottom: 0;\n",
"}\n",
"\n",
".xr-obj-type,\n",
".xr-array-name {\n",
" margin-left: 2px;\n",
" margin-right: 10px;\n",
"}\n",
"\n",
".xr-obj-type {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-sections {\n",
" padding-left: 0 !important;\n",
" display: grid;\n",
" grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
"}\n",
"\n",
".xr-section-item {\n",
" display: contents;\n",
"}\n",
"\n",
".xr-section-item input {\n",
" display: none;\n",
"}\n",
"\n",
".xr-section-item input + label {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label {\n",
" cursor: pointer;\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-item input:enabled + label:hover {\n",
" color: var(--xr-font-color0);\n",
"}\n",
"\n",
".xr-section-summary {\n",
" grid-column: 1;\n",
" color: var(--xr-font-color2);\n",
" font-weight: 500;\n",
"}\n",
"\n",
".xr-section-summary > span {\n",
" display: inline-block;\n",
" padding-left: 0.5em;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label {\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-section-summary-in + label:before {\n",
" display: inline-block;\n",
" content: '►';\n",
" font-size: 11px;\n",
" width: 15px;\n",
" text-align: center;\n",
"}\n",
"\n",
".xr-section-summary-in:disabled + label:before {\n",
" color: var(--xr-disabled-color);\n",
"}\n",
"\n",
".xr-section-summary-in:checked + label:before {\n",
" content: '▼';\n",
"}\n",
"\n",
".xr-section-summary-in:checked + label > span {\n",
" display: none;\n",
"}\n",
"\n",
".xr-section-summary,\n",
".xr-section-inline-details {\n",
" padding-top: 4px;\n",
" padding-bottom: 4px;\n",
"}\n",
"\n",
".xr-section-inline-details {\n",
" grid-column: 2 / -1;\n",
"}\n",
"\n",
".xr-section-details {\n",
" display: none;\n",
" grid-column: 1 / -1;\n",
" margin-bottom: 5px;\n",
"}\n",
"\n",
".xr-section-summary-in:checked ~ .xr-section-details {\n",
" display: contents;\n",
"}\n",
"\n",
".xr-array-wrap {\n",
" grid-column: 1 / -1;\n",
" display: grid;\n",
" grid-template-columns: 20px auto;\n",
"}\n",
"\n",
".xr-array-wrap > label {\n",
" grid-column: 1;\n",
" vertical-align: top;\n",
"}\n",
"\n",
".xr-preview {\n",
" color: var(--xr-font-color3);\n",
"}\n",
"\n",
".xr-array-preview,\n",
".xr-array-data {\n",
" padding: 0 5px !important;\n",
" grid-column: 2;\n",
"}\n",
"\n",
".xr-array-data,\n",
".xr-array-in:checked ~ .xr-array-preview {\n",
" display: none;\n",
"}\n",
"\n",
".xr-array-in:checked ~ .xr-array-data,\n",
".xr-array-preview {\n",
" display: inline-block;\n",
"}\n",
"\n",
".xr-dim-list {\n",
" display: inline-block !important;\n",
" list-style: none;\n",
" padding: 0 !important;\n",
" margin: 0;\n",
"}\n",
"\n",
".xr-dim-list li {\n",
" display: inline-block;\n",
" padding: 0;\n",
" margin: 0;\n",
"}\n",
"\n",
".xr-dim-list:before {\n",
" content: '(';\n",
"}\n",
"\n",
".xr-dim-list:after {\n",
" content: ')';\n",
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"\n",
".xr-dim-list li:not(:last-child):after {\n",
" content: ',';\n",
" padding-right: 5px;\n",
"}\n",
"\n",
".xr-has-index {\n",
" font-weight: bold;\n",
"}\n",
"\n",
".xr-var-list,\n",
".xr-var-item {\n",
" display: contents;\n",
"}\n",
"\n",
".xr-var-item > div,\n",
".xr-var-item label,\n",
".xr-var-item > .xr-var-name span {\n",
" background-color: var(--xr-background-color-row-even);\n",
" margin-bottom: 0;\n",
"}\n",
"\n",
".xr-var-item > .xr-var-name:hover span {\n",
" padding-right: 5px;\n",
"}\n",
"\n",
".xr-var-list > li:nth-child(odd) > div,\n",
".xr-var-list > li:nth-child(odd) > label,\n",
".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
" background-color: var(--xr-background-color-row-odd);\n",
"}\n",
"\n",
".xr-var-name {\n",
" grid-column: 1;\n",
"}\n",
"\n",
".xr-var-dims {\n",
" grid-column: 2;\n",
"}\n",
"\n",
".xr-var-dtype {\n",
