S\u1ed1 ch\u1eb5n v\u00e0 s\u1ed1 nguy\u00ean c\u00f3 nhi\u1ec1u nh\u01b0 nhau kh\u00f4ng? Nhi\u1ec1u b\u1ea1n ch\u01b0a k\u1ecbp suy ngh\u0129 \u0111\u00e3 tr\u1ea3 l\u1eddi \u201ckh\u00f4ng, kh\u00f4ng nh\u01b0 nhau, b\u1edfi v\u00ec s\u1ed1 ch\u1eb5n l\u00e0 m\u1ed9t b\u1ed9 ph\u1eadn c\u1ee7a s\u1ed1 nguy\u00ean\u201d. Ho\u1eb7c c\u0169ng kh\u00f4ng \u00edt ng\u01b0\u1eddi t\u1ecf \u00fd ho\u00e0i nghi v\u1ec1 c\u00e2u h\u1ecfi n\u00e0y, kh\u00f4ng n\u1eafm ch\u1eafc l\u1eafm n\u00ean tr\u1ea3 l\u1eddi: \u201cc\u00f3 th\u1ec3 nhi\u1ec1u nh\u01b0 nhau v\u00ec s\u1ed1 nguy\u00ean v\u00e0 s\u1ed1 ch\u1eb5n c\u00f3 \u0111\u1ed1i \u1ee9ng 1 – 1\u201d, Trong s\u1ed1 \u0111\u00f3 c\u00f3 b\u1ea1n vi\u1ebft l\u00ean b\u1ea3ng \u0111\u1ed1i \u1ee9ng 1 – 1 gi\u1eefa s\u1ed1 nguy\u00ean v\u00e0 s\u1ed1 ch\u1eb5n:<\/p>\n\n\n\n
Trong hai lo\u1ea1i \u00fd ki\u1ebfn th\u00ec ai \u0111\u00fang, ai sai?<\/p>\n\n\n\n
B\u1ea3n ch\u1ea5t v\u1ea5n \u0111\u1ec1 n\u00eau tr\u00ean ch\u00ednh l\u00e0 vi\u1ec7c so s\u00e1nh s\u1ef1 to nh\u1ecf c\u1ee7a hai t\u1eadp h\u1ee3p: t\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean v\u00e0 t\u1eadp h\u1ee3p s\u1ed1 ch\u1eb5n. Vi\u1ec7c so s\u00e1nh \u0111\u1ed9 to, nh\u1ecf c\u1ee7a hai t\u1eadp h\u1ee3p h\u1eefu h\u1ea1n kh\u00e1 \u0111\u01a1n gi\u1ea3n, nh\u01b0ng v\u1edbi c\u00e1c t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n th\u00ec th\u1ebf n\u00e0o l\u00e0 \u201cto nh\u1ecf\u201d so v\u1edbi nhau, v\u00e0 so s\u00e1nh \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n nh\u01b0 th\u1ebf n\u00e0o?<\/p>\n\n\n\n
\u0110\u1ed1i v\u1edbi m\u1ed9t t\u1eadp h\u1ee3p h\u1eefu h\u1ea1n th\u00ec d\u1ef1a v\u00e0o s\u1ed1 ph\u1ea7n t\u1eed c\u00f3 trong m\u1ed7i t\u1eadp h\u1ee3p \u0111\u1ec3 so s\u00e1nh v\u00e0 l\u00e0m th\u01b0\u1edbc \u0111o cho \u0111\u1ed9 to, nh\u1ecf. V\u00ed d\u1ee5:<\/p>\n\n\n\n
M\u1ed9t b\u1ed9 ph\u1eadn so v\u1edbi to\u00e0n th\u1ec3 (theo l\u1eadp lu\u1eadn c\u1ee7a l\u00ed thuy\u1ebft t\u1eadp h\u1ee3p) th\u00ec b\u1ed9 ph\u1eadn nh\u1ecf h\u01a1n to\u00e0n th\u1ec3.<\/p>\n\n\n\n
N\u1ebfu gi\u1eefa hai t\u1eadp h\u1ee3p c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u1ed1i \u1ee9ng 1 -1 gi\u1eefa c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a hai t\u1eadp h\u1ee3p th\u00ec ch\u00fang c\u00f3 \u0111\u1ed9 l\u1edbn nh\u01b0 nhau.<\/p>\n\n\n\n
Hai c\u00e1ch tr\u1ea3 l\u1eddi tr\u00ecnh b\u00e0y tr\u00ean kia ch\u00ednh l\u00e0 hai k\u1ebft qu\u1ea3 d\u1ef1a v\u00e0o hai ti\u00eau chu\u1ea9n kh\u00e1c nhau \u0111\u1ed1i v\u1edbi m\u1ed9t t\u1eadp h\u1ee3p \u0111\u01a1n gi\u1ea3n suy ra cho m\u1ed9t t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n.<\/p>\n\n\n\n
