1395. Count Number of Teams

Medium

There are n soldiers standing in a line. Each soldier is assigned a unique rating value.

You have to form a team of 3 soldiers amongst them under the following rules:

Choose 3 soldiers with index (i, j, k) with rating (rating[i], rating[j], rating[k]).
A team is valid if: (rating[i] < rating[j] < rating[k]) or (rating[i] > rating[j] > rating[k]) where (0 <= i < j < k < n).

Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).

Example 1:

Input: rating = [2,5,3,4,1]
Output: 3
Explanation: We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1).

Example 2:

Input: rating = [2,1,3]
Output: 0
Explanation: We can't form any team given the conditions.

Example 3:

Input: rating = [1,2,3,4]
Output: 4

Example 4:

Input: rating = [2173,478,1128,2138,785,159,819,2747,557,2422,2092,1105,1374,2450,1574,951,1290,1590,1929,1605,1646,2791,2701,2911,971,2066,493,1593,1537,257,205,1109,79,470,1790,221,180,1891,250,1798,75,2778,2302,1299,923,355,2399,2536,2628,2805,1046,1555,2178,2722,1843,754,1908,610,2933,613,2047,2296,2820,1815,2997,431,1320,11,1387,227,913,2530,1680,2136,2589,2027,2003,2699,1271,1831,666,1872,1268,62,399,1665,1508,2228,2079,1418,1937,2686,1429,58,1696,161,2476,1950,857,699,2792,1353,2901,2923,330,99,1711,2546,2405,1340,2456,664,2584,2741,60,488,2406,1988,1827,1514,1708,2043,513,789,1284,2132,1600,646,2660,552,2139,507,1256,374,1655,1899,2295,288,2606,1874,776,2361,1958,751,2759,386,438,644,1954,2788,2081,832,2230,2602,2222,919,2905,694,2793,2562,2867,1169,1732,1381,2462,1230,284,1624,2496,748,2107,385,1064,1267,2058,499,2203,215,88,585,525,1136,309,1851,2085,109,2809,517,409,2419,2384,2308,2292,1994,2943,1294,1781,1862,2841,2096,662,2014,2426,2821,2400,113,129,2193,2865,618,121,1038,1782,2468,2861,234,249,2967,1533,607,1453,1465,477,471,1778,2143,1050,1728,1332,1967,73,1698,626,1449,2833,2447,917,2500,1920,673,1234,1420,1659,880,584,2023,1281,1544,1380,2019,2131,1018,152,2268,2052,2372,1017,2807,1424,633,1726,523,373,2850,1025,2371,1405,2252,996,895,1475,1886,2002,1720,1826,381,1835,1666,2879,2255,182,2641,2680,2920,1336,2061,1969,394,858,480,2322,766,1176,2995,1691,681,2595,1758,745,2492,1212,2776,1177,1027,448,2866,2423,2156,701,1184,2294,612,1963,2928,2851,875,949,814,244,2930,2306,2515,1266,522,830,2364,2209,1168,1372,686,325,354,511,1860,2828,1504,2176,1189,2694,1838,392,594,1091,1183,368,862,1457,2191,1096,410,177,274,2033,5,1697,1573,504,2725,2859,2401,2122,1118,813,936,455,1115,671,690,1067,144,155,2060,1998,2242,1978,566,624,518,2086,76,1526,2219,2618,2180,2880,1301,166,2153,2202,944,2346,196,720,2529,1945,2772,1441,2715,2366,1578,838,464,194,1645,1020,1042,2474,1060,1314,1207,1245,890,2057,643,2540,2094,1529,932,2563,545,1153,803,1742,1102,2351,370,1369,1973,1837,2250,2121,178,266,521,2259,1850,2964,1964,726,1743,2410,716,2118,1265,2542,878,1924,532,812,2487,1417,2262,321,920,2217,497,1875,555,2662,898,1404,2408,253,65,1916,2486,445,797,1765,1376,1470,2181,2856,2554,2045,1415,2858,1842,248,1810,596,453,1816,1802,1517,397,760,2324,1930,2522,2216,736,297,2755,107,2110,2965,755,1261,2415,1395,1016,809,2913,1779,55,2297,1637,2691,67,1983,185,2080,656,1014,1795,2220,1024,2658,1610,361,2800,2448,1174,2425,1479,256,2605,2320,1832,1991,588,1019,2317,278,727,242,2586,1431,371,2293,1371,1445,2864,2548,773,1615,1868,582,2692,589,1489,2009,1905,2831,2084,2104,138,1580,446,389,847,2028,1262,68,889,1767,907,989,1152,203,2089,2328,417,1248,2843,1451,1972,1409,1519,2455,2383,943,683,108,2395,1773,2356,2337,839,1717,1777,1757,2115,2925,1430,1933,1005,2736,2958,1295,307,1028,597,739,51,157,2375,933,2385,292,905,280,893,1315,2323,1562,2435,1746,2090,985,420,2742,2949,304,842,1487,520,1556,2862,684,711,271,1283,2166,2545,425,429,1497]
Output: 14510756