" grid-column: 3;\n",
" text-align: right;\n",
" color: var(--xr-font-color2);\n",
"}\n",
"\n",
".xr-var-preview {\n",
" grid-column: 4;\n",
"}\n",
"\n",
".xr-var-name,\n",
".xr-var-dims,\n",
".xr-var-dtype,\n",
".xr-preview,\n",
".xr-attrs dt {\n",
" white-space: nowrap;\n",
" overflow: hidden;\n",
" text-overflow: ellipsis;\n",
" padding-right: 10px;\n",
"}\n",
"\n",
".xr-var-name:hover,\n",
".xr-var-dims:hover,\n",
".xr-var-dtype:hover,\n",
".xr-attrs dt:hover {\n",
" overflow: visible;\n",
" width: auto;\n",
" z-index: 1;\n",
"}\n",
"\n",
".xr-var-attrs,\n",
".xr-var-data {\n",
" display: none;\n",
" background-color: var(--xr-background-color) !important;\n",
" padding-bottom: 5px !important;\n",
"}\n",
"\n",
".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
".xr-var-data-in:checked ~ .xr-var-data {\n",
" display: block;\n",
"}\n",
"\n",
".xr-var-data > table {\n",
" float: right;\n",
"}\n",
"\n",
".xr-var-name span,\n",
".xr-var-data,\n",
".xr-attrs {\n",
" padding-left: 25px !important;\n",
"}\n",
"\n",
".xr-attrs,\n",
".xr-var-attrs,\n",
".xr-var-data {\n",
" grid-column: 1 / -1;\n",
"}\n",
"\n",
"dl.xr-attrs {\n",
" padding: 0;\n",
" margin: 0;\n",
" display: grid;\n",
" grid-template-columns: 125px auto;\n",
"}\n",
"\n",
".xr-attrs dt,\n",
".xr-attrs dd {\n",
" padding: 0;\n",
" margin: 0;\n",
" float: left;\n",
" padding-right: 10px;\n",
" width: auto;\n",
"}\n",
"\n",
".xr-attrs dt {\n",
" font-weight: normal;\n",
" grid-column: 1;\n",
"}\n",
"\n",
".xr-attrs dt:hover span {\n",
" display: inline-block;\n",
" background: var(--xr-background-color);\n",
" padding-right: 10px;\n",
"}\n",
"\n",
".xr-attrs dd {\n",
" grid-column: 2;\n",
" white-space: pre-wrap;\n",
" word-break: break-all;\n",
"}\n",
"\n",
".xr-icon-database,\n",
".xr-icon-file-text2 {\n",
" display: inline-block;\n",
" vertical-align: middle;\n",
" width: 1em;\n",
" height: 1.5em !important;\n",
" stroke-width: 0;\n",
" stroke: currentColor;\n",
" fill: currentColor;\n",
"}\n",
"</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (x: 2, y: 3)&gt;\n",
"array([[-1, 0, 1],\n",
" [ 3, 4, 5]])\n",
"Dimensions without coordinates: x, y</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>x</span>: 2</li><li><span>y</span>: 3</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-41ce01a6-452a-4602-adaa-4eaee063894b' class='xr-array-in' type='checkbox' checked><label for='section-41ce01a6-452a-4602-adaa-4eaee063894b' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-1 0 1 3 4 5</span></div><div class='xr-array-data'><pre>array([[-1, 0, 1],\n",
" [ 3, 4, 5]])</pre></div></div></li><li class='xr-section-item'><input id='section-f37712f9-e703-4c25-9f65-4d527b95fa7a' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f37712f9-e703-4c25-9f65-4d527b95fa7a' class='xr-section-summary' title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-8af3b93b-4af7-4662-8b4d-9b2c0da40018' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-8af3b93b-4af7-4662-8b4d-9b2c0da40018' class='xr-section-summary' title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
],
"text/plain": [
"<xarray.DataArray (x: 2, y: 3)>\n",
"array([[-1, 0, 1],\n",
" [ 3, 4, 5]])\n",
"Dimensions without coordinates: x, y"
]
},
"execution_count": 245,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = data[0:2, 0:3]\n",
"b"
]
},
{
"cell_type": "code",
"execution_count": 246,
"metadata": {},
"outputs": [
{
"data": {
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"\n",
".xr-header > div,\n",
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" width: auto;\n",
" z-index: 1;\n",
"}\n",
"\n",
".xr-var-attrs,\n",
".xr-var-data {\n",
" display: none;\n",
" background-color: var(--xr-background-color) !important;\n",
" padding-bottom: 5px !important;\n",
"}\n",