Th\u1ef1c ra trong hai ti\u00eau chu\u1ea9n th\u00ec ti\u00eau chu\u1ea9n hai l\u00e0 b\u1ea3n ch\u1ea5t. Ta h\u00e3y suy ngh\u0129 m\u1ed9t ch\u00fat t\u1eeb \u201cba\u201d c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c tr\u1eebu t\u01b0\u1ee3ng ho\u00e1 t\u1eeb nh\u1eefng s\u1ef1 v\u1eadt g\u00ec? M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u bi\u1ebft c\u00f3 th\u1ec3 c\u00f3 \u201ct\u1eadp h\u1ee3p ba con ch\u00f3\u201d, \u201ct\u1eadp h\u1ee3p ba ng\u01b0\u1eddi\u201d, \u201ct\u1eadp h\u1ee3p ba quy\u1ec3n s\u00e1ch\u201d v.v\u2026 Nh\u01b0 v\u1eady th\u00f4ng qua vi\u1ec7c quan s\u00e1t c\u00e1c s\u1ef1 v\u1eadt kh\u00e1c nhau tr\u00ean th\u1ef1c ti\u1ec5n ta c\u00f3 th\u1ec3 \u0111\u01b0a ra t\u1eadp h\u1ee3p \u201cba\u201d tr\u1eebu t\u01b0\u1ee3ng c\u00f3 c\u00f9ng \u0111\u1eb7c t\u00ednh.<\/p>\n\n\n\n
T\u1ea1i sao t\u1eadp h\u1ee3p \u201cba\u201d l\u1ea1i c\u00f3 c\u00f9ng t\u00ednh ch\u1ea5t m\u00e0 \u201ct\u1eadp h\u1ee3p b\u1ed1n ng\u01b0\u1eddi\u201d l\u1ea1i kh\u00f4ng c\u00f3 c\u00f9ng t\u00ednh ch\u1ea5t? \u0110i\u1ec3m ch\u1ee7 y\u1ebfu c\u1ee7a \u201cba\u201d l\u00e0 c\u00f3 c\u00f9ng t\u00ednh ch\u1ea5t c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp \u0111\u1ed1i \u1ee9ng 1 – 1 gi\u1eefa ch\u00fang: ba ng\u01b0\u1eddi ch\u0103n d\u1eaft ba con ch\u00f3 th\u00e0nh \u0111\u1ed1i \u1ee9ng gi\u1eefa \u201ct\u1eadp h\u1ee3p ba con ng\u01b0\u1eddi\u201d v\u1edbi \u201ct\u1eadp h\u1ee3p c\u1ee7a ba con ch\u00f3\u201d. Ba ng\u01b0\u1eddi \u0111\u1ecdc ba quy\u1ec3n s\u00e1ch ta thi\u1ebft l\u1eadp \u0111\u1ed1i \u1ee9ng 1 – 1 gi\u1eefa \u201ct\u1eadp h\u1ee3p ba ng\u01b0\u1eddi\u201d v\u1edbi \u201ct\u1eadp h\u1ee3p c\u1ee7a ba quy\u1ec3n s\u00e1ch\u201d.<\/p>\n\n\n\n
Theo ph\u01b0\u01a1ng th\u1ee9c t\u01b0 duy n\u00e0y ta c\u00f3 th\u1ec3 m\u1edf r\u1ed9ng cho t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n v\u00e0 th\u00e0nh l\u1eadp l\u00ed lu\u1eadn \u201c\u0111\u1ed9 to nh\u1ecf\u201d c\u1ee7a t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n. V\u1edbi hai t\u1eadp h\u1ee3p (h\u1eefu h\u1ea1n hay v\u00f4 h\u1ea1n) ta c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp s\u1ef1 \u0111\u1ed1i \u1ee9ng 1 – 2 ta n\u00f3i hai t\u1eadp h\u1ee3p c\u00f3 c\u01a1 s\u1ed1 nh\u01b0 nhau. N\u1ebfu nh\u01b0 m\u1ed9t t\u1eadp h\u1ee3p c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp m\u1ed1i quan h\u1ec7 \u0111\u1ed1i \u1ee9ng 1 – 2 v\u1edbi m\u1ed9t t\u1eadp h\u1ee3p kh\u00e1c th\u00ec