ၥ㢟ゎἲ࡟࠾ࡅࡿືⓗィ⏬ἲࡢ◊✲㸫࢔ࣝࢦࣜࢬ࣒ᐇᢏ᳨ᐃࡢၥ㢟ゎἲࢆ㏻ࡋ࡚㸫⎩⏕ 㝯ᘯ
A Study of a Solution to a Problem Using Dynamic Programming- From Practical Algorithm Skill Test –Takahiro Uryu

Abstract
In this paper,I verified the usefulness of Dynamic Programming and other techniques in problem solving. As an example,I took
up the question O of the PAST test conducted in December 2019.It has been found that applying Dynamic Programming is usefulwhen it is difficult to reach the correct answer because it takes a lot of time to implement the processing procedure as intended,asin the problem discussed this paper.However,even if the Dynamic Programming programming is applied,if the processing
procedure includes multiple loops,the correct answer may not be reached depending on the constraints.
In that case,it was confirmed that the calculation time could be reduced by searching for and implementing an idea to reduce thenumber of loops.

Keywords: Dynamic Programming, Coordinate compression, Memoization recursive function, Algorithm㸯㸬ࡣࡌࡵ࡟ ࢔ࣝࢦࣜࢬ࣒ᐇᢏ᳨ᐃ㸦㹎㸿㹑㹒㸧࡜ࡣࠊ➇ᢏࣉࣟࢢ࣑ࣛࣥࢢࢥࣥࢸࢫࢺࢆ㐠Ⴀࡍࡿ㸿㹲㹁㹭㹢㹣㹰ᰴᘧ఍♫ࡀᐇ᪋ࡍࡿ᳨ᐃ࡛ࠊࣉࣟࢢ࣑ࣛࣥࢢࢫ࢟ࣝࡀၥࢃࢀࡿၥ㢟ࡀ୚࠼ࡽࢀࠊไ㝈᫬㛫㸳᫬㛫௨ෆ࡟ࡑࡢゎἲࢆࣉࣟࢢ࣑ࣛࣥࢢࡋ࡚࢜ࣥࣛ࢖࡛ࣥᥦฟࡍࡿࡶࡢ࡛࠶ࡿࠋၥ㢟ࡣ㸯㸳ၥ୚࠼ࡽࢀࠊ㸯㸮㸮Ⅼ‶Ⅼ࡛᥇Ⅼࡉࢀࡿࠋ⋓ᚓࡋࡓⅬᩘ࡟ᛂࡌ࡚ࠊ࢚ࣥࢺ࣮ࣜࠊึ⣭ࠊ୰⣭ࠊୖ⣭ࠊ࢚࢟ࢫࣃ࣮ࢺࡢ㸳ẁ㝵࡛ࣛࣥࢡࡀㄆᐃࡉࢀࡿࠋ ᮏ✏࡛ࡣࠊ㸰㸮㸯㸷ᖺ㸯㸰᭶࡟ᐇ᪋ࡉࢀࡓ➨୍ᅇ࢔ࣝࢦࣜࢬ࣒ᐇᢏ᳨ᐃࡢ㹍ၥ㢟ࢆᑐ㇟࡜ࡋࠊࡑࡢゎἲ࡜ࡋ࡚➹⪅ࡀ㐺⏝ࡋࡓືⓗィ⏬ἲ࠾ࡼࡧࠊࡑࡢ௚ࡢᢏἲ࡟ࡘ࠸࡚ࡢ᭷⏝ᛶࢆ᳨ドࡋࠊືⓗィ⏬ἲ࡜࣮ࣝࣉฎ⌮ࢆ๐ῶࡍࡿ࢔࢖ࢹ࢔ࡢᐇ⿦ࡀィ⟬᫬㛫ࡢ๐ῶ࡟ຠᯝࡀ࠶ࡿࡇ࡜ࢆ☜ㄆࡋࡓࠋ㸰㸬ᗙᶆᅽ⦰ ไ⣙࠿ࡽศ࠿ࡿࡼ࠺࡟ࠊࡉ࠸ࡇࢁࡢ┠ࡣᑠࡉ࠸ᩘᏐ࠿ࡽ㡰␒࡟౑⏝ࡉࢀࡿ࡜ࡣ㝈ࡽ࡞࠸ࠋࡓࡔࡋࠊྠࡌᩘࡣ౑⏝ࡉࢀ࡞࠸ࠋࡇࡢၥ㢟࡛ࡣࠊ┠ࡢ኱ᑠ㛵ಀࡔࡅࡀྫྷ࿡ࡉࢀࡿࡢ࡛ࠊ┠࡟౑⏝ࡉࢀࡓᩘࢆ᪂ࡓ࡟  ࠿ࡽ㡰ḟ๭ࡾᙜ࡚┤ࡍᗙᶆᅽ⦰ࡢᢏἲࡀ㐺⏝࡛ࡁࡿࠋ ࣉࣟࢢ࣑ࣛࣥࢢゝㄒ F࡟ࡣ㐃᝿グ᠈ࢡࣛࢫࡢ PDS㸦෗ീࠊPDSSLQJ㸧ࡀ࠶ࡾࠊLQFOXGHPDS!ࢆᐉゝࡍࡿࡇ࡜࡛฼⏝ྍ⬟࡜࡞ࡿࠋ㐃᝿㓄ิࢡࣛࢫ࡜ࡣࠊ᳨⣴ྍ⬟࡞࣮࢟࡜ࡑࡢ࣮࢟࡟ᑐᛂࡍࡿ್ࢆ࣌࢔࡛ಖᣢࡋࠊ࣮࢟ࢆᣦᐃࡍࡿࡇ࡜࡛ᑐᛂࡍࡿ್ࢆ㧗㏿࡟ྲྀࡾฟࡍࡇ࡜ࡀ࡛ࡁࡿ௙⤌ࡳࢆᣢࡘࢡࣛࢫࡢࡇ࡜࡛࠶ࡿࠋ ࠙FRGHࠚࡢグ㏙࡟ࡼࡾࠊධຊࡉࢀࡓࡉ࠸ࡇࢁࡢ┠ࡢࢹ࣮ࢱࢆᗙᶆᅽ⦰ࡋ࡚ࠊ᪂ࡓ࡟㓄ิ E>L@>M@࡟᱁⣡ࡋࡓࠋ㸱㸬ືⓗィ⏬ἲ㸦'\QDPLF3URJUDPPLQJ㸧࡟ࡼࡿゎἲ ືⓗィ⏬ἲࡣィ⟬㔞ࢆῶࡽࡍタィᢏἲࡢࡦ࡜ࡘ࡜ࡋ࡚ᗈࡃ▱ࡽࢀ࡚࠾ࡾࠊࢺࢵࣉࢲ࢘ࣥ᪉ᘧ࡜࣎ࢺ࣒࢔ࢵࣉ᪉