"\n",
".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
".xr-var-data-in:checked ~ .xr-var-data {\n",
" display: block;\n",
"}\n",
"\n",
".xr-var-data > table {\n",
" float: right;\n",
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"\n",
".xr-var-name span,\n",
".xr-var-data,\n",
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" padding-left: 25px !important;\n",
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"\n",
".xr-attrs,\n",
".xr-var-attrs,\n",
".xr-var-data {\n",
" grid-column: 1 / -1;\n",
"}\n",
"\n",
"dl.xr-attrs {\n",
" padding: 0;\n",
" margin: 0;\n",
" display: grid;\n",
" grid-template-columns: 125px auto;\n",
"}\n",
"\n",
".xr-attrs dt,\n",
".xr-attrs dd {\n",
" padding: 0;\n",
" margin: 0;\n",
" float: left;\n",
" padding-right: 10px;\n",
" width: auto;\n",
"}\n",
"\n",
".xr-attrs dt {\n",
" font-weight: normal;\n",
" grid-column: 1;\n",
"}\n",
"\n",
".xr-attrs dt:hover span {\n",
" display: inline-block;\n",
" background: var(--xr-background-color);\n",
" padding-right: 10px;\n",
"}\n",
"\n",
".xr-attrs dd {\n",
" grid-column: 2;\n",
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" word-break: break-all;\n",
"}\n",
"\n",
".xr-icon-database,\n",
".xr-icon-file-text2 {\n",
" display: inline-block;\n",
" vertical-align: middle;\n",
" width: 1em;\n",
" height: 1.5em !important;\n",
" stroke-width: 0;\n",
" stroke: currentColor;\n",
" fill: currentColor;\n",
"}\n",
"</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray ()&gt;\n",
"array(12)</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-f14457b0-743f-4ec6-9299-5f46f22d0cba' class='xr-array-in' type='checkbox' checked><label for='section-f14457b0-743f-4ec6-9299-5f46f22d0cba' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>12</span></div><div class='xr-array-data'><pre>array(12)</pre></div></div></li><li class='xr-section-item'><input id='section-e0de656b-1e8c-4b32-ab34-c5fa94bdfdc4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-e0de656b-1e8c-4b32-ab34-c5fa94bdfdc4' class='xr-section-summary' title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-b2b5e419-c840-40c6-869f-0b4e04ef04f7' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b2b5e419-c840-40c6-869f-0b4e04ef04f7' class='xr-section-summary' title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
],
"text/plain": [
"<xarray.DataArray ()>\n",
"array(12)"
]
},
"execution_count": 246,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data[0:2, 0:3].sum()"
]
},
{
"cell_type": "code",
"execution_count": 247,
"metadata": {},
"outputs": [
{
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"\n",
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"\n",
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"}\n",
"\n",
".xr-attrs dt,\n",
".xr-attrs dd {\n",
" padding: 0;\n",
" margin: 0;\n",
" float: left;\n",
" padding-right: 10px;\n",
" width: auto;\n",
"}\n",
"\n",
".xr-attrs dt {\n",
" font-weight: normal;\n",
" grid-column: 1;\n",
"}\n",
"\n",
".xr-attrs dt:hover span {\n",
" display: inline-block;\n",
" background: var(--xr-background-color);\n",
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"}\n",
"\n",
".xr-attrs dd {\n",
" grid-column: 2;\n",
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"}\n",
"\n",
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".xr-icon-file-text2 {\n",
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"}\n",
"</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (y: 4)&gt;\n",
"array([2, 4, 6, 8])\n",