ng\u01b0\u1eddi ta n\u00f3i t\u1eadp h\u1ee3p th\u1ee9 nh\u1ea5t c\u00f3 c\u01a1 s\u1ed1 kh\u00f4ng l\u1edbn h\u01a1n t\u1eadp h\u1ee3p th\u1ee9 hai. T\u1eeb kh\u00e1i ni\u1ec7m kh\u00e1 tr\u1eebu t\u01b0\u1ee3ng l\u00e0 \u201cc\u01a1 s\u1ed1\u201d ta c\u00f3 th\u1ec3 so s\u00e1nh \u0111\u1ed9 l\u1edbn nh\u1ecf c\u1ee7a c\u01a1 s\u1ed1. C\u01a1 s\u1ed1 ch\u00ednh l\u00e0 \u0111\u01b0\u1ee3c suy r\u1ed9ng t\u1eeb kh\u00e1i ni\u1ec7m ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p h\u1eefu h\u1ea1n cho t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n.<\/p>\n\n\n\n
Theo \u0111\u1ecbnh ngh\u0129a \u0111\u00f3, t\u1eadp h\u1ee3p c\u00f3 c\u01a1 s\u1ed1 nh\u1ecf nh\u1ea5t trong c\u00e1c t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n ch\u00ednh l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean. B\u1edfi v\u00ec n\u1ebfu c\u00f3 m\u1ed9t t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n, c\u1ee9 m\u1ed7i l\u1ea7n ta r\u00fat ra m\u1ed9t ph\u1ea7n t\u1eed t\u1eeb t\u1eadp h\u1ee3p \u0111\u00f3, trong t\u1eadp h\u1ee3p v\u1eabn t\u1ed3n t\u1ea1i (d\u0129 nhi\u00ean kh\u00f4ng c\u00f3 ph\u1ea7n t\u1eed b\u1ecb r\u00fat ra), qu\u00e1 tr\u00ecnh r\u00fat ra c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p c\u00f3 th\u1ec3 li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n, v\u00e0 nh\u01b0 v\u1eady c\u00f3 th\u1ec3 thi\u1ebft l\u1eadp m\u1ed1i quan h\u1ec7 1 – 1 gi\u1eefa c\u00e1c ph\u1ea7n t\u1eed t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n \u0111\u00e3 x\u00e9t v\u1edbi t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean. Trong to\u00e1n h\u1ecdc ng\u01b0\u1eddi ta d\u00f9ng ch\u1eef Hy L\u1ea1p X \u0111\u1ec3 k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n (X \u0111\u1ecdc l\u00e0 Khi) v\u00e0 d\u00f9ng k\u00ed hi\u1ec7u X0 \u0111\u1ec3 k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean.<\/p>\n\n\n\n
Quay l\u1ea1i v\u1ea5n \u0111\u1ec1 \u0111\u1eb7t ra t\u1eeb ban \u0111\u1ea7u ta c\u00f3 th\u1ec3 suy ra t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 nguy\u00ean v\u00e0 s\u1ed1 ch\u1eb5n c\u00f3 c\u00f9ng m\u1ed9t s\u1ed1 gi\u1ed1ng nhau, t\u1ee9c s\u1ed1 nguy\u00ean v\u00e0 s\u1ed1 ch\u1eb5n c\u00f3 c\u00f9ng m\u1ed9t s\u1ed1 v\u00e0 t\u1eeb \u0111\u00f3 c\u00f3 c\u00f9ng \u0111\u1ed9 l\u1edbn nh\u01b0 nhau, t\u1ee9c s\u1ed1 nguy\u00ean v\u00e0 s\u1ed1 ch\u1eb5n nhi\u1ec1u nh\u01b0 nhau. S\u1ef1 th\u1ef1c th\u00ec c\u1ea3 hai t\u1eadp h\u1ee3p \u0111\u1ec1u c\u00f3 c\u01a1 s\u1ed1 l\u00e0 X0. Ta ch\u1ec9 c\u1ea7n s\u1eafp x\u1ebfp c\u00e1c s\u1ed1 nguy\u00ean