−1−ᘧ࡟኱ู࡛ࡁࡿࠋࢺࢵࣉࢲ࢘ࣥ᪉ᘧࡣࠊ୍ᗘィ⟬ࡋࡓ⤖ᯝࢆグ㘓ࡋ࡚࠾ࡁࠊ࠶࡜࡛฼⏝ࡍࡿ᪉ᘧ࡛ࠊ࣓ࣔ໬෌ᖐ࡜ࡶ࿧ࡤࢀࡿᢏἲ࡛࠶ࡿࠋ࣎ࢺ࣒࢔ࢵࣉ᪉ᘧࡣศ๭⤫἞ἲࠊࡲࡓࡣ₞໬ᘧ࣮ࣝࣉ࡜ࡶ࿧ࡤࢀࡿᢏἲ࡛࠶ࡿࠋ ౛࠼ࡤࣇ࢕࣎ࢼࢵࢳᩘิࢆồࡵࡿሙྜࠊᐃ⩏㏻ࡾࡢ⣲ᮔ࡞ィ⟬ἲࢆ᥇⏝ࡍࡿ࡜࠙FRGHࠚ࡟♧ࡋࡓࡼ࠺࡞ࣉࣟࢢ࣒ࣛ࡜࡞ࡿࠋ➹⪅ࡢ⎔ቃ࡛࠙FRGHࠚࢆ⏝࠸࡚ࣇ࢕࣎ࢼࢵࢳᩘิࡢ➨  㡯ࡲ࡛ࢆィ⟬ࡍࡿ࡜ࠊPV㸦 ⛊㸧࠿࠿ࡗࡓࠋ࠙FRGHࠚ࡟♧ࡍ࣓ࣔ໬෌ᖐࡢᡭἲࢆ᥇⏝ࡋࡓࢺࢵࣉࢲ࢘ࣥ᪉ᘧࡢࣉࣟࢢ࣒ࣛࢆ⏝࠸࡚ྠᵝࡢィ⟬ࢆᐇ⾜ࡍࡿ࡜ࠊฎ⌮᫬㛫ࡣ PV㸦 ⛊㸧࡛࠶ࡗࡓࠋࡲࡓࠊ࠙FRGHࠚ࡟♧ࡍ࣎ࢺ࣒࢔ࢵࣉ᪉ᘧࡢࣉࣟࢢ࣒ࣛࢆ⏝࠸ࡓሙྜࡢฎ⌮᫬㛫ࡶྠࡌࡃ PV㸦 ⛊㸧࡛࠶ࡗࡓࠋ ⣲ᮔ࡞ィ⟬ἲࢆ᥇⏝ࡍࡿ࡜ࠊࣇ࢕࣎ࢼࢵࢳᩘิࡢฎ⌮᫬㛫ࡣᴟ➃࡟ቑ࠼ࡿࠋ౛࠼ࡤ࠙FRGHࠚࢆ⏝࠸࡚ࣇ࢕࣎ࢼࢵࢳᩘิࡢ➨  㡯ࡲ࡛ࢆィ⟬ࡍࡿ࡜ࠊPV㸦 ศ  ⛊⛬ᗘ㸧࠿࠿ࡿࠋ୍᪉ࠊ࣓ࣔ໬෌ᖐࡢᡭἲࢆ᥇⏝ࡋࡓࢺࢵࣉࢲ࢘ࣥ᪉ᘧ࠙FRGHࠚ࡛ࡣ PV㸦 ⛊㸧ࠊ࣎ࢺ࣒࢔ࢵࣉ᪉ᘧ࠙FRGHࠚࡢィ⟬᫬㛫ࡶྠࡌࡃ PV㸦 ⛊㸧࡛࠶ࡗࡓࠋࡇࡢࡼ࠺࡟ືⓗィ⏬ἲࢆ㐺⏝ࡍࡿ࡜ၥ㢟ゎἲࡢฎ⌮᫬㛫ࢆ኱ᖜ࡟๐ῶ࡛ࡁࡿࡇ࡜ࡀࢃ࠿ࡿࠋ ௒ᅇࠊ᳨ドࡢᑐ㇟࡜ࡋ࡚ྲྀࡾୖࡆࡓ㹍ၥ㢟࡟࠾࠸࡚ࡣࠊGS>M@ࢆࠕM ࡀ࡛ࡓᚋࠊࡢࡇࡾఱᅇ᣺ࢀࡿ࠿ࡢᮇᚅ್ࠖ
࡜ࡋࠊGS>M@ࢆ M ࡢ㝆㡰࡟ィ⟬ࡍࡿࡇ࡜࡟ࡼࡗ࡚ࢺࢵࣉࢲ࢘ࣥ᪉ᘧࡢືⓗィ⏬ἲࢆ㐺⏝࡛ࡁࡿࠋ࠙FRGHࠚ࡟㢟ព㏻ࡾࡢฎ⌮ᡭ㡰ࢆᐇ⿦ࡋࡓࠋࡇࡢࢥ࣮ࢻ࡟ࡼࡗ࡚ṇゎࢆᚓࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡓࡔࡋࠊ
