Minimize the sum of errors of representative integers
Given n integers between [0,10000] as D1,D2...,Dn, where there may be duplicates, and n can be huge:
I want to find k distinct represent
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The integrity of this program was partly confirmed by a modified version of it used here to produce data that matched results obtained independently by @mhum.
It finds the exact minimal error value(s) and corresponding R values for a given data set and k value(s).
/************************************************************ This program can be compiled and run (eg, on Linux): $ gcc -std=c99 minimize-sum-errors.c -o minimize-sum-errors $ ./minimize-sum-errors ************************************************************/ #include#include #include //data: Data set of values. Add extra large number at the end int data[]={ 10,40,90,160,250,360,490,640,810,1000,1210,1440,1690,1960,2250,2560,2890,3240,3610,4000,4410,4840,5290,5760,6250,6760,7290,7840,8410,9000,9610,10240,99999,1,2,3,4,5,6,7,8,9,10,24,24,14,12,41,51,21,41,41,848,21, 547,3,2,888,4,1,66,5,4,2,11,742,95,25,365,52,441,874,51,2,145,254,24,245,54,21,87,98,65,32,25,14,25,36,25,14,47,58,58,69,85,74,71,82,82,93,93,93,12,12,45,78,78,985,412,74,3,62,125,458,658,147,432,124,328,952,635,368,634,637,874,124,35,23,65,896,21,41,745,49,2,7,8,4,8,7,2,6,5,6,9,8,9,6,5,9,5,9,5,9,11,41,5,24,98,78,45,54,65,32,21,12,18,38,48,68,78,75,72,95,92,65,55,5,87,412,158,654,219,943,218,952,357,753,159,951,485,862,1,741,22,444,452,487,478,478,495,456,444,141,238,9,445,421,441,444,436,478,51,24,24,24,24,24,24,247,741,98,99,999,111,444,323,33,5,5,5,85,85,85,85,654,456,5,4,566,445,5664,45,4556,45,5,6,5,4,56,66,5,456,5,45,6,68,7653,434,4,6,7,689,78,8,99,8700,344,65,45,8,899,86,65,3,422,3,4,3,4,7,68,544,454,545,65,4,6,878,423,64,97,8778,5456,5486,5485,545,5455,4548,81,999,8233,5223,8741,7747,7756,54,7884,5477,89,332,5999,9861,12545,9852,11452,5482,9358,9845,577,884,5589,5412,3669,32,6699,396,9629,953,321,45,5484,588,5872,85,872,87,1122,884,2458,471,22685,955,2845,6852,589,5896,2521,35696,5236,32633,56665,6633,326,5486,5487,8541,5495,2155,3,8523,65896,3852,5685,69536,1,1,1,1,1,2,3,4,5,6, }; //N: size of data set int N=sizeof(data)/sizeof(int); //SavedBundle: data type to "hold" memoized values needed (minimized error sums and corresponding "list" of R values for a given round) typedef struct _SavedBundle { long e; int head_index_value; int tail_offset; } SavedBundle; //sb: (pts to) lookup table of all calculated values memoized SavedBundle *sb; //holds winning values being memoized //Sort in increasing order. int sortfunc (const void *a, const void *b) { return (*(int *)a - *(int *)b); } /**************************** Most interesting code in here ****************************/ long full_memh(int l, int n) { long e; long e_min=-1; int ti; if (sb[l*N+n].e) { return sb[l*N+n].e; //convenience passing } for (int i=l+1; i Some sample results obtained:
Total data size: 375 k errSUM R values 3 475179 {1,5223,99999} 4 320853 {1,5223,56665,99999} 5 260103 {1,5223,7653,56665,99999} 6 210143 {1,5223,7653,32633,56665,99999} 7 171503 {1,421,5223,7653,32633,56665,99999} 8 142865 {1,412,2458,5223,7653,32633,56665,99999} 9 124403 {1,412,2458,5223,7653,32633,56665,65896,99999} 10 106790 {1,412,2458,5223,7653,9610,32633,56665,65896,99999} 11 93715 {1,412,2458,5223,7653,9610,22685,32633,56665,65896,99999} 12 81507 {1,412,848,2458,5223,7653,9610,22685,32633,56665,65896,99999} 13 71495 {1,412,848,2155,3610,5223,7653,9610,22685,32633,56665,65896,99999} 14 64243 {1,412,848,2155,3610,5223,6633,7747,9610,22685,32633,56665,65896,99999} 15 58355 {1,412,848,2155,3610,5223,6633,7653,8523,9610,22685,32633,56665,65896,99999} 16 53363 {1,65,412,848,2155,3610,5223,6633,7653,8523,9610,22685,32633,56665,65896,99999} 17 48983 {1,65,412,848,2155,3610,4548,5412,6633,7653,8523,9610,22685,32633,56665,65896,99999} 18 45299 {1,65,412,848,2155,3610,4548,5412,6633,7653,8523,9610,11452,22685,32633,56665,65896,99999} 19 41659 {1,65,412,848,2155,3610,4548,5412,6633,7653,8523,9610,11452,22685,32633,56665,65896,69536,99999} 20 38295 {1,65,321,441,848,2155,3610,4548,5412,6633,7653,8523,9610,11452,22685,32633,56665,65896,69536,99999} 21 35232 {1,65,321,441,848,2155,3610,4548,5412,6633,7653,8523,9610,11452,22685,32633,35696,56665,65896,69536,99999} 22 32236 {1,65,321,441,848,2155,3610,4410,5223,5455,6633,7653,8523,9610,11452,22685,32633,35696,56665,65896,69536,99999} 23 29323 {1,65,321,432,634,872,2155,3610,4410,5223,5455,6633,7653,8523,9610,11452,22685,32633,35696,56665,65896,69536,99999} 24 26791 {1,65,321,432,634,862,1690,2458,3610,4410,5223,5455,6633,7653,8523,9610,11452,22685,32633,35696,56665,65896,69536,99999} 25 25123 {1,65,321,432,634,862,1690,2458,3610,4410,5223,5455,5872,6633,7653,8523,9610,11452,22685,32633,35696,56665,65896,69536,99999} 26 23658 {1,65,321,432,634,862,1690,2458,3610,4410,5223,5455,5872,6633,7653,8233,8700,9610,11452,22685,32633,35696,56665,65896,69536,99999} 27 22333 {1,41,78,321,432,634,862,1690,2458,3610,4410,5223,5455,5872,6633,7653,8233,8700,9610,11452,22685,32633,35696,56665,65896,69536,99999} 28 21073 {1,41,78,321,432,634,862,1440,2155,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9610,11452,22685,32633,35696,56665,65896,69536,99999} 29 19973 {1,41,78,321,432,634,848,951,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9610,11452,22685,32633,35696,56665,65896,69536,99999} 30 18879 {1,41,78,321,432,634,848,951,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9358,9845,11452,22685,32633,35696,56665,65896,69536,99999} 