"Dimensions without coordinates: y</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>y</span>: 4</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-9cf09eaf-a011-456d-9bca-cea4885c0616' class='xr-array-in' type='checkbox' checked><label for='section-9cf09eaf-a011-456d-9bca-cea4885c0616' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>2 4 6 8</span></div><div class='xr-array-data'><pre>array([2, 4, 6, 8])</pre></div></div></li><li class='xr-section-item'><input id='section-794831ae-92e8-4f4b-967a-5cc022d44ddc' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-794831ae-92e8-4f4b-967a-5cc022d44ddc' class='xr-section-summary' title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-1ceb9915-0d93-46a0-bf08-a912d6afe2b2' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-1ceb9915-0d93-46a0-bf08-a912d6afe2b2' class='xr-section-summary' title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
],
"text/plain": [
"<xarray.DataArray (y: 4)>\n",
"array([2, 4, 6, 8])\n",
"Dimensions without coordinates: y"
]
},
"execution_count": 247,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data[0]+data[1]"
]
},
{
"cell_type": "code",
"execution_count": 248,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2, 4)"
]
},
"execution_count": 248,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.shape"
]
},
{
"cell_type": "code",
"execution_count": 249,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 249,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"not False and False"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\"\"\" temp = a[i]+maxend\n",
"\n",
" if a[i]<0:\n",
" if end: # maxend -> maxmiddle\n",
" end = False\n",
" left = endleft\n",
" right = i\n",
" maxmiddle = maxend\n",
"\n",
" \n",
" if a[i] < temp:\n",
" maxend = temp\n",
" else:\n",
" maxend=a[i]\n",
" endleft=i\n",
"\n",
" elif a[i]==0:\n",
" if maxend<0:\n",
" maxend=a[i]\n",
" endleft=i\n",
" \n",
" \n",
" \n",
" else: #a[i] > 0\n",
" if maxend <= 0:\n",
" maxend = a[i]\n",
" endleft = i\n",
" \n",
" else:\n",
" maxend = temp\n",
"\n",
" if maxend >= maxmiddle: #maxmiddle -> maxend\n",
" end = True \"\"\""
]
},
{
"cell_type": "code",
"execution_count": 250,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(8, 1, 6, False, 3, 7)"
]
},
"execution_count": 250,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def maxsum(a):\n",
" maxlast = a[0]\n",
" maxend = a[0] # a[0] can't be object 1.slow 2.same object as maxlast\n",
"\n",
" left = 0\n",
" right = 1\n",
"\n",
" endleft = 0\n",
"\n",
" end = True\n",
"\n",
" for i in range(1, len(a)):\n",
"\n",
" if maxend < 0:\n",
" maxend = a[i]\n",
" endleft = i\n",
"\n",
" else:\n",
" # if maxend == 0: # do you want keep?\n",
" # pass\n",
"\n",
" maxend += a[i]\n",
"\n",
" if maxend >= maxlast:\n",
" end = True\n",
" left = endleft\n",
" right = i+1\n",
" maxlast = maxend\n",
" else:\n",
" end = False\n",
"\n",
" return ( maxlast, left, right, end,maxend,endleft)\n",
"\n",
"\n",
"maxsum([-3, 1, -1, 2, 3, 3, -10, 3])\n"
]
},
{
"cell_type": "code",
"execution_count": 251,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 5, 6, True, 0, 5)"
]
},
"execution_count": 251,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"maxsum([-1,-1,-2,-5, -10,0])"
]
},
{
"cell_type": "code",
"execution_count": 252,
"metadata": {},
"outputs": [
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"data": {
"text/plain": [
"(13, 6, 7, True, 13, 6)"
]
},
"execution_count": 252,
"metadata": {},
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"source": [
"maxsum([-1,-1,2,3,-5, -10,13])"
]
},
{
"cell_type": "code",
"execution_count": 253,
"metadata": {},
"outputs": [],
"source": [
"ra = np.random.randint(-10,10, size=10000000)\n"
]
},
{
"cell_type": "code",
"execution_count": 254,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(428, 5812824, 5813283, False, 80, 9999828)"
]
},
"execution_count": 254,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"maxsum(ra)"
]
},
{
"cell_type": "code",
"execution_count": 255,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0., 0., 0.])"