࠙FRGHࠚ࡟ࡣ‫ڸ‬㸯࠿ࡽ‫ڸ‬㸱࡛♧ࡍࡼ࠺࡟࣮ࣝࣉฎ⌮ࡀ  㔜࡟࡞ࡿ㒊ศࡀྵࡲࢀࠊຠ⋡ⓗ࡜ࡣゝ࠼࡞࠸ࠋไ⣙࡟࠶ࡿࡼ࠺࡟᭱኱  ಶࡢࡉ࠸ࡇࢁࡀ࠶ࡿሙྜࠊィ⟬ᅇᩘࡣᑡ࡞ࡃ࡜ࡶ‫ڸ‬㸦┠ࡢ⥲ᩘ㸧‫ڸ‬㸦ࡉ࠸ࡇࢁࡢᩘ㸧‫ڸ‬㸦┠ⓗࡢ┠ࡢሙᡤࡢ᥈⣴㸧    㸦Ș㸧  ൨Ș ᅇ௨ୖࡀぢ㎸ࡲࢀࡿࠋࡇࡢィ⟬㔞ࡣ㸯ᅇ࠶ࡓࡾࡢฎ⌮࡟㸯࣐࢖ࢡࣟ⛊࠿࠿ࡿ࡜ࡋ࡚  ᪥௨ୖࡢィ⟬᫬㛫ࡀᚲせ࡛ࠊࣃࢯࢥ࡛ࣥṇゎࢆᚓࡿ࡟ࡣィ⟬㔞ࢆῶࡽࡍᕤኵࡀᚲ㡲࡜࡞ࡿࠋ㸲㸬ィ⟬㔞๐ῶࡢᕤኵ ᭱ึ࡟‫ࢆࣉ࣮ࣝࡢ ڸ‬๐ࡿ࢔࢖ࢹ࢔ࢆ᳨ウࡋࡓࠋࡍ࡭࡚ࡢࡉ࠸ࡇࢁ࡟ᑐࡋ࡚ࠊ┠ⓗࡢ┠ࡀ࠶ࡿ࠿࡝࠺࠿ࢆ඲᳨⣴ࡋ࡚࠸ࡿ㒊ศ࡛࠶ࡿࠋࡇࡢ㒊ศࢆᨵⰋࡋ࡚ࠊࡑࢀࡒࢀࡢ┠ࡀ࡝ࡢࡉ࠸ࡇࢁ࡟࠶ࡿࡢ࠿ࢆ⟶⌮ࡋ࡚࠾ࡅࡤࠊヱᙜࡍࡿࡉ࠸ࡇࢁࡔࡅࢆ᳨⣴ࡢᑐ㇟࡜ࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡘࡲࡾࠊࡉ࠸ࡇࢁࡢᩘࢆ Q ࡜ࡍࢀࡤࠊࡇࡢ஦๓ฎ⌮࡟ࡼࡾィ⟬㔞ࢆ Q ࡟๐ῶ࡛ࡁࡿࠋࡑࡇ࡛࠙FRGHࠚ࡟♧ࡍࡼ࠺࡞ฎ⌮ࢆ㏣ຍࡋࡓࠋලయⓗ࡟ࡣࠊࡑࢀࡒࢀࡢ┠ࡀ࡝ࡢࡉ࠸ࡇࢁ࡟࠶ࡿ࠿ࡢ᝟ሗࢆ᱁⣡ࡍࡿ㐃᝿グ᠈ࢡࣛࢫࡢ࢖ࣥࢫࢱࣥࢫ PS ࢆ‽ഛࡋࠊࡉ࠸ࡇࢁࡢ┠ M ࢆ᳨⣴࣮࢟࡜ࡋ࡚ M ࡢྵࡲࢀࡿࡉ࠸ࡇࢁࡢ್ࡀ⡆༢࡟♧ࡏࡿࡼ࠺࡟ᕤኵࡋࡓࠋ ࡉࡽ࡟ࠊ┠ⓗࡢ┠ࡢሙᡤࢆ᥈⣴ࡍࡿᡭ㡰ࡢᨵⰋࢆ᳨ウࡋࡓࠋ‫ࢁࡇ࠸ࡉࡣ࡛ ڸ‬ẖ࡟ M ࡼࡾ኱ࡁ࡞┠ࢆ᥈⣴ࡋࠊࡑࡢᮇᚅ್ࢆຍ⟬ࡍࡿࡇ࡜࡟ࡼࡾࠊࡑࢀࡽࡢ࠺ࡕࡢ᭱኱್࠿ࡽ GS>M@ࢆồࡵࡓࡀࠊࡉ࠸ࡇࢁẖ࡟ᮇᚅ್ࢆಖᣢࡍࡿኚᩘࢆ‽ഛࡍࢀࡤࠊM ࡢ┠ࡀࡦ࡜ࡘࡋ࠿࡞࠸ࡇ࡜࠿ࡽࠊຍ⟬ࡀᚲせ࡞ࡉ࠸ࡇࢁࡣࡦ࡜ࡘ࡞ࡢ࡛ࠊ᭦᪂ᅇᩘࢆ  ᅇ࡟ῶࡽࡍࡇ࡜ࡀ࡛ࡁࡿࠋ
