Created
April 19, 2014 11:13
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Fast and memory efficient fib calculation based off Ray Hightower's memoization method but with better memory usage (http://rayhightower.com/blog/2014/04/12/recursion-and-memoization/)
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| # Fibonacci numbers WITH memoization. | |
| # Initialize the memoization hash. | |
| @scratchpad = {} | |
| @max_fibo_size = 1_000_000_000_000 | |
| # Calculate the nth Fibonacci number, f(n). | |
| def fibo (n) | |
| val = if n <= 1 | |
| n | |
| elsif @scratchpad[n] != nil | |
| @scratchpad[n] | |
| else | |
| @scratchpad[n] = fibo(n-1) + fibo(n-2) | |
| end | |
| val | |
| end | |
| start = last_time = Time.now | |
| puts "%-13s | %-20s | %21s | %21s" % ['fib(n)', 'fib(n) length', '"lap" time', 'total time'] | |
| # Display the Fibonacci sequence. | |
| (1..@max_fibo_size).each do |number| | |
| result = fibo(number) | |
| if number % 100_000 == 0 | |
| puts "%-13d | %-20d | %21.10f | %21.10f" % [number, result.to_s.length, Time.now - last_time, Time.now - start] | |
| last_time = Time.now | |
| end | |
| # memory cleaning | |
| clean_count = 1000 | |
| if number % (clean_count || 50) == 0 | |
| @scratchpad.delete_if do |k, v| | |
| k < (number - 10) | |
| end | |
| clean_count -= 100 | |
| GC.start | |
| end | |
| end |
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| On a Macbook Air, 1.6GHz i5, 4GB 1333 MHz DDR3, these were the results, keep in mind memory usage was only jumping up and down by about 100MB at the later points. Adding memory tracking to the results might be a nice addition, but I wasn't too fussed. | |
| fib(n) | fib(n) length | "lap" time | total time | |
| 100000 | 20899 | 0.6711800000 | 0.6712200000 | |
| 200000 | 41798 | 1.4236230000 | 2.0949410000 | |
| 300000 | 62696 | 2.2117460000 | 4.3067670000 | |
| 400000 | 83595 | 2.9075600000 | 7.2143990000 | |
| 500000 | 104494 | 3.5052390000 | 10.7197010000 | |
| 600000 | 125393 | 4.1065500000 | 14.8263210000 | |
| 700000 | 146291 | 4.8694530000 | 19.6958440000 | |
| 800000 | 167190 | 5.3894240000 | 25.0853370000 | |
| 900000 | 188089 | 6.1762100000 | 31.2616150000 | |
| 1000000 | 208988 | 7.0838860000 | 38.3455770000 | |
| 1100000 | 229887 | 7.9771220000 | 46.3227930000 | |
| 1200000 | 250785 | 8.8556020000 | 55.1784660000 | |
| 1300000 | 271684 | 9.2819300000 | 64.4604660000 | |
| 1400000 | 292583 | 10.0042190000 | 74.4647550000 | |
| 1500000 | 313482 | 11.4200230000 | 85.8848490000 | |
| 1600000 | 334380 | 19.7896170000 | 105.6745440000 | |
| 1700000 | 355279 | 19.8605040000 | 125.5351180000 | |
| 1800000 | 376178 | 22.9959830000 | 148.5311730000 | |
| 1900000 | 397077 | 24.2299470000 | 172.7611940000 | |
| 2000000 | 417975 | 26.8378020000 | 199.5990870000 | |
| 2100000 | 438874 | 25.9927830000 | 225.5919420000 | |
| 2200000 | 459773 | 28.4008180000 | 253.9928330000 | |
| 2300000 | 480672 | 28.7940970000 | 282.7870010000 | |
| 2400000 | 501570 | 29.2828760000 | 312.0699450000 | |
| 2500000 | 522469 | 32.9236840000 | 344.9937040000 | |
