UVa : 136 (Ugly Numbers)


Data type:
Long integer

Algorithm:


Two = Three = Five = 1 [First ugly number]

long Minimum () {
    if ( (2 * Two) minimum than (3 * Three) and (5 * Five) ) then
        return (2 * Two) and update : Two = Next ugly number

    else if ( (3 * Three) minimum than (2 * Two) and (5 * Five) ) then
        return (3 * Three) and update : Three = Next ugly number

    else if ( (5 * Five) minimum than (3 * Three) and (2 * Two) ) then
        return (5 * Five) and update : Five = Next ugly number
}

consecutive two returned value would be same, so carefully choose distinct value.
Or,

we can manually find the 1500th ugly number, tho it’s a time consuming process.

List of ugly numbers, below 10000
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025, 2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700, 2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840, 3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000, 5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776, 8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720

The 1500’th ugly number is 8 5_ _6 3 3 _ 2. // fill the blanks with same digit.

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