࠙FRGHࠚ࡛ࢃ࠿ࡿࡼ࠺࡟ࠊィ⟬ᅇᩘࡣ‫ڸ‬㸦┠ࡢᩘ㸧‫ڸ‬㸦≉ᐃࡢࡉ࠸ࡇࢁ㸧Ș  Ș࡜࡞ࡾࠊィ⟬᫬㛫ࢆ᭱኱  ศࡢ  ࡟๐ῶࡍࡿࡇ࡜ࡀ࡛ࡁࡓࠋ㸳㸬ࡲ࡜ࡵ ௒ᅇྲྀࡾୖࡆࡓၥ㢟ࡢࡼ࠺࡟ࠊ㢟ព㏻ࡾࡢฎ⌮ᡭ㡰ࢆᐇ⿦ࡍࡿ࡜ィ⟬᫬㛫ࡀ࠿࠿ࡾࠊṇ⟅࡟ࡓ࡝ࡾ╔ࡅ࡞࠸ሙྜࠊືⓗィ⏬ἲࡢ㐺⏝ࡀ᭷⏝࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡗࡓࠋࡓࡔࡋࠊືⓗィ⏬ἲࢆ㐺⏝ࡋ࡚ࡶฎ⌮ᡭ㡰࡟ከ㔜࣮ࣝࣉࡀྵࡲࢀࢀࡤࠊไ⣙࡟ࡼࡗ࡚ࡣṇ⟅࡟ࡓ࡝ࡾ╔ࡅ࡞࠸ሙྜࡀ࠶ࡿࠋࡑࡢሙྜࠊ࣮ࣝࣉࡢᩘࢆῶࡽࡍ࢔࢖ࢹ࢔ࢆᶍ⣴ࡋ࡚ᐇ⿦ࡍࡿࡇ࡜࡛ࠊィ⟬᫬㛫ࢆ๐ῶ࡛ࡁࡿࡇ࡜ࡀ☜ㄆ࡛ࡁࡓࠋ௒ᅇ➹⪅ࡀసᡂࡋࡓࣉࣟࢢ࣒ࣛࡢ࣊ࢵࢲ࣮㒊ศࢆ࠙FRGHࠚ࡟♧ࡋࡓࠋࡇࡢࢥ࣮ࢻࡢ $W&RGHU ࡛ࡢᐇ⾜᫬㛫ࡣPV ࡛࠶ࡗࡓࠋ㸴㸬ཧ⪃ᩥ⊩ Ώ㒊᭷㝯ࠕ࢔ࣝࢦࣜࢬ࣒࡜ࢹ࣮ࢱᵓ㐀࣐ࠖ࢖ࢼࣅฟ∧ࠊ ᖺ $W&RGHUࠕ࢔ࣝࢦࣜࢬ࣒ᐇᢏ᳨ᐃࠖ
㸦᭱⤊㜀ぴ᪥  ᖺ  ᭶  ᪥㸧KWWSVSDVWDWFRGHUMS ➨୍ᅇ 3$672 ၥ㢟 ゎㄝ㸦᭱⤊㜀ぴ᪥  ᖺ  ᭶  ᪥㸧
KWWSVZZZ\RXWXEHFRPZDWFK"Y F7:233G,, OLVW 3//H-=JRS<.DUX\)<<4PS*$J(Z\J, LQGH[  W V−2−㸵㸬ཧ⪃㈨ᩱ
 ➹⪅ࡢ⎔ቃ㸸ࣁ࣮ࢻ࢚࢘࢔
ࣀ࣮ࢺࣃࢯࢥࣥ '(//$/,(1:$5(5㸦 ᖺ〇㸧ࣉࣟࢭࢵࢧ L+.&38#*+]
࣓ࣔࣜ *%
 ࣅࢵࢺ࣮࢜࣌ࣞࢩࣙࣥࢩࢫࢸ࣒[ ࣮࣋ࢫ   ࢯࣇࢺ࢚࢘࢔
0LFURVRIW9LVXDO6WXGLR&RPPXQLW\9HUVLRQ
9LVXDO&
࠙FRGHࠚ
3$672 ၥ㢟ࡉ࠸ࡇࢁࡢᮇᚅ್ F
LQFOXGHLRVWUHDP!FLQFRXW࡞࡝ࡢᇶᮏⓗ࡞ධฟຊᶵ⬟ࢆ฼⏝ࡍࡿࡇ࡜ࢆᐉゝࡍࡿLQFOXGHPDS!㐃᝿グ᠈ࢡࣛࢫࢆ฼⏝ࡍࡿࡇ࡜ࢆᐉゝࡍࡿ
DOJRULWKP!PD[PLQVRUW࡞࡝ࢆ㛵ᩘࢆ౑࠺ࡇ࡜ࢆᐉゝࡍࡿ
GHILQHUHS LQ IRU LQWL L Q L 