| 2600000 | 543368 | 33.4547460000 | 378.4485200000 | |
| 2700000 | 564267 | 31.9239960000 | 410.3725900000 | |
| 2800000 | 585166 | 32.2382960000 | 442.6109560000 | |
| 2900000 | 606064 | 34.0890400000 | 476.7000750000 | |
| 3000000 | 626963 | 36.3909580000 | 513.0911050000 | |
| 3100000 | 647862 | 36.6725440000 | 549.7637230000 | |
| 3200000 | 668761 | 38.9875430000 | 588.7513370000 | |
| 3300000 | 689659 | 40.2937750000 | 629.0451820000 | |
| 3400000 | 710558 | 41.4298560000 | 670.4751090000 | |
| 3500000 | 731457 | 41.3124930000 | 711.7876710000 | |
| 3600000 | 752356 | 42.1188530000 | 753.9065960000 | |
| 3700000 | 773254 | 54.8486630000 | 808.7553630000 | |
| 3800000 | 794153 | 44.3187000000 | 853.0741450000 | |
| 3900000 | 815052 | 45.8851530000 | 898.9593740000 | |
| 4000000 | 835951 | 48.5969450000 | 947.5564010000 | |
| 4100000 | 856849 | 48.7242510000 | 996.2807220000 | |
| 4200000 | 877748 | 49.3997300000 | 1045.6805220000 | |
| 4300000 | 898647 | 51.3350000000 | 1097.0155950000 | |
| 4400000 | 919546 | 52.5409690000 | 1149.5566320000 | |
| 4500000 | 940445 | 55.9916640000 | 1205.5483690000 | |
| 4600000 | 961343 | 55.5529590000 | 1261.1014000000 | |
| 4700000 | 982242 | 57.2026100000 | 1318.3040800000 | |
| 4800000 | 1003141 | 58.9713320000 | 1377.2754830000 | |
| 4900000 | 1024040 | 61.1155080000 | 1438.3910620000 | |
| 5000000 | 1044938 | 61.7297210000 | 1500.1208540000 | |
| 5100000 | 1065837 | 64.2228450000 | 1564.3437700000 | |
| 5200000 | 1086736 | 64.6556510000 | 1628.9994910000 | |
| 5300000 | 1107635 | 66.8015300000 | 1695.8010930000 | |
| 5400000 | 1128533 | 69.5491380000 | 1765.3503060000 | |
| 5500000 | 1149432 | 69.4005440000 | 1834.7509270000 | |
| 5600000 | 1170331 | 70.8520690000 | 1905.6030670000 | |
| 5700000 | 1191230 | 72.3932810000 | 1977.9964120000 | |
| 5800000 | 1212128 | 84.2181280000 | 2062.2146400000 | |
| 5900000 | 1233027 | 76.2510680000 | 2138.4657960000 | |
| 6000000 | 1253926 | 76.7570620000 | 2215.2229310000 | |
| 6100000 | 1274825 | 79.2525720000 | 2294.4755860000 | |
| 6200000 | 1295724 | 81.8460140000 | 2376.3216700000 | |
| 6300000 | 1316622 | 82.7099670000 | 2459.0317080000 | |
| 6400000 | 1337521 | 84.5187850000 | 2543.5505610000 | |
| 6500000 | 1358420 | 98.7259780000 | 2642.2766110000 | |
| 6600000 | 1379319 | 90.5337290000 | 2732.8104110000 | |
| 6700000 | 1400217 | 90.1910050000 | 2823.0014820000 | |
| 6800000 | 1421116 | 91.9817880000 | 2914.9833400000 | |
| 6900000 | 1442015 | 94.2419230000 | 3009.2253310000 | |
| 7000000 | 1462914 | 95.6597320000 | 3104.8851310000 | |
| 7100000 | 1483812 | 98.0150460000 | 3202.9002490000 | |
| 7200000 | 1504711 | 100.1612910000 | 3303.0616100000 | |
| 7300000 | 1525610 | 101.9747080000 | 3405.0363880000 | |
| 7400000 | 1546509 | 105.3058710000 | 3510.3423290000 | |
| 7500000 | 1567407 | 108.3341190000 | 3618.6765170000 | |
| 7600000 | 1588306 | 108.2226030000 | 3726.8991920000 | |
| 7700000 | 1609205 | 112.2643650000 | 3839.1636280000 | |
| 7800000 | 1630104 | 113.8652030000 | 3953.0289040000 | |
| 7900000 | 1651003 | 114.3012260000 | 4067.3302010000 | |