th\u00e0nh d\u00e3y 0, 1, -1, 2, -2, 3, -3\u2026kh\u00f4ng m\u1ed9t s\u1ed1 nguy\u00ean n\u00e0o c\u00f3 th\u1ec3 l\u1ecdt ra ngo\u00e0i b\u1ea3ng s\u1eafp x\u1ebfp, v\u00e0 do \u0111\u00f3 ta \u0111\u00e3 thi\u1ebft l\u1eadp m\u1ed9t \u0111\u1ed1i \u1ee9ng 1-1 gi\u1eefa t\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean v\u00e0 t\u1eadp h\u1ee3p s\u1ed1 t\u1ef1 nhi\u00ean. T\u1eeb \u0111\u00f3 c\u00f3 th\u1ec3 ch\u1ee9ng minh c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 c\u0169ng c\u00f3 c\u01a1 s\u1ed1 l\u00e0 X0. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp \u0111\u1ec3 th\u1ea5y c\u01a1 s\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 l\u00e0<\/p>\n\n\n\n
X0.<\/p>\n\n\n\n
\u0110\u01b0\u01a1ng nhi\u00ean c\u0169ng c\u00f3 c\u00e1c t\u1eadp h\u1ee3p c\u00f3 c\u01a1 s\u1ed1 kh\u00e1c X0. D\u01b0\u1edbi \u0111\u00e2y ta s\u1ebd ch\u1ee9ng minh t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 th\u1ef1c l\u00e0 lo\u1ea1i t\u1eadp h\u1ee3p nh\u01b0 v\u1eady.<\/p>\n\n\n\n
Ch\u00fang ta \u0111\u00e3 th\u1ea5y t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n \u0111\u01b0\u1ee3c m\u1edf r\u1ed9ng t\u1eeb c\u01a1 s\u1ed1 t\u1eadp h\u1ee3p h\u1eefu h\u1ea1n nh\u01b0ng gi\u1eefa c\u01a1 s\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n v\u00e0 t\u1eadp h\u1ee3p h\u1eefu h\u1ea1n c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t r\u1ea5t l\u1edbn.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: S\u1ed1 nguy\u00ean; S\u1ed1 ch\u1eb5n; T\u1eadp h\u1ee3p; C\u01a1 s\u1ed1.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
S\u1ed1 ch\u1eb5n v\u00e0 s\u1ed1 nguy\u00ean c\u00f3 nhi\u1ec1u nh\u01b0 nhau kh\u00f4ng? Nhi\u1ec1u b\u1ea1n ch\u01b0a k\u1ecbp suy ngh\u0129 \u0111\u00e3 tr\u1ea3 l\u1eddi \u201ckh\u00f4ng, kh\u00f4ng nh\u01b0 nhau, b\u1edfi v\u00ec s\u1ed1 ch\u1eb5n l\u00e0 m\u1ed9t b\u1ed9 ph\u1eadn c\u1ee7a s\u1ed1 nguy\u00ean\u201d. Ho\u1eb7c c\u0169ng kh\u00f4ng \u00edt ng\u01b0\u1eddi t\u1ecf \u00fd ho\u00e0i nghi v\u1ec1 c\u00e2u h\u1ecfi n\u00e0y, kh\u00f4ng n\u1eafm ch\u1eafc l\u1eafm n\u00ean tr\u1ea3 l\u1eddi: \u201cc\u00f3 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7684","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7684","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7684"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7684\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7684"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7684"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7684"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}