Constraints:

n == rating.length
3 <= n <= 1000
1 <= rating[i] <= 10⁵
All the integers in rating are unique.

Hint:

BruteForce, check all possibilities.

Solution:

To solve this problem, we can follow these steps:

Let's implement this solution in PHP: 1395. Count Number of Teams

<?php
// Example usage:
$rating1 = [2, 5, 3, 4, 1];
$rating2 = [2, 1, 3];
$rating3 = [1, 2, 3, 4];
$rating4 = [2173, 478, 1128, 2138, 785, 159, 819, 2747, 557, 2422, 2092, 1105, 1374, 2450, 1574, 951, 1290, 1590, 1929, 1605, 1646, 2791, 2701, 2911, 971, 2066, 493, 1593, 1537, 257, 205, 1109, 79, 470, 1790, 221, 180, 1891, 250, 1798, 75, 2778, 2302, 1299, 923, 355, 2399, 2536, 2628, 2805, 1046, 1555, 2178, 2722, 1843, 754, 1908, 610, 2933, 613, 2047, 2296, 2820, 1815, 2997, 431, 1320, 11, 1387, 227, 913, 2530, 1680, 2136, 2589, 2027, 2003, 2699, 1271, 1831, 666, 1872, 1268, 62, 399, 1665, 1508, 2228, 2079, 1418, 1937, 2686, 1429, 58, 1696, 161, 2476, 1950, 857, 699, 2792, 1353, 2901, 2923, 330, 99, 1711, 2546, 2405, 1340, 2456, 664, 2584, 2741, 60, 488, 2406, 1988, 1827, 1514, 1708, 2043, 513, 789, 1284, 2132, 1600, 646, 2660, 552, 2139, 507, 1256, 374, 1655, 1899, 2295, 288, 2606, 1874, 776, 2361, 1958, 751, 2759, 386, 438, 644, 1954, 2788, 2081, 832, 2230, 2602, 2222, 919, 2905, 694, 2793, 2562, 2867, 1169, 1732, 1381, 2462, 1230, 284, 1624, 2496, 748, 2107, 385, 1064, 1267, 2058, 499, 2203, 215, 88, 585, 525, 1136, 309, 1851, 2085, 109, 2809, 517, 409, 2419, 2384, 2308, 2292, 1994, 2943, 1294, 1781, 1862, 2841, 2096, 662, 2014, 2426, 2821, 2400, 113, 129, 2193, 2865, 618, 121, 1038, 1782, 2468, 2861, 234, 249, 2967, 1533, 607, 1453, 1465, 477, 471, 1778, 2143, 1050, 1728, 1332, 1967, 73, 1698, 626, 1449, 2833, 2447, 917, 2500, 1920, 673, 1234, 1420, 1659, 880, 584, 2023, 1281, 1544, 1380, 2019, 2131, 1018, 152, 2268, 2052, 2372, 1017, 2807, 1424, 633, 1726, 523, 373, 2850, 1025, 2371, 1405, 2252, 996, 895, 1475, 1886, 2002, 1720, 1826, 381, 1835, 1666, 2879, 2255, 182, 2641, 2680, 2920, 1336, 2061, 1969, 394, 858, 480, 2322, 766, 1176, 2995, 1691, 681, 2595, 1758, 745, 2492, 1212, 2776, 1177, 1027, 448, 2866, 2423, 2156, 701, 1184, 2294, 612, 1963, 2928, 2851, 875, 949, 814, 244, 2930, 2306, 2515, 1266, 522, 830, 2364, 2209, 1168, 1372, 686, 325, 354, 511, 1860, 2828, 1504, 2176, 1189, 2694, 1838, 392, 594, 1091, 1183, 368, 862, 1457, 2191, 1096, 410, 177, 274, 2033, 5, 1697, 1573, 504, 2725, 