| 8000000 | 1671901 | 116.6008800000 | 4183.9311540000 | |
| 8100000 | 1692800 | 118.7781360000 | 4302.7093620000 | |
| 8200000 | 1713699 | 125.6885380000 | 4428.3979960000 | |
| 8300000 | 1734598 | 122.3463940000 | 4550.7444710000 | |
| 8400000 | 1755496 | 123.2608760000 | 4674.0054180000 | |
| 8500000 | 1776395 | 125.7767000000 | 4799.7821940000 | |
| 8600000 | 1797294 | 127.3217620000 | 4927.1040290000 | |
| 8700000 | 1818193 | 142.6963930000 | 5069.8004940000 | |
| 8800000 | 1839091 | 132.3448160000 | 5202.1453780000 | |
| 8900000 | 1859990 | 133.2586150000 | 5335.4040650000 | |
| 9000000 | 1880889 | 136.1275600000 | 5471.5316960000 | |
| 9100000 | 1901788 | 138.3854740000 | 5609.9172390000 | |
| 9200000 | 1922686 | 142.0560960000 | 5751.9734060000 | |
| 9300000 | 1943585 | 141.8788880000 | 5893.8523640000 | |
| 9400000 | 1964484 | 146.2905230000 | 6040.1429640000 | |
| 9500000 | 1985383 | 146.7824960000 | 6186.9255500000 | |
| 9600000 | 2006281 | 162.3883820000 | 6349.3140780000 | |
| 9700000 | 2027180 | 150.6406610000 | 6499.9548210000 | |
| 9800000 | 2048079 | 153.8561580000 | 6653.8110510000 | |
| 9900000 | 2068978 | 160.3674650000 | 6814.1786170000 | |
| 10000000 | 2089877 | 160.3539200000 | 6974.5326280000 | |
| 10100000 | 2110775 | 162.2257630000 | 7136.7584650000 | |
| 10200000 | 2131674 | 164.3632040000 | 7301.1217580000 | |
| 10300000 | 2152573 | 166.8829970000 | 7468.0048250000 | |
| 10400000 | 2173472 | 168.9921220000 | 7636.9970190000 | |
| 10500000 | 2194370 | 171.4993070000 | 7808.4963980000 | |
| 10600000 | 2215269 | 173.7570950000 | 7982.2535640000 | |
| 10700000 | 2236168 | 178.8824420000 | 8161.1360770000 | |
| 10800000 | 2257067 | 180.7242680000 | 8341.8604150000 | |
| 10900000 | 2277965 | 182.5922110000 | 8524.4526970000 | |
| 11000000 | 2298864 | 195.5978760000 | 8720.0506720000 | |
| 11100000 | 2319763 | 188.2496670000 | 8908.3004290000 | |
| 11200000 | 2340662 | 190.7901160000 | 9099.0906840000 | |
| 11300000 | 2361560 | 204.8128880000 | 9303.9036460000 | |
| 11400000 | 2382459 | 195.9118340000 | 9499.8155450000 | |
| 11500000 | 2403358 | 198.6109950000 | 9698.4266120000 | |
| 11600000 | 2424257 | 213.9461940000 | 9912.3729000000 | |
| 11700000 | 2445156 | 205.6800740000 | 10118.0530590000 | |
| 11800000 | 2466054 | 209.0088840000 | 10327.0620200000 | |
| 11900000 | 2486953 | 209.8021410000 | 10536.8642350000 | |
| 12000000 | 2507852 | 212.4198570000 | 10749.2841650000 | |
| 12100000 | 2528751 | 215.9069340000 | 10965.1911730000 | |
| 12200000 | 2549649 | 220.5192050000 | 11185.7104510000 | |
| 12300000 | 2570548 | 221.5003700000 | 11407.2108940000 | |
| 12400000 | 2591447 | 229.7355600000 | 11636.9465260000 | |
| 12500000 | 2612346 | 228.4625590000 | 11865.4091610000 | |
| 12600000 | 2633244 | 230.4370730000 | 12095.8463020000 | |
| 12700000 | 2654143 | 233.2925230000 | 12329.1388980000 | |
| 12800000 | 2675042 | 236.7446300000 | 12565.8836000000 | |
| 12900000 | 2695941 | 242.4511330000 | 12808.3349150000 | |
| 13000000 | 2716839 | 243.2051090000 | 13051.5402250000 |
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