XVLQJQDPHVSDFHVWGGRXEOHGS>@ ^`ືⓗィ⏬ἲ ࣓ࣔ໬࡛౑⏝
LQWD>@>@ ^`ࡉ࠸ࡇࢁ
LQWE>@>@ ^`ᗙᶆᅽ⦰ᚋࡢࡉ࠸ࡇࢁ
࠙FRGHࠚᗙᶆᅽ⦰ධຊࢹ࣮ࢱ ᗙᶆᅽ⦰ᚋ ࡉ࠸ࡇࢁ ^`     ^` ࡉ࠸ࡇࢁ ^`Ѝ ෗ീ Ѝ ^` ࡉ࠸ࡇࢁ ^`㸦PDSSLQJ㸧  ^`LQWPDLQ ^LQWQFLQ!!QPDSLQWLQW!GLFHᗙᶆᅽ⦰ࡢసᴗ⏝㐃᝿グ᠈ࢡࣛࢫGLFH ࢆࡘࡃࡿUHS LQ UHS MQ ^FLQ!!D>L@>M@ྛࡉ࠸ࡇࢁ࡟᭩࠿ࢀ࡚࠸ࡿ┠ࡢᩘࢆཷࡅྲྀࡿ
GLFH>D>L@>M@@ ㄞࡳ㎸ࢇࡔ┠ࡢᩘࢆ࣮࢟࡟ࡋ࡚㐃᝿グ᠈ࢡࣛࢫ GLFH ࡟᱁⣡ࡍࡿࠋᑐᛂࡍࡿ್ࡣྲྀᩒ࠼ࡎ  ࡜ࡍࡿࠋ
`
LQWQXP IRU DXWR[GLFH ^
GLFH>[ILUVW@ QXP᳨⣴࣮࢟ࡢ᪼㡰࡟グ᠈ࡉࢀ࡚࠸ࡿࡢ࡛ࠊ㡰␒࡟ᑐᛂࡍࡿ್ࢆኚ᭦ࡍࡿࠋQXP`ධຊࡉࢀࡓ┠ࡢᩘ㸦᳨⣴࣮࢟[ILUVW㸧࡜ࠊ᪼㡰࡟௜ࡅ࠿࠼ࡓᩘ್㸦್ [VHFRQG㸧ࡀᑐᛂࡋ࡚࠸ࡿࠋUHS LQ UHS MQ ^E>L@>M@ GLFH>D>L@>M@@`L ␒┠ࡢࡉ࠸ࡇࢁࡢ┠ M ࡣᗙᶆᅽ⦰ࡉࢀ࡚ E>L@>M@࡟ಖᏑࡉࢀࡓࠋ
−3−)LERQDFFLQXPEHU ࣇ࢕࣎ࢼࢵࢳᩘิ        
࠙FRGHࠚᐃ⩏㏻ࡾࡢ෌ᖐ࡟ࡼࡿࣇ࢕࣎ࢼࢵࢳᩘิࡢィ⟬ἲ
LQWILE LQWQ ^
LI Q  UHWXUQ
UHWXUQILE Q ILE Q `
࠙FRGHࠚ࣓ࣔ໬෌ᖐ࡟ࡼࡿࣇ࢕࣎ࢼࢵࢳᩘิࡢィ⟬ἲ
ERROIODJ>@IDOVHᮍィ⟬WUXHィ⟬῭
LQWGS>@ィ⟬⤖ᯝࡢ࣓ࣔ㡿ᇦ
LQWILE LQWQ ^
LI Q  UHWXUQ
LI IODJ>Q@ WUXH UHWXUQGS>Q@GS>Q@ ILE Q ILE Q 
IODJ>Q@ WUXHUHWXUQGS>Q@`
࠙FRGHࠚ࣎ࢺ࣒࢔ࢵࣉ᪉ᘧࡢືⓗィ⏬ἲ࡟ࡼࡿࣇ࢕࣎ࢼࢵࢳᩘิࡢィ⟬ἲ