]
},
"execution_count": 255,
"metadata": {},
"output_type": "execute_result"
}
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"source": [
"a\n",
"b = 3\n",
"np.zeros(b)"
]
},
{
"cell_type": "code",
"execution_count": 256,
"metadata": {},
"outputs": [],
"source": [
"def max_matrix_add(mat):\n",
"\n",
" if isinstance(mat, xr.DataArray):\n",
" mat = mat.to_numpy()\n",
"\n",
" maxlast = 0\n",
" left = 0\n",
" right = 0\n",
" top = 0\n",
" bottom = 0\n",
"\n",
" rows_size, cols_size = mat.shape\n",
"\n",
" for _top in range(0, rows_size):\n",
" rows_add = np.zeros(cols_size)\n",
"\n",
" for _bottom in range(_top, rows_size):\n",
" rows_add += mat[_bottom]\n",
"\n",
" max, l, r, *_ = maxsum(rows_add)\n",
"\n",
" print(rows_add)\n",
" print(max,l,r)\n",
"\n",
" if max > maxlast:\n",
" maxlast, left, right, top, bottom = (max, l, r, _top, _bottom+1)\n",
" \n",
" return (maxlast, left, right, top, bottom)\n"
]
},
{
"cell_type": "code",
"execution_count": 257,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
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},
"execution_count": 257,
"metadata": {},
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"source": [
"data = [[-1, 0, 1, 2],\n",
" [ 3, 4, 5, 6]]\n",
"\n",
"data"
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{
"cell_type": "code",
"execution_count": 258,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-3, -1, -1, -4],\n",
" [ 2, 3, -2, -5],\n",
" [ 4, 2, -1, -3]])"
]
},
"execution_count": 258,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data2 = np.random.randint(-5,5,(3,4))\n",
"data2"
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1, 2, -3, -9])"
]
},
"execution_count": 259,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data2[0] + data2[1]"
]
},
{
"cell_type": "code",
"execution_count": 260,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-3. -1. -1. -4.]\n",
"-1.0 2 3\n",
"[-1. 2. -3. -9.]\n",
"2.0 1 2\n",
"[ 3. 4. -4. -12.]\n",
"7.0 0 2\n",
"[ 2. 3. -2. -5.]\n",
"5.0 0 2\n",
"[ 6. 5. -3. -8.]\n",
"11.0 0 2\n",
"[ 4. 2. -1. -3.]\n",
"6.0 0 2\n"
]
},
{
"data": {
"text/plain": [
"(11.0, 0, 2, 1, 3)"
]
},
"execution_count": 260,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max_matrix_add(data2)"
]
},
{
"cell_type": "code",
"execution_count": 261,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 261,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xr2 = xr.DataArray(data2, dims=(\"x\", \"y\"))\n",
"isinstance(xr2, xr.DataArray)\n"
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {},
"outputs": [
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"</style><pre class='xr-text-repr-fallback'>&lt;xarray.DataArray (y: 4)&gt;\n",
"array([-1., 2., -3., -9.])\n",
"Dimensions without coordinates: y</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.DataArray</div><div class='xr-array-name'></div><ul class='xr-dim-list'><li><span>y</span>: 4</li></ul></div><ul class='xr-sections'><li class='xr-section-item'><div class='xr-array-wrap'><input id='section-bbb687b0-bb4f-416a-8bfc-50df1ce8e82f' class='xr-array-in' type='checkbox' checked><label for='section-bbb687b0-bb4f-416a-8bfc-50df1ce8e82f' title='Show/hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-array-preview xr-preview'><span>-1.0 2.0 -3.0 -9.0</span></div><div class='xr-array-data'><pre>array([-1., 2., -3., -9.])</pre></div></div></li><li class='xr-section-item'><input id='section-f3a6b696-a3c7-4ce6-ba58-d443b1a4a50f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f3a6b696-a3c7-4ce6-ba58-d443b1a4a50f' class='xr-section-summary' title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-b2132f46-c4f4-46a1-ad1d-44a69ff7ace4' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b2132f46-c4f4-46a1-ad1d-44a69ff7ace4' class='xr-section-summary' title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
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"text/plain": [
"<xarray.DataArray (y: 4)>\n",
"array([-1., 2., -3., -9.])\n",
"Dimensions without coordinates: y"
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},
"execution_count": 266,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"z4 = np.zeros(4) \n",
"z4 += xr2[0]\n",
"\n",
"z4 += xr2[1]\n",
"\n",
"z4\n"
]
},
{
"cell_type": "code",
"execution_count": 263,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<xarray.DataArray (y: 4)>\n",
"array([-3., -1., -1., -4.])\n",
"Dimensions without coordinates: y\n",
"<xarray.DataArray ()>\n",
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"<xarray.DataArray (y: 4)>\n",
"array([-1., -1., -3., -9.])\n",
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"array(-1.) 1 3\n",
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"array(-2.) 0 4\n",
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"array([-4., 5., -3., -8.])\n",
"Dimensions without coordinates: y\n",
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"array(-4.) 0 4\n",
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"text": [
"[-3. -1. -1. -4.]\n",
"-1.0 2 3\n",
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"2.0 1 2\n",
"[ 3. 4. -4. -12.]\n",
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"5.0 0 2\n",
"[ 6. 5. -3. -8.]\n",
"11.0 0 2\n",
"[ 4. 2. -1. -3.]\n",
"6.0 0 2\n"
]
},
{
"data": {
"text/plain": [
"(11.0, 0, 2, 1, 3)"
]
},
"execution_count": 264,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max_matrix_add(xr2.to_numpy())"
]
}
],
"metadata": {
"interpreter": {
"hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
},
"kernelspec": {
"display_name": "Python 3.10.4 64-bit",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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