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Saturday, January 29, 2011

Trace lambda in Scheme to display recursion tree

When doing recursions in Scheme programming sometime its useful to see the growth of the recursion tree for debugging or even to get an intuition about approaches to improve the algorithm like dynamic programming. Following is a pure recursive insertion sort, obviously not the efficient implementation, yet it illustrate the use of trace procedure.

(define insert (lambda (val sorted)
(if (null? sorted)
(list val)
(if (< val (car sorted))
(cons val sorted)
(cons (car sorted) (insert val (cdr sorted)))))))

(define sort (lambda (vals)
(if (null? vals)
vals
(insert (car vals) (sort (cdr vals))))))

(trace insert)
(trace sort)





(sort '(7 6 5 9 3 4 2 8))

|(sort (7 6 5 9 3 4 2 8))
| (sort (6 5 9 3 4 2 8))
| |(sort (5 9 3 4 2 8))
| | (sort (9 3 4 2 8))
| | |(sort (3 4 2 8))
| | | (sort (4 2 8))
| | | |(sort (2 8))
| | | | (sort (8))
| | | | |(sort ())
| | | | |()
| | | | (insert 8 ())
| | | | (8)
| | | |(insert 2 (8))
| | | |(2 8)
| | | (insert 4 (2 8))
| | | |(insert 4 (8))
| | | |(4 8)
| | | (2 4 8)
| | |(insert 3 (2 4 8))
| | | (insert 3 (4 8))
| | | (3 4 8)
| | |(2 3 4 8)
| | (insert 9 (2 3 4 8))
| | |(insert 9 (3 4 8))
| | | (insert 9 (4 8))
| | | |(insert 9 (8))
| | | | (insert 9 ())
| | | | (9)
| | | |(8 9)
| | | (4 8 9)
| | |(3 4 8 9)
| | (2 3 4 8 9)
| |(insert 5 (2 3 4 8 9))
| | (insert 5 (3 4 8 9))
| | |(insert 5 (4 8 9))
| | | (insert 5 (8 9))
| | | (5 8 9)
| | |(4 5 8 9)
| | (3 4 5 8 9)
| |(2 3 4 5 8 9)
| (insert 6 (2 3 4 5 8 9))
| |(insert 6 (3 4 5 8 9))
| | (insert 6 (4 5 8 9))
| | |(insert 6 (5 8 9))
| | | (insert 6 (8 9))
| | | (6 8 9)
| | |(5 6 8 9)
| | (4 5 6 8 9)
| |(3 4 5 6 8 9)
| (2 3 4 5 6 8 9)
|(insert 7 (2 3 4 5 6 8 9))
| (insert 7 (3 4 5 6 8 9))
| |(insert 7 (4 5 6 8 9))
| | (insert 7 (5 6 8 9))
| | |(insert 7 (6 8 9))
| | | (insert 7 (8 9))
| | | (7 8 9)
| | |(6 7 8 9)
| | (5 6 7 8 9)
| |(4 5 6 7 8 9)
| (3 4 5 6 7 8 9)
|(2 3 4 5 6 7 8 9)
(2 3 4 5 6 7 8 9)

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David Wilson, a historian, believed that the gas industry would account for 40 percent of Soviet fuel production by the end of the century. His theory did not come to fruition because of the USSR's collapse.[81] The USSR, in theory, would have continued to have an economic growth rate of 2–2.5 percent during the 1990s because of Soviet energy fields[clarification needed].[
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It remained stable during most years, although in the 1970s, it went down slightly, probably because of alcohol abuse. Most western sources put the blame on growing alcohol abuse and poor health care; this theory was also implicitly accepted by the Soviet authorities. At the same time, infant mortality began to rise. After 1974, the government stopped publishing statistics on this. This trend can be partly explained by the number of pregnancies rising drastically in the Asian part of the country where infant mortality was highest, while declining markedly in the more developed European part of the Soviet Union.
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Sometimes, the word 'Europe' is used in a geopolitically limiting way[18] to refer only to the European Union or, even more exclusively, a culturally defined core. On the other hand, the Council of Europe has 47 member countries, and only 27 member states are in the EU.[19] In addition, people living in insular areas such as Ireland, the United Kingdom, the North Atlantic and Mediterranean islands and also in Scandinavia may routinely refer to "continental" or "mainland" Europe simply as Europe or "the Continent"
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In September 1918, when the call was made to disband eight battalions, there followed a series of "mutinies over disbandment" where the ranks refused to report to their new battalions. In the AIF, mutiny was one of two charges that carried the death penalty, the other being desertion to the enemy. Instead of being charged with mutiny, the instigators were charged as being AWOL and the doomed battalions were eventually permitted to remain together for the forthcoming battle, following which the survivors voluntarily disbanded
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Each division comprised three mounted light horse brigades. The Anzac Mounted Division was so named becaused it contained the one mounted brigade from New Zealand – the New Zealand Mounted Rifles Brigade. Likewise the Australian Mounted Division was originally named the Imperial Mounted Division because it contained the British 5th and 6th Mounted (Yeomanry) Brigades.
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Although it is likely that schoolboys were taught by monks well beforehand, by 1179 Westminster School had certainly become a public school (i.e., a school available to members of the public from across the country, so long as they could pay their own costs, rather than private tuition provided to the nobility) as a decree of Pope Alexander III required the Benedictine monks of the Abbey at Westminster to provide a charity school to local boys.
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Collectively, African Americans are more involved in the American political process than other minority groups in the United States, indicated by the highest level of voter registration and participation in elections among these groups in 2004.[95] African Americans collectively attain higher levels of education than immigrants to the United States.[95] African Americans also have the highest level of Congressional representation of any minority group in the U.S.
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