LQWILE LQWQ ^LI Q  UHWXUQ
LQWI 
LQWI 
LQWI 
IRU LQWL LQL ^I III II I`
UHWXUQI
࠙FRGHࠚ㢟ព㏻ࡾࡢฎ⌮ᡭ㡰㸦ࢼ࢖࣮ࣈ࡞᪉ἲ㸧‫ڸ‬IRU LQWM QXPM! M ^QXPᗙᶆᅽ⦰ᚋࡢ┠ࡢ᭱኱್GS>M@ M ࡀฟࡓᚋࠊ࠶࡜ఱᅇ᣺ࢀࡿ࠿ࡢᮇᚅ್ࡢ᭱኱್‫ڸ‬UHS LQ ^Qࡉ࠸ࡇࢁࡢᩘ
GRXEOHFXU ‫ڸ‬UHS N LI E>L@>N@!M FXU GS>E>L@>M@@M ࡼࡾࡶ኱ࡁ࡞┠ࡀ࠶ࢀࡤᮇᚅ್ࢆຍ⟬GS>M@ PD[ GS>M@FXU ᮇᚅ್ࡢ᭱኱್ࢆ GS>M@࡟ಖᏑ−4−``
GRXEOHP[ UHS LQ ^Qࡉ࠸ࡇࢁࡢᩘ
GRXEOHDQV 
UHS M DQV GS>E>L@>M@@DQVྛࡉ࠸ࡇࢁࡢᮇᚅ್P[ PD[ P[DQV P[ ࡀ୍␒ᮇᚅ್ࡢ኱ࡁ࡞ࡉ࠸ࡇࢁࡢᮇᚅ್`
SULQWI ͆OI?Q͇P[ UHWXUQ࠙FRGHࠚྛ┠ࡀ࡝ࡢࡉ࠸ࡇࢁ࡟ྵࡲࢀࡿࡢ࠿ࢆ⟶⌮ࡍࡿ㒊ศࢆ࠙FRGHࠚ࡟㏣ຍࡍࡿ
PDSLQWLQW!PS‫ ڸ‬㏣グධຊࡉࢀࡓ┠ࡢᩘ㸦᳨⣴࣮࢟[ILUVW㸧࡜ࠊ᪼㡰࡟௜ࡅ࠿࠼ࡓᩘ್㸦್ [VHFRQG㸧ࡀᑐᛂࡋ࡚࠸ࡿࠋUHS LQ UHS MQ ^
E>L@>M@ GLFH>D>L@>M@@PS>E>L@>M@@ L‫ ڸ‬㏣グ`L ␒┠ࡢࡉ࠸ࡇࢁࡢ┠ M ࡣᗙᶆᅽ⦰ࡉࢀ࡚ E>L@>M@࡟ಖᏑࡉࢀࡓࠋ
E>L@>M@ࡀ L ␒┠ࡢࡉ࠸ࡇࢁ࡟࠶ࡿࡇ࡜ࢆ PS ࡛⟶⌮ࡍࡿ࠙FRGHࠚྛࡉ࠸ࡇࢁࡢᮇᚅ್ࢆಖᣢࡍࡿኚᩘ Y ࢆ‽ഛࡋࠊ᭦᪂ᅇᩘࢆ  ᅇ࡟๐ῶࡍࡿGRXEOHY>Q@Qࡉ࠸ࡇࢁࡢᩘ
UHS LQ Y>L@ 
GRXEOHP[BY GS>QXP@ QXPᗙᶆᅽ⦰ᚋࡢ┠ࡢ᭱኱್‫ڸ‬IRU LQWM QXPM! M ^‫ڸ‬LQWL PS>M@M ࡢ┠ࡢ࠶ࡿࡉ࠸ࡇࢁࡣ Lࠊࡉ࠸ࡇࢁ L ࡢࡳ᭦᪂ࡍࢀࡤࡼ࠸ UHS N ^