31 17786 {1,41,78,321,432,634,848,951,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 32 16801 {1,41,78,321,432,634,848,943,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 33 15821 {1,41,78,218,321,432,634,848,943,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 34 14900 {1,41,78,218,321,421,544,634,848,943,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7653,8233,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 35 14185 {1,41,78,218,321,421,544,634,848,943,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7290,7747,8410,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 36 13503 {1,41,78,218,321,421,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7290,7747,8410,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 37 12859 {1,21,45,78,218,321,421,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5872,6633,7290,7747,8410,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 38 12232 {1,21,45,78,218,321,421,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5664,5872,6633,7290,7747,8410,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 39 11662 {1,21,45,78,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5664,5872,6633,7290,7747,8410,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 40 11127 {1,21,45,78,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 41 10623 {1,21,45,78,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 42 10121 {1,21,41,65,85,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,4410,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 43 9637 {1,21,41,65,85,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,3852,4410,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 44 9207 {1,21,41,65,85,218,321,412,444,544,634,741,862,951,1440,1960,2458,2845,3610,3852,4410,4840,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 45 8804 {1,21,41,65,85,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3610,3852,4410,4840,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 46 8409 {1,21,41,65,85,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,11452,12545,22685,32633,35696,56665,65896,69536,99999} 47 8014 {1,21,41,65,85,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6633,7290,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 48 7636 {1,21,41,65,85,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6250,6633,7290,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 49 7273 {1,21,41,65,85,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 50 6922 {1,21,41,65,85,124,218,321,412,444,544,634,741,862,943,1122,1690,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 51 6584 {1,21,41,65,85,124,218,321,412,444,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4840,5223,5455,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 52 6283 {1,21,41,65,85,124,218,321,412,444,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4840,5223,5412,5477,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 53 5983 {1,21,41,65,85,124,218,321,412,444,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4840,5223,5412,5477,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 54 5707 {1,21,41,65,85,124,218,321,412,444,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 55 5450 {1,21,41,65,85,124,218,321,412,441,478,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 56 5196 {1,21,41,65,85,124,218,321,412,441,478,544,634,741,862,943,1122,1440,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 57 4946 {1,21,41,65,85,124,218,321,412,441,478,544,634,741,862,943,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 58 4722 {1,5,21,41,65,85,124,218,321,412,441,478,544,634,741,862,943,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 59 4536 {1,5,21,41,65,85,124,218,321,412,441,478,544,634,741,862,943,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 60 4352 {1,5,21,41,65,85,124,218,321,412,441,478,544,634,741,848,872,951,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 61 4172 {1,5,21,41,65,85,124,218,321,357,412,441,478,544,634,741,848,872,951,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 62 3995 {1,5,21,41,65,85,124,218,321,357,412,441,478,544,634,741,848,872,951,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8410,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 63 3828 {1,5,21,41,65,85,124,218,321,357,412,441,478,544,634,741,848,872,943,985,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8410,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 64 3680 {1,5,21,41,65,85,124,218,321,357,412,441,478,544,634,741,848,872,943,985,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4000,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8410,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 65 3545 {1,5,21,32,45,65,85,124,218,321,357,412,441,478,544,634,741,848,872,943,985,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4000,4410,4548,4840,5223,5412,5477,5664,5872,6250,6633,6760,7290,7653,7747,7840,8233,8410,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999} 66 3418 {1,5,21,32,45,65,85,124,218,321,357,412,441,478,544,634,741,848,872,943,985,1122,1440,1690,1960,2155,2458,2845,3240,3610,3852,4000,4410,4548,4840,5223,5412,5477,5664,5872,5999,6250,6633,6760,7290,7653,7747,7840,8233,8410,8523,8700,9000,9358,9610,9845,10240,11452,12545,22685,32633,35696,56665,65896,69536,99999}The output started slowing down on the PC too much before it reached 100 rows (of the possible 375).
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