2859, 2401, 2122, 1118, 813, 936, 455, 1115, 671, 690, 1067, 144, 155, 2060, 1998, 2242, 1978, 566, 624, 518, 2086, 76, 1526, 2219, 2618, 2180, 2880, 1301, 166, 2153, 2202, 944, 2346, 196, 720, 2529, 1945, 2772, 1441, 2715, 2366, 1578, 838, 464, 194, 1645, 1020, 1042, 2474, 1060, 1314, 1207, 1245, 890, 2057, 643, 2540, 2094, 1529, 932, 2563, 545, 1153, 803, 1742, 1102, 2351, 370, 1369, 1973, 1837, 2250, 2121, 178, 266, 521, 2259, 1850, 2964, 1964, 726, 1743, 2410, 716, 2118, 1265, 2542, 878, 1924, 532, 812, 2487, 1417, 2262, 321, 920, 2217, 497, 1875, 555, 2662, 898, 1404, 2408, 253, 65, 1916, 2486, 445, 797, 1765, 1376, 1470, 2181, 2856, 2554, 2045, 1415, 2858, 1842, 248, 1810, 596, 453, 1816, 1802, 1517, 397, 760, 2324, 1930, 2522, 2216, 736, 297, 2755, 107, 2110, 2965, 755, 1261, 2415, 1395, 1016, 809, 2913, 1779, 55, 2297, 1637, 2691, 67, 1983, 185, 2080, 656, 1014, 1795, 2220, 1024, 2658, 1610, 361, 2800, 2448, 1174, 2425, 1479, 256, 2605, 2320, 1832, 1991, 588, 1019, 2317, 278, 727, 242, 2586, 1431, 371, 2293, 1371, 1445, 2864, 2548, 773, 1615, 1868, 582, 2692, 589, 1489, 2009, 1905, 2831, 2084, 2104, 138, 1580, 446, 389, 847, 2028, 1262, 68, 889, 1767, 907, 989, 1152, 203, 2089, 2328, 417, 1248, 2843, 1451, 1972, 1409, 1519, 2455, 2383, 943, 683, 108, 2395, 1773, 2356, 2337, 839, 1717, 1777, 1757, 2115, 2925, 1430, 1933, 1005, 2736, 2958, 1295, 307, 1028, 597, 739, 51, 157, 2375, 933, 2385, 292, 905, 280, 893, 1315, 2323, 1562, 2435, 1746, 2090, 985, 420, 2742, 2949, 304, 842, 1487, 520, 1556, 2862, 684, 711, 271, 1283, 2166, 2545, 425, 429, 1497];

// Print results
echo numTeams($rating1) . "\n"; // Output: 3
echo numTeams($rating2) . "\n"; // Output: 0
echo numTeams($rating3) . "\n"; // Output: 4
echo numTeams($rating4) . "\n"; // Output: 14510756

?>

Explanation:

The code iterates over each soldier (position j) and counts how many soldiers on its left are less than and greater than it (leftLess and leftMore).
Similarly, it counts how many soldiers on its right are less than and greater than it (rightLess and rightMore).
A valid team can be formed in two ways:
1. Soldiers on the left are less and soldiers on the right are greater (leftLess * rightMore).
2. Soldiers on the left are greater and soldiers on the right are less (leftMore * rightLess).
The total number of teams is accumulated in the $count variable.

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