So I was solving Construct Binary Tree from Inorder and Postorder Traversal and I got myself more less working solution that got accepted.

But it was not the fastest one.

But then I though — how do I profile buildTree function and see what actually takes time in my program?

Golang has an excellent set of tool available, just check an output of go tool. One of the items in a list you’ll see is pprof which is a Golang profiler.

pprof requires graphviz to be installed.

So I have this file structure:

slash3b@Kerrisk ~/G/awesomeProject1> tree .
.
├── awesome.go
├── awesome_test.go
└── go.mod

0 directories, 3 files

awesome.go contains my implementation for the problem:

package awesomeProject1

type TreeNode struct {
	Val   int
	Left  *TreeNode
	Right *TreeNode
}

var inorder = []int{-999, -998, -997, -996, -995, -994, -993, -992, -991, -990, -989, -988, -987, -986, -985, -984, -983, -982, -981, -980, -979, -978, -977, -976, -975, -974, -973, -972, -971, -970, -969, -968, -967, -966, -965, -964, -963, -962, -961, -960, -959, -958, -957, -956, -955, -954, -953, -952, -951, -950, -949, -948, -947, -946, -945, -944, -943, -942, -941, -940, -939, -938, -937, -936, -935, -934, -933, -932, -931, -930, -929, -928, -927, -926, -925, -924, -923, -922, -921, -920, -919, -918, -917, -916, -915, -914, -913, -912, -911, -910, -909, -908, -907, -906, -905, -904, -903, -902, -901, -900, -899, -898, -897, -896, -895, -894, -893, -892, -891, -890, -889, -888, -887, -886, -885, -884, -883, -882, -881, -880, -879, -878, -877, -876, -875, -874, -873, -872, -871, -870, -869, -868, -867, -866, -865, -864, -863, -862, -861, -860, -859, -858, -857, -856, -855, -854, -853, -852, -851, -850, -849, -848, -847, -846, -845, -844, -843, -842, -841, -840, -839, -838, -837, 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1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000}

func buildTree(inorder []int, postorder []int) *TreeNode {
	root := &TreeNode{}

	if len(postorder) == 1 {
		root.Val = postorder[0]
		return root
	}

	root.Val = postorder[len(postorder)-1]

	assemble(root, inorder, postorder)

	return root
}

func assemble(n *TreeNode, inorder, postorder []int) {
	rootIndex := findIndex(inorder, n.Val)
	leftPart := inorder[:rootIndex]
	rightPart := inorder[rootIndex+1:]

	if len(leftPart) != 0 {
		idx, rootVal := findRoot(leftPart, postorder)
		n.Left = &TreeNode{Val: rootVal}
		assemble(n.Left, leftPart, postorder[:idx])
	}

	if len(rightPart) != 0 {
		idx, rootVal := findRoot(rightPart, postorder)
		n.Right = &TreeNode{Val: rootVal}
		assemble(n.Right, rightPart, postorder[:idx])
	}
}

func findIndex(list []int, val int) int {
	for k, v := range list {
		if v == val {
			return k
		}
	}

	return -1
}

func findRoot(inorder, postorder []int) (int, int) { // root index and root value
	for i := len(postorder) - 1; i >= 0; i-- {
		for _, inorderValue := range inorder {
			if postorder[i] == inorderValue {
				return i, inorderValue
			}
		}
	}
	return -1, -1
}

One of the ways to profile a method, is to create a benchmark test.

So here is what I have in awesome_test.go:

package awesomeProject1

import "testing"

func BenchmarkAwesome(b *testing.B) {
	for n := 0; n < b.N; n++ {
		buildTree(inorder, postorder)
	}
}

Now in order to profile solution, you have to run benchmark test for this, like so:

go test -bench . -cpuprofile=cpu_profile.pprof

Along with test binary, in the project directory you’ll find a new file with pprof extension. Now, you can view profiler data as simple as:

slash3b@Kerrisk ~/G/awesomeProject1> go tool pprof -http=":8000" cpu_profile.pprof
Serving web UI on http://localhost:8000

Web UI is really easy to use and it has a lot to offer — top, flame graph, diassembly, source code view and so much more. Exploration of UI I’ll leave as an exercise to the reader.

What if I just want a bit simpler information like, top? Well, pprof has a lot of options and ways to view profiler data, for example you can just do go tool pprof cpu_profile.pprof and it will open up interactive interface, where you can run command top and view the following:

slash3b@Kerrisk ~/G/awesomeProject1> go tool pprof cpu_profile.pprof
File: awesomeProject1.test
Type: cpu
Time: Dec 27, 2021 at 1:32am (EET)
Duration: 7.94s, Total samples = 7.97s (100.42%)
Entering interactive mode (type "help" for commands, "o" for options)
(pprof) top
Showing nodes accounting for 7.79s, 97.74% of 7.97s total
Dropped 57 nodes (cum <= 0.04s)
Showing top 10 nodes out of 23
      flat  flat%   sum%        cum   cum%
     3.99s 50.06% 50.06%      3.99s 50.06%  awesomeProject1.findRoot
     3.31s 41.53% 91.59%      3.31s 41.53%  awesomeProject1.findIndex
     0.17s  2.13% 93.73%      7.82s 98.12%  awesomeProject1.assemble
     0.14s  1.76% 95.48%      0.34s  4.27%  runtime.mallocgc
     0.07s  0.88% 96.36%      0.07s  0.88%  runtime.nextFreeFast (inline)
     0.06s  0.75% 97.11%      0.07s  0.88%  runtime.heapBitsSetType
     0.04s   0.5% 97.62%      0.04s   0.5%  runtime.madvise
     0.01s  0.13% 97.74%      0.05s  0.63%  runtime.(*pageAlloc).scavengeOne
         0     0% 97.74%      0.32s  4.02%  awesomeProject1.BenchmarkAwesome
         0     0% 97.74%      0.33s  4.14%  awesomeProject1.buildTree
(pprof) 

As you might notice findRoot and findIndex are taking all the time to execute 🤔 Solution is definitely soboptimal and I yet has to figure how to improve it. I’d go with hash map for both inorder and postorder sequences… but I need maps to have the same sequence of elements which is not quite possible. Hash maps in golang have pseudo-random order which kind of breaks it for me.