LI E>L@>N@ M ^Y>L@ GS>M@

EUHDN``LI P[BYY>L@ P[BY Y>L@GS>M@ P[BY`➨୍ᅇ࢔ࣝࢦࣜࢬ࣒ᐇᢏ᳨ᐃ㸦㹎㸿㹑㹒㸧㹍ၥ㢟ၥ㢟ᩥ ೫ࡾࡢ࡞࠸㸴㠃ࡉ࠸ࡇࢁࡀ 1 ಶ࠶ࡾࠊL ␒┠ࡢࡉ࠸ࡇࢁ ӌLӌ1 ࡢ M ␒┠ࡢ㠃 ӌMӌ ࡟ࡣᩚᩘ $LM ࡀ᭩࠿ࢀ࡚࠸ࡿࠋ㧗ᶫྩࡣࠊ ಶࡢࡉ࠸ࡇࢁࢆ㑅ࢇ࡛  ᅇ᣺ࡿࠊ࡜࠸࠺᧯సࢆ⧞ࡾ㏉ࡍࠋࡓࡔࡋࠊ ᅇ┠௨㝆ࡢ᧯స࡛ࠊ๓ᅇࡢ᧯స࡛ฟࡓ┠ࡼࡾᑠࡉ࠸࠿ྠࡌ┠ࡀฟ࡚ࡋࡲࡗࡓࡽࠊ᧯సࢆࡸࡵࡿࠋྛᅇ࡟࡝ࡢࡉ࠸ࡇࢁࢆ᣺ࡿ࠿ࡣࠊ๓ᅇ࡟ฟࡓ┠ࢆぢ࡚࠿ࡽ㑅ࡪࡇ࡜ࡀ࡛ࡁࡿࠋ 㧗ᶫྩࡣࠊ࡛ࡁࡿࡔࡅࡉ࠸ࡇࢁࢆከࡃ᣺ࡾࡓ࠸࡜⪃࠼࡚࠸ࡿࠋ᧯సࡀ⾜ࢃࢀࡿᅇᩘࡢᮇᚅ್ࡀ᭱኱໬ࡉࢀࡿࡼ࠺࡞㑅ᢥࡀ⾜ࢃࢀࡓ࡜ࡁࡢ᧯సᅇᩘࡢᮇᚅ್ࢆồࡵࡼࠋไ⣙࣭ӌ1ӌ

−5−࣭ӌ$LMӌ
࣭$LM ࡣࡍ࡭࡚␗࡞ࡿࠋ
࣭ධຊ୰ࡢ್ࡣࡍ࡭࡚ᩚᩘ࡛࠶ࡿࠋฟຊ᧯సᅇᩘࡢᮇᚅ್ࢆ⾲ࡍᐇᩘࢆฟຊࡏࡼࠋࢪࣕࢵࢪࡢฟຊ࡜ࡢ⤯ᑐㄗᕪࡲࡓࡣ┦ᑐㄗᕪࡀ  ௨ୗ࡛࠶ࢀࡤṇゎ࡜ุᐃࡉࢀࡿࠋධຊ౛㸯ฟຊ౛㸯
ධຊ౛㸰


ฟຊ౛㸰3UREOHP6WDWHPHQW
:HKDYH1XQELDVHGVL[VLGHGGLFH7KHMWKIDFH ӊMӊ RIWKHLWKGLH ӊLӊ1 KDVDQLQWHJHU$LM
ZULWWHQRQLW
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ZKHQWKHFKRLFHVDUHPDGHWRPD[LPL]HWKLVQXPEHU
&RQVWUDLQWV࣭ӊ1ӊ࣭ӊ$LMӊ࣭$LMDUHDOOGLIIHUHQW࣭$OOYDOXHVLQLQSXWDUHLQWHJHUV㸦ฟ඾ KWWSVDWFRGHUMSFRQWHVWVSDVWRSHQWDVNVSDVWBR㸧−6−